Measurement Quantization Describes History of Universe—Quantum Inflation, Transition to Expansion, CMB Power Spectrum

Developing a comprehensive model of the early universe that describes events and conditions prior to recombination has proved difficult. Using a new approach, we express Heisenberg’s uncertainty principle in terms of measures and counts of those measures to resolve an expression consisting entirely of counts. The description allows us to resolve explicit values for discrete measures. With these values, we present new expressions describing the earliest epoch and the transition event that initiates expansion. We determine the quantity, age, density, and temperature of the cosmic microwave background (CMB). Moreover, we approach the CMB power spectrum anew, describing each mass/energy distribution, its physical significance, its peak temperature, and the effects of relativity. We do not engage in fitting or modification of the existing laws of physics. The approach is classical and correlates both quantum and cosmological phenomena with descriptive expressions that are measurable, verifiable, and falsifiable.


Introduction
The cosmic microwave background (CMB) has offered a significant amount of data with which to understand the processes, conditions and events that make up the earliest epoch of our universe. Among them, measurements of the CMB may be presented as a power spectrum revealing five bell-like curves each describing physical traits of our universe [1]. Nonetheless, after some 30 years, we are uncertain as to what the physical significance is of some of these curves, how they are related, and whether they represent matter, energy or a more complex combination of phenomena.
We propose an approach that allows us to answer these questions without modification of the known laws of nature or using untested hypotheses. The presentation rests upon evidence presented for the physical significance of fundamental units of measure [2]. With this, we introduce a more accommodative nomenclature. Distance, for example, would be expressed as some count n L of fundamental units of length l f . The approach and nomenclature are referred to as measurement quantization (MQ).
MQ is neither a new theory nor conjectured insight. The results presented are built by applying MQ to our existing understanding of classical mechanics. Recognizing the physical significance of MQ expressions enables us to unravel relationships that underlie the laws and constants of our universe. As such, we may describe the history of the universe from the earliest epoch to the present. We resolve the conditions that lead to the CMB and its present-day properties-quantity, age, density, and temperature.
We should emphasize, the presentation is not subject to one set of measurement data or restricted to one field of science (i.e., MQ may be used to resolve measurable values in optics, gravity, energy, particle physics, and cosmology).
The presentation is also not one of generalizations, such as greater energy, lesser volume, and invariant correlations of broadly defined physical properties. Rather, we use MQ to describe measurable values that can be verified or falsified.
By example, we resolve peak temperatures and corresponding multipole moments of each abscissa and ordinate of the power spectrum representation of the CMB-the peak multipole moments of each distribution, their relationship, and their physical significance. We use MQ to describe the rate of universal expansion-Hubble's constant-its correlation to a physically significant discrete measure, the effects of relativity between epochs, and the physical conditions and events that end the earliest epoch and initiate expansion. The MQ approach also allows for expressions describing the physical properties of spacetime, what is curved, and why it is curved. Moreover, it allows us to resolve greater cosmological questions such as whether the universe is flat, open or closed.
The approach begins with an analysis of Heisenberg's uncertainty principle written in MQ form. We shall also make use of the Pythagorean Theorem, observations of the speed of light, and the expression for escape velocity. We need no additional observations or laws of nature with which to proceed.
We remark that the presentation consists of several ancillary properties, among them being a lack of conjectures and axioms other than those fundamentals of modern theory we attribute to classical mechanics. The expressions are largely temporal in approach and geometric in presentation. More importantly, some properties of the CMB are shown to be correlated to the quantization of measure with respect to the frame of the observer. Finally, we adjust the expressions for effects of relativity, which are a consequence of the time dilation between the earliest and present epochs.
From a broader view, this research has little effect on the existing body of literature discussing recombination or expansion. Rather, the events described herein occur following the initial formation of a quantum singularity and the time elapsed thereafter up to the trigger event that initiates expansion. We refer to this period as the quantum inflationary epoch. The epoch is terminated by a trigger event, a physical process to be described, but otherwise summarized as a consequence of discrete measure applicable to quantum singularities. After instantiating the expansionary epoch, temperatures cool to approximately 3000 K over a period of 2.7 years. Finally, we arrive at more thoroughly studied periods of our universal history such as recombination, decoupling, and the dark ages.
We shall spend most of our time on the first two periods. For instance, we demonstrate that a period of faster-than-light expansion is not needed to explain the present-day heterogeneous and homogenous properties of our universe.
That said, MQ does describe a lengthy quantum expansionary period that describes conditions for which inflation theory is conjectured. MQ also offers a physical description of the CMB power spectrum not as a phenomenon consisting of mass and energy, but as mass that has differing physical characteristics with respect to elapsed time and relative distance (i.e., what is measured presently, what will be measured with elapsed time, and what cannot be measured because of the expansion of space). We refer to these geometries as temporal properties of observation. Both the ΛCDM and MQ approaches make parallel predictions, but the MQ approach offers a clearer understanding of the physical characteristics of each distribution: dark energy, dark matter, and visible matter ( [3] Eqs. 109, 110, 113, 115).

Theoretical Landscape
Over the last two decades, research into the early and present universe has focused on the measure of the CMB as is commonly presented in a graph of temperature versus the multipole moment. Many features of our universe have been redefined as some aspect of this data, such as whether the universe is flat, open or closed-a flat universe being consistent with a dark energy multipole moment around 220 [4]. The distributions themselves-dark energy, dark and visible matter-have been identified and assigned distinct properties, although broadly speaking we recognize that they may not be physically distinct or entirely physical [5]. The approach has been one of hindsight, putting together a historical puzzle with insights from the existing and improving data while filling in the gaps with theories (i.e., inflation) that at best recognize a transition from one known set of environmental conditions to another. Overall, the model is known as lambda cold dark matter (ΛCDM).
To ground the reader as to the accomplishments thus far, we briefly discuss some of the highlights and details of the approach, but before we begin, we bring to the reader's attention that this paper and the efforts of ΛCDM do not share a lot of common ground. That is, MQ describes the earliest epoch from singularity up to recombination. Whereas there are expressions that describe the ensuing expansion following the trigger event that ends the quantum inflationary epoch, the physical processes of recombination-what is generally the birth ground of ΛCDM research-is not in the same physical regime as MQ. We may compare the two as using electromagnetism to describe fluid dynamics. Not only are the laws that govern each discipline largely unrelated, but rarely would one attempt to correlate them. Although MQ provides a physically significant understanding of the power spectrum of the CMB, it is not to say that it is the whole story. The power spectrum is only partly a story of the temporal properties of observation; it reveals a physical process from which we have yet more to learn.
To that end, we broadly note that ΛCDM describes the power spectrum as a consequence of two physical processes. The first effect concerns the inward pull of gravitation with respect to the outward pressure of baryonic/photon plasma.
There exists physical support that the early universe consisted of baryonic matter and photons interacting in a gravitational potential constrained by dark matter.
The correlation to dark matter exists only with respect to the 26.8% mass/energy distribution identified as such. Over time, mass concentrations mutually attract via gravity, but as concentrations increased, there was also an increasing pressure which caused repulsion [6]. This gravity/pressure approach is usually modeled using the theory of sound waves such that the baryon density is set to correspond to the CMB temperature.
The second effect concerns the field of acoustics and correlation of those disciplines to measurements of the sound horizon. One may use an expansion of Laplace's spherical harmonics to decompose the density field and then look at one single mode or enkelt mode. Although inflation produces compression/decompression oscillations of equal magnitude, models suggest that with elapsed time the oscillations separate into the known distributions (for example, dark energy, dark matter, visible matter). This latter phase is characterized by falling temperatures because of the expansion of space. As temperatures drop to 3000 K a period of neutral hydrogen is allowed (aka., recombination).
Thereafter, photons travel freely throughout the universe, which in turn freezes the CMB oscillations that we measure today.
As a final piece to this chronological puzzle, there is no measurable mechanism to address the homogenous observations of the CMB temperature. This is known as the horizon problem [7]. In opposition to the cited paper, it is conjectured that there may have existed a short period of exponential expansion, which increased the size of the universe by a factor of roughly 10 23 within 10 −34 seconds; values vary depending on the model. Short, initially rapid, expansionary periods are more broadly viewed as pertaining to the inflation period and are recognized as a placeholder between two epochs of better-known physical conditions.
With regards to gaps in the historical record, there are periods with a very high level of physical correspondence to theory whereas there are other periods during which an experimental measure has not yet been devised. For the latter, there are placeholders-conjectured evolutionary periods-that fill the gaps between better known periods. It should be noted that placeholders grounded in physically significant endpoints are nevertheless conjectures regarding the physical conditions between those endpoints. The lack of detail overall is such that we fail to achieve the goal of an underlying physical mechanism that explains the sequence of events [8]. While we may resolve a nearly correct story of our history, this does not actually resolve an understanding of that history. This is where MQ offers new details.

Physical Significance of Measure
Perhaps from the earliest of human endeavor, we have attempted to quantify an understanding of measure. What is it? What are its underpinnings? Is it possible to define measure by something more fundamental? What does measure have to do with our understanding of the power spectrum of the CMB or the history of our universe?
Measure serves a role not dissimilar to equations, a tool of the trade. The three measures (length, duration, mass) are used to describe the properties of … well … most everything. As such, we cannot understand the power spectrum until we understand measure. Seemingly, this should be an unnecessary place to begin if it were not for the fact that we know so little of measure. We, for instance, cannot answer the questions: Does measure exist outside of the observable universe? Why are the three measures related? Are there phenomena in the universe that have properties with no correspondence to measure? A more mathematical approach to these questions may be furthered in consideration of the Pythagorean Theorem, this being the simplest expression with which we may describe the measure of length. There are three terms associated with measure, a count of a reference phenomenon n La = 1, a known count of that reference n Lb and an unknown count of the reference n Lr . Whether one is using SI units, counts of fundamental units or any other measurement nomenclature is unimportant. What is notable is that there are three terms, each representing a physically distinct measure with respect to an observer. The theorem brings to our attention that, at a minimum, the phenomenon of measure is a composite of information with respect to three distinct measurement frameworks.
Likewise, one may argue that the reference and the known count may be known simultaneously with respect to the frame of the observer, but an equivalent argument may be made that a count measure cannot be known without a reference, thus complicating the prerequisite of simultaneity (the phenomenon of measure is one that exists in the present). Of equal difficulty, using modern day EM-echo ranging (LIDAR), it may be argued that the measures of n La and n Lb can be simultaneously known by an observer sidestepping the challenges of consolidating the distinct measurement frames where and when n La and n Lb are resolved. Nonetheless, this introduces time, and whereas this approach offers the hope of consolidation with respect to the observer's frame, it merely introduces an alternative dimension-time-with a new uncertainty, the physical correlation of time to length. Finally, the physical process by which information is consolidated (i.e. the comparison of a reference to an unknown length) is not defined. When discussing an observer's frame, we mean to resolve a description of the physics applicable at a given space at an instant in time t f with respect to the consolidated information.
Thus, with respect to the evolution of modern theory, we ask, what are the three frames? Modern theory recognizes two, that of the target and that of the observer. However, as we have demonstrated, the phenomenon of measure is a composite of three and it is our inability to quantify this prerequisite and then clarify its ramifications with respect to the laws of nature that underpins the claim; we lack an understanding of measure.
To lay the foundation for the birth and evolution of our universe, we must begin with measure. We approach the topic in a way that does not fix or assume specific properties but allows for enough variation that we may resolve quantifiable properties. This is accomplished with a nomenclature that divides measure into two components. Specifically, for every measure … for example, time … we shall not write the symbol t. Rather, we express time as a count n T of some fundamental measure t p . Naturally, this opens the door to the possibility that time is countable or that there exists a physically significant fundamental unit of time, but not necessarily. The new nomenclature only introduces the possibility of discreteness, yet leaves the door open to non-discreteness. Whether measure varies, is bounded, has physical significance or is entirely meaningless must be resolved from the physical record. Indeed, that is where we begin.
Consider then, that the speed of light may be described as a count n L of length units l p divided by a count n T of a fundamental unit of time t p , then (1) For guidance only, we also consider Planck's unit expressions [9] for length l p and mass m p , Journal of High Energy Physics, Gravitation and Cosmology Using Heisenberg's expression to describe the uncertainty associated with the position σ X and momentum σ P of a particle, We may resolve physically significant values for n L , n M , and n T . The uncertainty principle asserts a limit to the precision with which certain canonically conjugate pairs of particle properties may be known. However, this differs from our goal of resolving the certain minimum measurements of a particle at the threshold, ħ/2.
Therefore, we introduce a special case of the use of variances. Whereas the expression for variance is usually written to describe the certain properties of many targets, we modify this usage to describe the certain properties of many measurements whereby the measurement, whether applicable or even physically significant, is uncertain. With this understanding, we then consider the solution for only the minimum count values for length, mass, and time such that the conjugate pair is equal to the threshold at ħ/2; that is, One might argue that the substitution of the variance of a physical quantity for the uncertainty of that quantity is not physically clear. In response, we consider that the canonically conjugate pair that we seek to resolve is a certain value, identified by the conjectured set of minimum count values for length, mass, and time. That is, we distinguish the uncertain state of a particle from the certain state we seek to describe. We accomplish this by considering the minimal case of a variance of many certain measures sorting out each dimension separately.
To the extent that the minimal count N is reducible to a certain measure describing a single particle, we consider measures when N = 2. The variance terms for position and momentum reduce such that there is a certain length Note also that the count n L for the change in velocity is distinct from the position count n Lr , the latter describing the distance between the observer and the particle. We have ( ) with these constraints, it follows that the minimum count values at the threshold ħ/2 correspond to a minimum distance n Lr l p and a momentum consisting of a minimum mass n M m p , a minimum length n L l p and a minimum time n T t p . Re-placing the value ħ with the result from Equation (5) 2 Lr M L T n n n n = . (10) Notably, the reference measures cancel out leaving a description that consists of only count terms. In MQ, we recognize such descriptions as geometric relations. That said, the result does not imply that the fundamental units of measure are physically significant or that the counts are integers. To resolve the count values requires that we identify additional constraints, starting with a description of G composed exclusively of Planck Units. Dividing Planck's mass by Planck's length from Equation (2) and Equation (3), we then have A final constraint, the upper bound relation between length and mass counts, may be resolved by considering the expression for the escape velocity. Using the expression for G at the bound v = c, such that     (23) Thus, we may state that each of the counts is physically significant describing a lower threshold to measure. O 1 : There are physically significant fundamental units of measure: length, mass, and time.
The mathematical approach taken makes no assumptions about the relationships between measures, the discreteness of measure or the physical significance of measure. Our ability to correlate a physically significant phenomenon with discrete counts of reference measures is entirely an outcome of our existing understanding of light, the uncertainty principle, and the escape velocity.

Discreteness of Measure
Having established the physical significance of a lower threshold to measure, consider now a macroscopic measure (i.e., any distance greater than the reference l p ). For instance, consider a stick 10.00l p in length and another 10.25l p in length. Can the difference, be measured? No. A difference length is physically the same as any other length and with respect to the Heisenberg uncertainty principle, difference lengths less than the reference l p (i.e., n L = 1) cannot be measured. Thus, we may resolve that all macroscopic length measures may be observed only as precisely as a whole-unit count of the reference measure.
Although the above extensible result is definitive for the entire measurement domain, let us consider one more approach, a difference greater than l p such that one stick is 10.00l p and the other is 15.25l p .
15.25 10.00 5.25 In this case, the difference measure is physically significant. However, to argue that measure is non-discrete is valid only if this measure is also different from a whole-unit count, that is, five units of the reference. To test, we again compare the two lengths, 5.25 5.00 0.25 (26) This case is the same as the first. Thus, all measures are physically significant only for a whole-unit count of the reference. We may then recognize that: The fundamental measures are discrete and countable. O 3 : The fundamental measures each define a reference.

Measurement Frameworks
Thus far we have demonstrated that measure has a lower threshold and that all measures are confined to a whole-unit count of some reference measure. We have not identified a means to confirm the number of physically significant measurement frameworks necessary for measure. We have only established that measure with respect to the observer is discrete.
To further our observations, we bring to the reader's attention that measure is a property of references. Therefore, given that the leading edge of the universe expands at the speed of light, we recognize that the universe can have no external reference. Therefore, the property of measure with respect to the universe must be non-discrete.
This may be summarized as follows. Matter exists with non-discrete measurement properties because there exists no external reference to the universe. Indeed, for all observers in the universe, matter is and can only be a discrete count of physically significant fundamental units of measure. O 4 : Measure with respect to the observer is discrete. O 5 : Measure with respect to the universe is non-discrete.
To develop its mathematical description, we describe the discrete and non-discrete measurement frames of reference as frameworks. To demonstrate a physically significant property of matter correlated to these frameworks, we devise an experiment described by three frameworks, one of which has the property of non-discrete measure and the remaining two of which are discrete. The experiment also carries two design prerequisites. First, the design must not introduce additional measures such as angles. Second, all information necessary for measure must be available to the observer at every instant in time. With these prerequisites, the three frameworks are: • A discrete framework describing where properties of the reference are observed ( AB : the observational framework).
• A discrete framework describing where count properties of the reference are observed ( BC : the measurement framework).
• The non-discrete framework describing the observed phenomenon ( AC : the target framework). For clarification, all three frameworks are described in Figure 1 using the traditional understanding of a Cartesian coordinate system. With this, we then recognize differences in the discreteness of measure with respect to the different origins of information (i.e., the frameworks). The observational framework-the framework of the observer-differs from the traditional understanding only in that measure is a count function of a discrete length reference equal to one. The measurement framework, which shares properties of the observational framework, is a count function of the reference. Finally, the target framework is described by the non-discrete framework of the universe that identifies (i.e., contains) the phenomenon. Although we present all three frameworks collectively from the observer's point-of-view, we are careful to note the differing measurement properties of each framework. Journal of High Energy Physics, Gravitation and Cosmology With this understanding, we then recognize that the design must resolve how information regarding the count value of the measurement framework is obtained by an observer relative to the observational framework. We also reiterate that the design must allow for a singular expression that correlates all three frameworks.
We propose, then, a system consisting of a grid of points that are a fixed count of a reference measure in separation (along the shortest axis). There must be enough points to form at least one square such that each hypotenuse of the square is also equal in separation. To ascertain initially the distance between any two points, we propose that at each point a laser pulse rangefinder is used along with the time-of-flight principle to ascertain whether each of the axes are equal in distance as agreed upon in advance of setting up the experiment. It is as such that we may ascertain whether the angular measure for each point is either along a line or at 90 degrees (except for those points that follow a hypotenuse). The design does not require that we introduce angular measure into our understanding of the discrete and non-discrete properties of length measure. The experiment also does not initially incorporate time as the experiment is performed only after it is set up.
Note there are the two frameworks, that of A and that of C of which A certifies the length AB (the observational framework) and C certifies the length BC (the measurement framework). There is a third framework (the target framework), of which both A and C and the unknown length AC are members. Thus, we need only the presence of members A and C in the target framework to define all information in the system.
Using the Pythagorean Theorem, then . Given that only a discrete reference count of the measure of AC is permitted in the observational framework, we find the difference 1.414 − 1.000 = 0.414 l p to describe a physically significant property of the universe. What phenomenon this difference describes between the discrete frameworks of A and C and the non-discrete framework AC of the universe is the subject of the next section.

Results
To achieve the goal-a measurable, verifiable, and falsifiable description of the CMB power spectrum-we proceed with a brief description of gravity. The sections to follow will be concise although more in depth discussions may be found in References [2] [3] [10] [11].

Gravity
We no longer need Planck's Unit definitions as a guide to measure. For one, the Planck expressions are approximate in that they do not take into account the measurement skewing effects of discrete measures. For this reason, the MQ approach to measure is identified by subscripting f to variables, specifically, l f for length, m f for mass, and t f for time.
Continuing with our prior observations, note that Figure 2 describes each of the three frameworks identified in Section 2. The long side c of a right-angle triangle is then resolved using the Pythagorean Theorem where side a is always the reference count 1 and side b is some known count of that reference.
Importantly, a count of 1 on side a is prerequisite to any count along side b to resolve side c. If an argument were presented that side a was arbitrary (i.e., a = 2), we would find a description that "assumes" a reference count of two units of the reference not explicitly incorporated into the definition of our reference.
This presents a factor representation of the framework that conceals the discrete count properties we are attempting to describe. Thus, side a = 1 is prerequisite for all considerations of side b in any understanding of the unknown distance along side c, We are now ready to resolve a difference between the discrete and non-discrete descriptions for this experiment. To describe the observer's experience, we conjecture that any non-integer count of the reference along the unknown length AC relates to a change in distance and may be described by rounding up (repulsion) or down (attraction). The remainder lost to rounding is denoted by Q L . For all solutions, Q L is less than half and thus attractive, as is evidenced by Q L 's Because side c always rounds down, we find that n Lr always equals n Lb . Thus, we always refer to the 'observed measure count' as n Lr . Moreover, note that the reference measure against which all counts are measured is defined by n La = 1. With this, we have composed an expression for gravity such that the loss of the remainder relative to the whole-unit count is Q L /n Lr . Together, Q L and n Lr are conjectured to represent an important dimensionless ratio that describes gravity. We proceed with that hypothesis by presenting the ratio in meters per second squared (ms −2 ). We multiply by l f for meters and divide by 2 f t to describe the distance loss at the maximum sampling rate of one sampling every t f seconds per second, Note also that the quantity is scaled and hence requires a scaling constant. As we shall learn later, this scaling constant is fundamental to the relation describing the three measures. To proceed, we multiply by the speed of light c and divide by a scaling constant S. Setting This understanding of gravity arises as a difference between the discrete measure with respect to an inertial frame and the non-discrete measure with respect to the universe. Comparing the expression with that of Newton's G/r 2 we see a decrease in distance between the two curves that is immeasurable beyond the sixth-significant-figure precision for all distances greater than 2.247l f . The difference may also be described as a function of Q L n Lr , a term that approaches 1/2 with increasing distance. Further described in Appendix A, we identify both the expression and the skewing effect arising from the discrete measure as the Informativity differential.
Discussed also in Appendix B, we replace the term S with θ si , not because the measure is radian for all contexts, but to bring to the attention of the reader that the value of θ si = 3.26239 radians is constant in all physical contexts. After resolving several expressions, we shall return in Sec. H to discuss unit analysis of expressions containing this constant.

Fundamental Measures
With a definition for quantum gravity, we may now resolve physically significant values for the fundamental measures. How we resolve these measures is important. Specifically, the Informativity differential is a distance-sensitive skewing effect in the length measure. For distances of 10 4 l f , this effect is less than can be measured. However, the measure of ħ is a quantum property where the effect is significant. To the extent that Q L n Lr = 1/2 is acceptable for the measure of c and G, we need to avoid an approach that uses ħ. For the purposes of these calculations, we recall that the units for θ si are kilograms meters per second. This is not the case for all described phenomena, an aspect that shall be addressed later. Thus, the values for each of the three measures, Appendix C, are: There are two approaches that may be used to resolve the fundamental expression-the simplest expression that relates the three measures. One, we may use Equation (13) to replace G such that Moreover, in MQ nomenclature, we often ignore the Informativity differential, presenting expressions as though we were describing a macroscopic phenomenon. In such cases, we make the substitution of Q L n Lr with the value 1/2. We refer to this procedure as the unexpanded form of the expression. Conversely, the expanded form of the fundamental expression is (37) Likewise, each of the fundamental expressions is also affected by the Informativity differential and has expanded counterparts. Calculation of the Informativity differential Q L n Lr does require several steps, but when describing quantum phenomena, especially phenomena less than 2.247l f , the precision is important.
A more detailed description is offered in Appendix A.

Size of the Universe
The three properties of measure-discreteness, countability, and physical signi-ficance with respect to the discrete and non-discrete measurement frameworks-may now be used to describe the earliest epoch of our universe and the transition that leads to the expansionary epoch we observe today. We no longer need additional concepts or experimental results to describe the constants or laws of nature other than the descriptions introduced so far. However, before we launch into an analysis of the CMB power spectrum, we need to characterize the expansion itself. We begin with expressions that correlate the expansion with the fundamental measures starting with the unexpanded form of the fundamental expression, which describes the expansion of the universe as a function of elapsed time, while there are multiple paths by which to approach a description of these phenomena, it might be argued that the expansion of the universe is in part assumed based on a correlation between the fundamental expression and the rate of expansion. Building on this approach as a conjecture, then it may equally be argued that the value of m f is a prediction of that conjecture. To that end, we find the conjecture physically significant to five digits, constrained by the precision of our measure of the age of the universe and the comparison mass If follows that with H U a universal constant of rate 2θ si m·s −1 per universe, the critical density of the universe is an accurate description of the universe, correlated to its age and diameter. The constant rate of expansion also tells us that the universe is flat, neither accelerating nor decelerating.

What Are the Multipole Moment Oscillations?
We begin with a few commonly used terms in MQ. For one, we refer to the ratio Likewise, we identify the one-to-one ratio of a unit of fundamental mass per unit of fundamental time m f /t f as the mass frequency. There is no specific term used to identify the ratio m f /l f , but the ratio is also an important physical bound.
Another way to describe measurement frequencies is to express each bound as a rate. Doing so filters out the target dimension such that all measures are fixed and equal to the inverse of the fundamental time, In the same way that length frequency describes an upper bound to measure, we may also resolve macroscopic properties of our universe using the same nomenclature. For instance, length and mass frequency expressions that describe the universe may be resolved by taking the product of the age of the universe A U , the radial system constant θ si and the corresponding dimensional frequency. To the extent that the elapsed time with respect to the present is approximately Note that the use of θ si reflects the rate of universal expansion as learned from the fundamental expression [Equation (37)]. Note also that, in this instance, θ si caries no units. The dimensionless nature of θ si when describing the universe is because the universe has no external reference. That is, θ si serves in the capacity of a self-defining value (i.e., ity of stars about a galactic core are described by Naturally, it seems confusing that gravity is constrained to some subset of the mass that can be measured within a galaxy, but when we understand the difference between an instant in time (which corresponds to the visible mass) and what can be observed in an interval of elapsed time (the observable mass), we see how mass frequency describes an upper bound constraint ongravity that differs from the total mass of stars that make up a galaxy. To resolve a precise understanding of the fundamental mass and its relationship to the visible, observable, and total mass, we shall need a few more expres-

sions. Rearranging the expressions for n T and R U such that
, and We shall also need the expression for critical density, a formal definition of the relationship between critical density and critical mass, and the MQ form of the gravitational constant from Equation (13).
To assist in the dimensional analysis, we use a capital M for a mass in kilograms but retain the same subscript as for the term written as a percentage of the total mass of the universe. For example, M obs describes the observable mass in kilograms. Conversely, Ω obs describes the observable mass as a percentage (i.e., 31.6%) of the total mass of the universe Ω tot .
Note also that the temporal approach offered by MQ provides a different naming structure for mass distributions from that of modern theory. There is what maybe measured presently Ω vis , what may be measured given an infinite amount of elapsed time Ω obs , the difference between these two values Ω uobs , the unobserved, and finally that which can never be measured as that mass exists at a point for which light will not reach the observer because of the expansion of space, i.e., dark mass Ω dkm . It follows that Note also that the dark mass distribution Ω dkm is identified in modern theory as dark energy Ω Λ . We do not use this term in MQ because we identify the distribution as mass that will never be observed due to the expansion of space. Likewise, Ω c is identified in modern theory as dark matter. We do not use this term but instead identify the distribution as Ω uobs . The unobserved mass is that mass that is presently not visible but is given an infinite interval of elapsed time.
There are two important values at work in the expressions that follow such that each is a percentage of the total mass distribution Ω tot representing all the mass in the universe: • Fundamental mass Ω f is that percentage of mass that corresponds to the upper count bound of m f that can be observed per t f relative to the total mass distribution Ω tot (i.e., Recall that the observable mass Ω obs plus dark mass Ω dkm represent all the mass in the universe and thus the dark mass is 1 − Ω obs , assuming Ω tot = 1. The right-hand side of the equality reduces to the form, We may now focus on the right-hand side of the equality. Given the critical density of the universe ( ) and where we know the observable mass distribution Ω obs , we multiply the critical density by the volume of the universe V U to give the total mass of the universe M tot . We then multiply this result by the observable distribution Ω obs to resolve the observable mass M obs . Combined with the expression above, we take advantage of the relation replacing the distributions with the associated SI descriptions.
Thus, 1 1 obs ( ) Because the sum of the observable Ω obs and dark mass distributions Ω dkm must equal one-the two measures account for all mass in the universe-we then combine Note that the dark mass distribution Ω dkm matches what in current theory we identify as dark energy Ω Λ . The match is not coincidental, just as it is not coincidental that the total mass in the universe is the sum of the observable and dark mass, or that the unobserved mass is the difference between the observable and visible (this being the value we associate with dark matter Ω c ). The distributions are as we have described from the outset, what is presently visible Ω vis , the sum of what is and will be visible Ω obs , and the difference Ω uobs [11] and what will never be visible because of the expansion of space Ω dkm . The distributions are a consequence of their temporal geometry each correlated to one another.
Proceeding, the locally defined speed of the expansion at the outer edge of the universe is the speed-of-light in SI units Equation (44) and Ω tot = 1. Similarly, the velocity equal to twice the radial expansion v U is the ratio of the observable to visible distributions Ω obs /Ω vis with respect to the total. Thus, the visible distribution may be resolved as well, Note that we have approached a temporal understanding of mass in the universe but arrived at the same values we measure with respect to ΛCDM and what are more commonly understood as dark energy, dark and visible matter; see Figure 3. The relationship is not coincidental. However, the concepts are intertwined. That is, the CMB power spectrum is a time dependent function. When we measure the CMB across the universe, we aggregate time periods, that which is local and near to the present and that which is distant, near to the past. The aggregation gives us a temporal view of the CMB across the history of the universe.
In addition, in that each of these distributions is a function of θ si -a constant value-this tells us that the distributions are invariant with respect to time. One may also notice the absence of the Informativity differential Q L n Lr from each of the distribution expressions. This absence reminds us that the distributions are geometric. If they were physically distinct mass phenomena constrained to a variable distance relation to the observer, then the Informativity differential would apply. Likewise, relativistic differences between mass moving at high velocities (i.e., distant in the past) and low velocities (i.e., close to the present) would apply. Such modifications would then skew these distributions away from the measured values we recognize today. None apply because the distributions are a consequence of the geometry.

Peak Oscillation Coordinates and the Effects of Expansion?
A power spectrum plot of the CMB yields five curves that are from left to right recognized as dark energy, observable matter, dark matter, matter without identification, and finally visible matter. Every second curve is also recognized with respect to optical properties as a compression curve. Finally, we recognize that the curve is a plot of the temperature of the CMB with respect to multipole moments. Whereas the visible distribution is readily recognized as representing all the visible mass in the universe, dark energy and dark matter have remained elusive.
MQ, in contrast, can resolve a clearer understanding of this graph as a temporal distribution of the spectrum with respect to an observer. MQ differs in approach in that all the mass/energy in the universe is recognized at the outset of the problem and then classifies the respective distributions according to that which can measure in the present Ω vis , that which can be measured given enough time Ω obs , the difference between these two Ω uobs , and that which will never be measured due to the expansion of space Ω dkm . The descriptions match those of the standard model to the same precision as our best measurement data.
In the expressions that follow, a new distribution term, Ω v is present. This distribution describes the fifth bell-like curve in the CMB power spectrum. Its physical description is in part known as an instance of decompression but is otherwise not discussed or associated with a specific phenomenon. In contrast, in Section 3.7, the physical meaning of M acr is discussed, but for now it serves primarily as a convenient term that reduces the nomenclature. Using 3 2 acr si M θ = , we take the distributions resolved above, reduce them such that they each share a common denominator (M acr + θ si ) and then resolve the value of each oscillation as the ordinate, thereby identifying the peak of each distribution. For example, with the abscissa representing the multipole moment l, we then exhibit each l as a function of θ si . As noted, the distributions are a temporal geometry, and as such the scaling is a function of π with an increasing exponent ( v Ω Ω Ω = π π π ). There are also two intermediary points Ω obs and Ω v that demonstrate a specific, but not well understood, pattern; : , acr Then, for consistency, the temperature value of the y-coordinate may be resolved using the factor ( ) However, there is one final step. The presentation must be adjusted for the expansion of space, The expression is further clarified by substitution using the fundamental expression 2 . More importantly, the expression describes the radial expansion θ si with respect to the proper distance. The power spectrum is also a function of the multipole moment-a repeating function of 2π. Therefore, combining the radial expansion of space along with the optical properties of the power spectrum, we find describes the skewing effects of measurement distortion in the left term of the unity expression. We must divide each x-value except Ω dkm and Ω tot to resolve the x-coordinate value. The MQ description matches to three significant figures corresponding to the most precise values available in the measurement data.
The effect is not applied to Ω dkm . As a temporal description of mass/energy, the Ω dkm distribution has not and will never be measurable. Thus, it cannot be subject to the effects of measurement distortion. The total Ω tot must be adjusted accordingly. Notably, ( ) 2 3 0.975160 si θ π = is a sizable value. Only with respect to a temporal description of the power spectrum can it be known to which distributions we must apply this effect. As such, we find many correlations to physical measurements are finely constrained by a MQ interpretation.
We bring to the reader's attention the point that because MQ describes a period of quantum inflation over a period of 363,309 years followed by an expansion, this does not change the order of events in the calculation of the power spectrum during and at recombination. However, it does affect the initial conditions. First, the horizon problem is resolved without a faster-than-light inflationary period. Second, because the universal mass is accreting with elapsed time, we find that nearly all the mass accumulated up to the time of recombination constitutes the CMB we see today, and this is verified with a match to observational data to four significant figures [14]. Third, it addresses a more fundamental question-Why is there a specific amount of CMB; why not more or even less plasma CMB?
Finally, we note some common correlations between the distributions:

Spacetime Curvature
With respect to spatial curvature, there exist two notable applications, that concerning the universe and that concerning gravitation. Having completed a discussion of gravitation, we now discuss the phenomena of curvature that are cosmological in scale. Specifically, we discuss a flat universe as described with respect to a constant rate of expansion as presented in Equations (42)-(45).
Along with the fundamental expression, then The expression is collaborated with respect to multiple measurements, for instance, by gravitational curvature, by the predicted value of the fundamental mass m f , by each of the CMB distribution values, Ω dkm , Ω obs , Ω uobs , and Ω vis and by the multipole moment of Ω dkm as presented in Equation (81) WMAP measurements of the CMB suggest that a value of around 220 is indicative of a flat universe, but a precise measure is difficult as the value is a function of several phenomena with an additional uncertainty in the initial conditions. Conversely, the MQ expressions are a function of one measure, θ si , providing for a precise and straight-forward physical interpretation. Moreover, θ si is a predicted value Equation (C9) matching the six-significant-figure measurements described by Shwartz and Harris in their 2011 paper regarding the quantum entanglement of X-rays at the degenerate frequency of a maximally entangled Bell state [15].
We also bring to the reader's attention the fundamental expression that describes the one-to-one correlation between measure and expansion. The arguments for an expanding or contracting universe would impact our understanding of the relative values of the fundamental measures. Notably, this is not observed and there is a limited number of counterarguments along these lines of thought. For instance, one might argue for a variation in the rate of expansion such that the speed of light remains fixed while the value of the fundamental mass m f varies. Alternatively, one might propose a variation in both l f and t f such that the speed of light and m f both remain fixed. One may also argue that a third unknown compensates the undesired variation as the rate of expansion varies. However, in considering any of these conjectures, we would also have to address changes in the orbital positions of the electron orbits as described by this MQ form of the fine structure constant, (99) Therefore, if the fundamental mass is constant, the speed of light is constant; if stable atoms are also a necessary part of our stellar history, then there is physical support for a constant rate of universal expansion in a flat universe.
We take this moment to point out that because the fine structure constant is typically measured with respect to quantum phenomena, it is important to describe the value in the MQ expanded form (i.e., Q L n Lr ) or there will be a significant error in the predicted value ( Therefore, we find that curvature is never a feature of the spacetime itself, but rather a consequence of discreteness, such that the loss of fractional counts Q L of the reference length l f leads to the appearance of a curved spacetime. In MQ, we recognize this effect as the Informativity differential (Appendix A), The expression is usually taken at its macroscopic limit of Q L n Lr = 1/2 such that the value of Q L is so small as to be physically insignificant. For additional expressions describing spatial curvature and the MQ approach to measurement distortion presently described by SR and GR, the reader may refer to "Measurement Quantization Unifies Relativistic Effects …" [10].

Mass Accretion
As discussed in Section 3.4, each mass distribution is a function of the radial system constant θ si . As such, the distributions are fixed. Consider now Equation Unavoidably, the mass of the universe must be increasing across all distributions such that each of the distributions remains fixed relative to the other. Using Equation (95) , and as such, all constants may be written entirely as a function of fundamental measures.
We take this moment to discuss frames of reference and their importance in the description of phenomena. Noting that our understanding of length measure may always be reduced to a description that requires the Pythagorean Theorem, we find ourselves asking, how many physically significant frames of reference are needed to describe the phenomenon of distance? The Pythagorean Theorem, at a minimum, has three terms. Therefore, should not measure require three physically significant frames of reference and if this is readily agreed to, then what are they? In MQ terminology, the third frame is referred to as the self-defining framework.
We often refer to descriptions of the universe as self-defining because there is no reference external to the universe with which to anchor our understanding of such descriptions. Conversely, phenomena are called self-referencing if they are expressed in terms that have definitions based on other terms that are then given meaning with respect to the terms first mentioned. Collectively, the division helps orient the reader as to two distinct classes of phenomena with respect to a framework. This completes the formal definition of the three frameworks, namely, the observational framework, the measurement framework, and the self-defining framework of the universe containing the observed target.

Trigger Ending Quantum Inflation, Initiating Expansion
During the earliest epoch, the universe cannot expand because the internal spacetime provides no opportunity to reference points outside of the quantum bubble. To understand quantum referencing, we begin with a review of the three frameworks: the reference, measurement, and target frameworks. Measure has physical significance only when a composite of the information from each of these frameworks. Therein, the quantum referencing we observe today is mitigated during the earliest epoch. Presently, a physically significant measure exists such that side a describes the reference count n a = 1, side b describes some count of the reference (both sides a and b are discrete), and side c describes a non-discrete reference count between the observer and the target. However, what if the size of the universe is such that side b describes a count less than two?
In this instance, there exists no means by which to distinguish the count n b from the reference count. In other words, side b may be any non-discrete value, but with respect to the observer indistinguishable from the reference count n a = 1. This, in fact, describes the presently defined properties of side c. We therefore modify our understanding of side b when describing measure in the quantum inflationary epoch with the non-discrete count term n bn . The description applies during the entire epoch. We next consider a universe that has expanded sufficiently such that ( ) More specifically, a radial length count of 2 rounds down (i.e., 2 1.414 ≈ ), back inside the quantum bubble. However, a radial length count of 3 rounds up (i.e., 3 1.732 ≈ ), outside of the quantum bubble. Until the universe reaches a radial length count equal to 3 ; the rate of expansion is constrained. We shall resolve the expressions describing this quantum inflationary period in the following section but take this moment to point out one final detail. One might ask, why does the expansion not stall when it reaches a radial length count of 5 ?
At 5 there are new points of reference inside the quantum bubble that are a distance 3 f l from the outer edge. As before, this count of the ref- erence measure l f rounds up and allows the expansion to continue uninterrupted.
Finally, there remains a well-known argument surrounding the coincidence between mathematics as a tool describing nature and nature which appears to abide by the laws of mathematics. We do not broach this subject here but remark that the tradition of providing examples of physical measurement that corresponds with mathematical expression is an important tool of science. It is our ability to correlate this approach with the measurement data that the presentation is made.

Quantum Inflation
We begin with the fundamental expression broken out in terms of counts of the fundamental measures as described in Equation (35). Note, we have added a prefix u to denote that the expression is a self-defining representation of the universe, As such, the expression describes a universe that expands at the speed of light.
To modify the expression appropriately, we must recognize a differing count n Lu of l f other than that afforded by the relation To avoid confusion, we One might ask, what is the role of critical density ρ c considering that the rate of mass accretion 3 2 si θ is constant? Indeed, mass density is increasing with elapsed time so what we find is a rate of expansion that is decreasing as reflected in the expansion velocity v i with respect to the leading edge. The steady rate of mass accretion, in turn, depends on the system constant (i.e., in our case 2θ si ) associated with a quantum fluctuation such that there could be many such fluctuations in a multiverse. Nonetheless, without a system constant that falls in an acceptable range, the fluctuation never reaches sufficient size to transition to an expansionary epoch. Moreover, the system constant also determines the radius of electrons about the atomic core. Thus, an expansion that is too small or too great will result in a universe that cannot form baryonic matter.
However, as we shall demonstrate, this incredibly slow and decreasing velocity is not what brings quantum inflation to an end. For that, we must return to the definition of fundamental length. Taking the integral of the velocity expression with respect to time (the constant of integration is 0), we obtain an expression for the radius of the universe ( ) at which point external referencing is permitted and the leading edge of the universe then expands at the speed of light relative to that edge.

Time Dilation between the Quantum and Expansionary Epochs
The quantum and expansionary epochs describe periods of our evolutionary history with differing frames of reference. The difference is subject to a relativistic offset, one which must be accounted for to align calculations of the CMB age properly with respect to elapsed time in our present epoch.
In MQ, we refer to this as the universal expansion H U , the expansion of space.
This differs from the motions of galaxies within space, which must be resolved separately. There is no specific correlation between the two, but it is conjectured that baryonic mass remains nearly static in space with respect to where it originates.

Discussion
MQ has enabled us to offer physically significant descriptions of phenomena we observe in nature. Bearing in mind that MQ is a nomenclature, and hence what we present is little more than classical mechanics written in a less familiar form.
More significant, is that the expressions demonstrate a physical correspondence that matches the measurement data.
By example, we look to expressions describing the fundamental units themselves, each which matches the 2014 CODATA to six significant figures. We also look to the calculation of θ si and gravitational curvature. Taking the value for either produces the other with the same level of physical correspondence. The calculation of Hubble's constant and the volume and mass of the universe are also in agreement. Moreover, the quantity, age, density, and temperature of the CMB again match the data. The calculation of the fine structure constant resolves a significant and long-standing discrepancy with the measurement data.
Looking to the power spectrum of the CMB, the distributions are in correspondence. The effects of relativity with respect to several phenomena are each reflected in the calculations, each aligning with the measurement data.
While these calculations provide opportunity for establishing a physical significance, we emphasize that it is the description that is under investigation, not the approach. The approach is classical, a field that already enjoys a century of published support.
Perhaps it would be of significance to then consider the mathematical implications of MQ. Does math play a role in physical behavior? Are the laws of physics derivatives of mathematical structure or is mathematics merely a tool coincident with our interest in describing nature?
Indeed, these are questions that have arisen in this presentation. In response, we should focus our attention on the scientific method. These questions are not the subject of this paper. For centuries, the community has been complacent with the coincidence of mathematics to describe nature. That a universe of radius 3 units of fundamental length should so accurately describe nature is irrelevant. The goal, as has always been central to the field of physics, is to find the math that provides the greatest correspondence, to present a mathematical story that is measurable, verifiable, and falsifiable. For that, MQ provides several examples to six digits of physical significance.
As such, we hope that these considerations have not been a distraction. Yes, MQ brings mathematics even more into the limelight. And yes, there will likely be even more debate about the role of math in describing nature. However, at least for now, our focus is in providing new tools and new ways with which to understand the early universe. We have, with MQ, revealed that the power spectrum is in part a function of elapsed time, that there is no dark energy or dark matter [11]; rather, it is all matter. What we are seeing reflects a history of information corresponding to that which we measure presently, what will be measurable, and that which can never be measured. MQ offers the ability to correlate the quantum to the cosmological with equal footing in gravity as well as electromagnetism. In this light, we have presented some insight to questions that have until this point been a mystery.
To end, we remark that observations of the physical significance of fundamental units of measure require the interpretations presented. However, they do not necessarily exclude some conjectures, such as inflation theory. At present, there is no support for inflation from the early universe events described using MQ, but this does not mean that inflation theory describes something that never happened. Rather, we add MQ to the collection of tools used in determining the physical significance of inflation among other conjectures that have filled the gaps in our understanding of the early chronology of the universe.
Throughout the paper, the term Q L n Lr is used repeatedly and is referred to as the Informativity differential in recognizing the central role it plays in describing how fractional values less than the theoretical limit reflect a distortion effect in distance measurements. Knowing the limits to Q L n Lr is essential to resolving the fundamental measures. This product is obtained from Equation (28)  In the initial presentation, we identify sides a, b, and c such that side b has some count n Lb of reference l f . We later reconsider side c such that Lc Lr L n n Q = + and Lb Lr n n = . Because our focus is then on side c, we drop the n Lb term and use n Lr throughout all expressions when discussing MQ.
The approach is justified in that what is measured always equals a whole-unit count of a fundamental measure, and with n La = 1, we find that n Lr must equal n Lb for all values. This is easily verified in that the highest value for Q L is obtained for n Lb = 1 where ( ) Conversely, if we divide by n Lr , then add n Lr , square, subtract 2 Lr n , and divide by 2, we find that (A3) Q L decreases with increasing n Lr until the left term drops out. Distance does not need to be considerable to reduce the Informativity differential to 0.5. At just 10 4 l f , Q L n Lr rounds to 0.5 to nine significant figures.