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This article poses the question of a minimum cosmological constant, i.e. vacuum energy at the start of the cosmological evolution from a near singularity. We pose this comparing formalism as given by Berry (1976) as to a small time length, and compare that in its entirety to compare this value given by Berry (1976) with a minimum time length at the start of cosmological space-time evolution. Using the methodology of Zeldovich (1972) as to a problem with electron-positron pair production we also propose another upper bound to the problem of minimum time length which may be accessible to experimental inquiry. This then makes the problem of minimum time length a way of specifying a magnetic field dependence of the cosmological constant, which has major implications to answering if quintessence, i.e. a changing cosmological vacuum energy, or a constant for the “cosmological constant” problem. Our answer is an initial value for the cosmological vacuum energy 10
^{10} - 10
^{20} times greater than today which suggests either Quintessence, or if still a constant, a much better value for this parameter than what is suggested by traditional field theory methods. In closing we review how our construct supports work done by Corda, as to early universe models and what the implications are, as to the choices we have made.

We first of all cite that there exists formalism of Berry [

Berry’s results [

We will compare this answer with a minimum time step consistent with Non linear Electrodynamics NLED and use it to obtain a Non linear Electrodynamics NLED bound on the

If we consider the role of an electromagnetic charge, as freely given in this presentation, we should also look at a derivation of what Zel’dovich [

Again to generalize this Equation (2), we consider if the electric field is such that the commensurate bulk charge will have the following relationship to the given electromagnetic charge, to read as, if when

Picking the time variation as given by

Equation (3) has a deeper meaning. That that not only is there a net “magnetic” monopole charge, as given in Equation (4), that there is a minimum non zero “energy density” of the electric and magnetic field (E and M), as given by either

In doing so we will characterize the values to be set for Equation (4) as follows. i.e.

“radii” of the universe due to electro dynamics given in [

The next section will give inputs into these values and will be used to show how non linear electrodynamics may -influence an upper bound choice for the minimum time step which may arise in the start of the evolution of the universe

In this section we will lay out arguments given in [

Then the numerical density of the electron-positron pair may be given as

We will next begin to analyze what should be for

To engage on this, we use the Zeldovich [

We assume that the net frequency remains in Initial nucleation invariant, but that the initial and final volumes change, by an amount we will quantify next, i.e. start with an initial to final radii of

Then

This is the simplest interpretation of the consequence of varying energy density. Now for background to confirm it:

Making use of [

Implying if c is the speed of light, and

i.e. in [

This has a positive value only if input (E and M?) frequency

In this situation we will be setting

Then if, initially, Equation (15) is large, due to a very large initial vacuum energy parameter

The above scale factor should be such that the value of Eq. (17) should be in its smallest, i.e. 480,000 times proportionately larger than a Planck length of

Then, we will have that

Equation (18) puts a strong constraint upon the frequency and magnetic field strength, whereas Equation (12) gives a strong set of values as to allowed E, so as to have, then

This value for the square of the electric field should be then put into obtaining

The numerical “density” of electron-positron pairs drops as when the frequency

i.e. for low frequency, we have a collapse to the Planck time frequency value, whereas, the minimum time step rises as frequency

Whereas this may tie into a massive graviton mass as given by the author as spin off of massive gravitons given in [

i.e. the time step is then independent upon elementary arguments as to massive graviton mass. Furthermore, even if [

And there is a relationship between Equation (24) and Equation (22), as well as a density functional which may relate to initially scaled mass

The easiest case to consider is, if the

Then we are looking at

Here,

We will next then discuss how our work is connected to what Corda has brought up in work which is to discriminate between different cosmological models. This section is copied from the paper to be published [

Quoting from [

“Thus, if advanced projects on the detection of GWs will improve their sensitivity allowing to perform a GWs astronomy (this is due because signals from GWs are quite weak) [

We argue that a third polarization in Gravitational waves from the early universe may be detected, if there is proof positive that in the pre Planckian regime that the Corda conjecture [

“The case of massless Scalar-Tensor Gravity has been discussed in [

This ends our recap of the section given in [

What we are arguing for is that the choice of the vacuum energy as given by Equation (27) may give conclusive proof as to satisfy the Corda conjecture and his supposition as to the existence of an additional polarization [^{rd} polarization. Which will be a way to determine the final disposition of GR as THE theory of Cosmology, or open up the possibility of alternate theories. It is an issue which we think will require extreme diligence. While ending our query as to the possible existence of a third polarization we should mention what would be the supreme benefit of our upcoming analysis of Equation (27), namely how to avoid the conflating of dust, with gravitational waves, i.e. the tragic Bicep 2 mistake [

The main agenda would be in utilization of Equation (27) to help nail down a range of admissible frequencies which would be to avoid [

The previously done work by the author as to graviton production invoking nonlinear electrodynamics in cosmology was re-introduced for the purpose as to density functions which are used to create an upper bound to the largest initial time step, in cosmological evolution. Counter intuitively, Equation (22) has no connection as to the scaled value of a vacuum energy as given in Equation (23), which suggests that when frequency rises, as may be connected to alternative values of cosmology, that different processes as to graviton production, as exemplified by Equation (25) still keep a sharp independence as to initial time size as we state it for Equation (22). Keep in mind, that what is being attempted is to upgrade work represented by Maggiore [

Equation (27) and Equation (28) in themselves argue for an NLED influenced cosmological “vacuum energy”, i.e. what we observe, initially is that the above, using ^{10} - 10^{20}, arguing that some form of quintessence is argued for. But this value of Equation (27) is far lower than the 10^{120} overshoot, obtained by traditional QFT methods [

We wish to point to an earlier paper by Beckwith, and Glinka [

We wish to confirm, experimentally, what has been brought up as to vacuum energy, and the critical detail of stating, as done in our document that ^{10} - 10^{20}, arguing that some form of quintessence is argued for. After this is confirmed, speculations as to conflating gravitons, directly with dark energy may be investigated experimentally. Sadly, the author sees little hope of confirming if the multiverse construction of [

This work is supported in part by National Nature Science Foundation of China grant No. 11375279.

Andrew WalcottBeckwith, (2016) Non Linear Electrodynamics Contributing to a Minimum Vacuum Energy (“Cosmological Constant”) Allowed in Early Universe Cosmology. Journal of High Energy Physics, Gravitation and Cosmology,02,25-32. doi: 10.4236/jhepgc.2016.21003