Does our universe conform with the existence of a universal maximum energy-density $\rho^{uni}_{max}$ ?

Recent astronomical observations of high redshift quasars, dark matter-dominated galaxies, mergers of neutron stars, glitch phenomena in pulsars, cosmic microwave background and experimental data from hadronic colliders do not rule out, but they even support the hypothesis that the energy-density in our universe most likely is upper-limited by $\rho^{uni}_{max},$ which is predicted to lie between $2$ to $3$ the nuclear density $\rho_0.$ Quantum fluids in the cores of massive NSs with $\rho \approx \rho^{uni}_{max}$ reach the maximum compressibility state, where they become insensitive to further compression by the embedding spacetime and undergo a phase transition into the purely incompressible gluon-quark superfluid state. A direct correspondence between the positive energy stored in the embedding spacetime and the degree of compressibility and superfluidity of the trapped matter is proposed. In this paper relevant observation signatures that support the maximum density hypothesis are reviewed, a possible origin of $\rho^{uni}_{max}$ is proposed and finally the consequences of this scenario on the spacetime's topology of the universe as well as on the mechanisms underlying the growth rate and power of the high redshift QSOs are discussed.


Introduction
Based on the recent theoretical and observational studies, it is argued in this paper that: • If ρ uni max indeed exist, then the remnant of the merger of the two neutron stars in GW170817 should be a massive neutron stars (NS) whose core is made of an incompressible quark-gluon superfluid that obeys the laws of quantum field theories [see Fig. 1 and reference : 8]. However, the ambient media remain compressible and dissipative, though these properties are doomed to where a 0 = 16πG 2 /c 3 ≈ 10 −6 and β v , β c , ρ correspond to the relative fluid velocity, v/c, sound speed, V s /c and the density of the inflowing matter through the boundary in units of 10 −10 g/cc, respectively.
Here M/t are in units of 5 where τ corresponds to the elapsed time for a SMBH of initial mass M 0 to reach M(τ ). For M(τ )/M 0 = 100 and M 0 = 1, we obtain roughly: O(10 9 ) Super-Eddington Accr.
collapse of clouds, collision and merger.
R LSO here is the last stable orbit, where β v = β c ≈ 1.

Dark matter in the early universe
Dark matter (DM) in cosmology is an essential pillar for understanding the entire cosmic web: starting from structure formation, clusters of galaxies and galaxy formation down to stellar-mass objects.
Except for gravitational interaction with normal matter, the physics of dark matter continues to be a conundrum in understanding our universe.
For the present discussion, we select three properties that support the constant density hypothesis: When a massive ultra-compact object 1   which is a limiting case of: Microscopically ∆r is limited from below by the average separation between two arbitrary baryons ∆ bb .
Using ∆r = ∆ bb and ∆ε∆t ≈ , we obtain that ∆r 10 10 × ∆ bb . Among others, this implies that incompressibility is a macroscopic property, but that quantum fluids must fulfill on the microscopic scale at r = 0. In this case, the pressure here ceases to behave as a local thermodynamical quantity and it becomes solely a Lagrangian multiplier: a mathematical term that dictates the global dynamics of the quantum fluid, which in turn depends strongly on the topology of the embedding spacetime. This pseudo-pressure should be carefully constructed, so that its transition into the ultrabaric regime remains forbidden, dp/asdε ≥ 1, and therefore causality condition is grossly violated [see Fig. 7 in 16].
Indeed, we consider the following observational signatures to support our scenario: • The discrete events of glitches observed in pul- -In theṖ − P diagram, almost all observed glitching pulsars appear to be younger than 10 7 yr and their magnetic fields are stronger than 10 11 Gauss.
Obviously, the reaction time scale of the core at the verge of collapse is of order micro-seconds, which is Although this rate is expected to be even higher in the early universe, yet isolated NSs older than one Gyr have not been observed. The topology of the spacetime embedding DEOs is of a bimetric type, which in turn prohibits their merger and makes them to excellent BHs and DM-candidates.

Hadronic collisions: LHC and RHIC
Among many recent explorations related to particle collisions in labs, there are several discoveries that should be relevant for the present discussion: Recalling that QGPs are imperfect due to unitarity, the cross-sections of colliding particles ought to be bounded from below. Indeed, based on infinitely coupled supersymmet-ric Yang-Mills gouge theory (SYM) and using anti-de Sitter space/conformal field theory (ADS/CFD) duality conjecture, the lower-limit was verified to be: which is roughly equal to the lower-limit obtained using the uncertainty principle [36].
where α vis denotes the effective viscous velocity in units of the sound speed and α the corresponding viscous length scale in units of r b .
Given that elliptic flows start shaping already during the initial expansion, then α 2 λ α vis α should be of order unity, which yields the Reynolds number: This implies that η s , η should be more sensitive to temperature's variation than entropy, i.e., where the domain of integration, D n+1 , is bounded by the surfaces S n and S n+1 , and g jk is the spacetime metric. As UCOs cooldown, the topology of the manifold D n+1 changes from a curved into flat one, and therefore ∆E g tot becomes free. As the matter has reached the maximum compressibility limit at zero-entropy, ∆E g tot cannot be absorbed locally, and therefore it is conjectured that this energy goes into enhancing the surface tension, i.e. the "bag energy" confining the enclosed continuum of gluon-quark medium.
For ρ = ρ uni max , the energy per particle may be estimated as follows: since the separation between baryons vanishes, i.e. ∆ bb = 0 (see Fig. 4). In this state the distance between quarks initially belonging to different baryons reduces to ∆ qq = qq , which is assumed to be the smallest possible distance between quarks at T = 0. By reducing ∆ qq to qq , an energy of order ε + ≈ c /(2 qq ) ≈ 1/3 GeV becomes available, but which cannot be absorbed locally 3 .
where r b is the radius of the a baryon at zerotemperature.
Under normal terrestrial conditions, the nuclear density is roughly n 0 ≈ 0. 16

5).
On the other hand, using uni min ≈ r b , the resulting resonance energy amounts to ∆ε ≈ 0.23 GeV.
Summing over all possible numbers of quark-bonds, would yield roughly the rest energy of an individual baryon.
Based thereon, the volume of a massive NS at the end of its luminous lifetime would be the sum of the volumes of the enclosed baryons at zerotemperature, i.e.  While R t=∞ N S here is larger than the corresponding Schwarzschild radius, it is still smaller than the last stable orbit, though these comparisons are irrelevant, as the spacetime inside R t=∞ N S is Minkowski flat and not curved Schwarzschild.
Recalling that the action of compression of baryons by the embedding curved spacetime under zero entropy conditions, is to mainly transform the positive energy ∆E g tot (see Eq.11) into storable energy dW.
From global energy conservation, one finds: ∆V i ), (15) where V consists of the sum of compressible space between baryons, ∆V bb , and those of the incompressible gluon-quark plasma inside baryons at zerotemperature, V b 0 . For a given number N of baryons, is a radius-dependent quantity which is expected to increase as the surface of the object is approached.
Once the neighboring baryons are compressed together and came into direct contact with each other (see Fig. 4), ∆V i reaches the lower limit: where ∆E g tot | t=0 is the initial gravitational energy stored in the curved spacetime embedding a newly born pulsar (see Fig.5). In the absence of destructive external forces, the gravitational and thermodynamical properties of DEOs suggest that these should be long-living objects with a lifetime most likely much longer than the current age of the universe. Once a fully evolved DEO starts decaying, its hadronization process goes instantly, thereby liberating its total ∆E g tot | t=0 . Recalling that the DEOs are governed by one single speed, the further details]. Also, noting that the onset of hyperon production occurs for ρ ≥ 2 ρ 0 , the formation of incompressible gluon-quark superfluid in their cores is a viable scenario. In the latter case, however recent studies of the internal structure of the NSs in GW170817 using sophisticated EOSs with tidal deformability, predict their radii to be roughly 11 km. Our scenario predicts that isolated NSs would end up their luminous lifetime as DEOs having radii of order R t=∞ N S ≈ 10 km, which is a reasonable prediction, when noting that the volume of isolated NSs should shrink as they evolve on the cosmic time.
the conditions to be imposed on Q 2 at both boundaries are identical and therefore α s (Q 2 ) must remain constant. In fact the Chiral symmetry is fully restored ( qq = 0) in this regime, which grants the core dynamical stability on cosmic timescales.

The bimetric universe and CMB radiation
While the existence of a universal maximum energy density promotes the hypothesis that our universe is infinitely large and old, it suggest that it went neither through an inflationary phase nor creating BHs. Here a race starts between the outward-oriented ultra-relativistically propagation of fluid flows and topology fitting of the embedding spacetime. Hence two fronts were created: The hardonization front that must go through the entire cluster, and the topological front, "f 1 " at the interface between the flat the curved spacetimes (see Fig.6). Although the material front propagates at ultra-relativistic speed, the topological front "f 1 " propagates with the speed of light. This generates a time delay that increases with the cosmic age. Note that the hardonization front is associated with the creation of interacting particles, generating entropy, and turning the matter into compressible dissipative media. In the course of this process, the embedding spacetime ought to undergo a topological change from Minkowski flat into a curved Schwarzschild. However, as the amount of energy that goes into curving the embedding spacetime is finite, the curvature should decrease as the expansion goes on, thereby asymptotically converging into a perfectly flat spacetime (see Fig. 6).
Mathematically, let the rest mass-energy of the cluster of DEOs on the verge of an LBB explosion be E cl .
As the cluster is embedded in a flat spacetime, the gravitational energy vanishes, i.e.. E g = 0. Assuming mass-energy conservation, then the total energy shortly before and after LBB should remain constant, i.e.: where E b cl is the rest energy of the total baryons at the nuclear density, ρ 0 , and zero-entropy. E vac cl is the work needed for compressing the constituents in the system from ρ 0 , up to the maximum compressibility limit, where ρ = ρ uni max . E g is the gravitational energy, which is calculated from the integral: Based thereon, the total mass involved in the big bang may be predicated as follows: for an average density of ρ now ≈ 10 −29 g/cc, and a radius of R uni > c × τ uni age ≈ 10 28 cm, we obtain a total mass of E b cl ≈ 5 × 10 22 M . Inside the DEO cluster the density is roughly uniform and has the value ρ uni max . This yields a radius of approximately 2 AU for the DEO cluster. Note that a SMBH with R S = 2 AU yields an enclosed mass of roughly Indeed, the cluster of DEOs presented here has a uniform density and is embedded in a Minkowski spacetime, so that the necessity for an exponential growth to smooth out density irregularities becomes it unnecessary.

Summary & Discussion
In this paper, we have discussed the possibility that our universe may permit the existence of a universal maximum energy density ρ uni max , which characterizes the state of incompressible superfluids at the center of massive NSs. Based on theoretical and observational studies of pulsars and neutron stars, ρ uni max is predicted to lie between 2 × ρ 0 and 3 × ρ 0 . • The cosmological origin of high redshift QSOs and dark matter in the early universe conform with our scenario that the universe should be infinitely large and old.
• The dominance and origin of chemical abundance of the light elements in the universe is a natural consequence of the collective decay clusters of DEOs that led to LBB explosion through which hardonizion operated efficiently.
• The scenario of a bimetric universe provides a simple and reasonable explanation to the flatness problem of the universe, the origin of dark matter and dark energy. One of the far-reaching consequences here is that the big bang should be a recurrent phenomenon in our infinitely large and old universe. Indeed, the existence of a maximum universal density ρ U ni cr would render the inflationary phase unnecessary and would naturally explain why our universe escaped its collapse into a giant BH.
The scenario here predicts that massive stars should have sufficient time to collapse into massive UCOs, cooldown and to subsequently turn invisible at the end of their luminous lifetimes. Their further collapse into BHs is prohibited by the existence of ρ U ni cr , at which the topology of the embedding spacetime changes into a Minkowski-type spacetime (see Hujeirat 2021 in preparation).
Nevertheless, our scenario addresses several new problems that need to be answered, such as: