An accelerating and rotating Planck-Hubble universe ( A very simple model of quantum cosmology )

With reference to Planck scale, increasing support for large scale cosmic anisotropy and preferred directions and by considering an increasing ratio of Hubble parameter to angular velocity, right from the beginning of Planck scale, we make an attempt to estimate ordinary matter density ratio, dark matter density ratio, mass, radius, temperature, age and expansion velocity (from and about the baby universe in all directions). We would like suggest that, from the beginning of Planck scale, 1) Dark matter can be considered as a kind of cosmic foam responsible for formation of galaxies. 2) Cosmic angular velocity decreases with square of the decreasing cosmic temperature. 3) Increasing ratio of Hubble parameter to angular velocity plays a crucial role in estimating increasing cosmic expansion velocity and decreasing density ratios of dark matter and ordinary matter. 4) There is no need to consider dark energy for understanding cosmic acceleration.


Introduction
According to current notion of modern cosmology, if the known laws of physics are extrapolated to the highest density regime, the result is a singularity which is typically associated with the Big Bang [1,2].Unfortunate thing is that, pre or post conditions and parameters of big bang physics are absolutely unknown.In this critical scenario, in a quantitative approach, it may not be wrong to consider a 'growing' or 'evolving' phase of 'Planck scale'.Even though massive nature is unclear -with known physical laws, Planck scale can be assigned with certain 'mass', certain 'radius', certain 'volume', certain 'density', certain 'temperature' and certain 'pressure' etc. Clearly speaking, Planck mass can be considered as a characteristic massive seed of the evolving universe and big bang can be replaced with an evolving Planck ball.Planck mass can be called as the 'baby universe'.Thus, by replacing 'big bang' with a growing Planck ball, in a hypothetical approach, an evolving model of quantum cosmology can be developed [3,4].Since Planck scale is associated with Quantum theory and 'spin' is a basic property of quantum mechanics, it may not be wrong to consider a growing and rotating model [5][6][7][8][9][10][11][12][13] of a Planck ball from and about the baby universe in all directions.Center of the growing universe seems to depend on the location of the assumed Planck seed under consideration.Note-1: For the above symbols, subscript 0 denotes current value and subscript pl denotes Planck scale value.

Proposed assumptions
With respect to our earlier publications [14,15], in this paper we review the basic assumptions.
1) Ratio of Hubble parameter to angular velocity is, can be considered as the cosmic expansion velocity.
3) Cosmic radius can be expressed with 4) Dark matter can be considered as a kind of cosmic foam responsible for formation of galaxies [16,17,18].

Note points:
(1) Assumption 1 indicates the role of Planck scale in entire cosmic evolution.Using the number t  , density ratios of dark matter and ordinary matter can be studied.(2) Assumption 2 can be considered as a simplified form of Hubble's law applied to the expanding universe as whole.Assumption 2 can be understood in terms of cosmic kinetic energy and temperature in the following way.During cosmic evolution, a) Kinetic energy of matter is inversely proportional to cosmic temperature.b) Based on assumption 1, cosmic temperature can be shown to be inversely proportional to t  .c) Hence, cosmic expansion velocity can be shown to be proportional to 1 4 .

Role of the Planck scale in entire cosmic evolution
We make an attempt to implement the 'Planck scale' in the entire cosmic evolution.We define the Planck scale Hubble parameter,   This value can be compared with other estimates [5][6][7][8][9][10][11][12][13].
In a simplified form, cosmic temperature can be expressed as, 4. Estimating the trend of density ratios of ordinary matter, dark matter and total matter

Total matter density ratio
With the help of defined 1 ln and with reference to the current observed we are making an attempt to estimate the past values of   OM t  and   .


We hope that, at Planck scale, there exits ordinary matter as well dark matter in certain proportions.
Based on these relations, it is possible to show that, Based on assumption 2 and relation (7),

Relation between dark matter density ratio and ordinary matter density ratio
Unless we know the physical nature and properties of dark matter, it may not be possible to thoroughly analyze the density ratios of dark matter and ordinary matter.other such kind of relations can be developed in a verifiable approach and percentages of dark matter and ordinary matter can be explored [16].
See figure 1 plotted with relations (8), (10) and (11).Blue curve represents a decreasing trend of ordinary matter density ratio, black curve represents a decreasing trend of dark matter density ratio and green curve represents a decreasing trend of total matter density ratio.
Here, it is very importnt to note that, even though density ratios of ordinary matter and dark matter are assumed have a decreasing trend, their mass content can be shown to be increasing with incleasing cosmic radius and volume.In terms of   See table 1 for the current and Planck scale physical parameters.

Cosmic scale factor and red shift
With reference to the proposed relations (1) and ( 3) and with reference to the current definitions of cosmic redshift and scale factor, it is possible to show that,

To estimate the current cosmic age
From the beginning of cosmic evolution, based on the proposed cosmic expansion velocities, cosmic age can be approximated with the following relation. where can be considered as average expansion velocity.

t 
For a temperature of 3000 K, it is possible to show that,   Cosmic age corresponding to a temperature of T=3000K can be estimated to be, This estimation is 19.37 times less than the current estimations and needs further study.

Velocity and distance relation
In all directions, from and about the hypothetical baby universe, current galactic receding speeds can be approximated with, a) Relation ( 19) can be compared with currently believed Hubble's law for the current expanding universe.
b) For a distance of

Cosmological constant problem
With reference to proposed concepts, ratio of the Planck scale critical density to the current critical density is, pl pl This idea can be considered as a characteristic tool for constructing a model of 'quantum gravity' with cosmic evolution.

Horizon problem
If one is willing to consider the concept of 'matter causes the space-time to curve', 'horizon problem' can be understood.According to big bang model, during its evolution, as the universe is expanding, thermal radiation temperature decreases and matter content increases.As matter content increases, at any stage of evolution, it is possible to have an increasing radius of curvature.For the current case,   and there is no scope for 'causal disconnection' of distant visible matter.

Cosmic inflation
With our model, without considering 'inflation' concepts, starting from the Planck scale, it is possible to have a current cosmic radius of 14.772 Gpc and it is consistent with current observations of 14.25 Gpc.Our estimated cosmic age corresponding to 2.7 K is around 21.66 billion years whereas big bang model estimation is 13.8 billion years.At lower time scales, our estimated cosmic age corresponding to 3000 K is around 19,614 years whereas big bang model estimation is 3,80,000 years.
Point to be discussed in depth is, with big bang and inflation, after 3,80,000 years of evolution, cosmic temperature is 3000 K where as in our model, without big bang and inflation, after 19,614 years of cosmic evolution, temperature is 3000K.From this, it is very clear to say that, compared to big bang and inflation, in our model temperature drop is faster in the beginning and slower in the later stages.This can be considered as a hint for the observed large scale 'Isotropic' nature of CMBR.

Cosmic acceleration and expansion velocity
Based on this expression, for the Planck scale,   From figure 2, it is very clear that, right from the beginning of cosmic evolution, cosmic expansion velocity seems to have an increasing trend.To some extent, this can be compared with currently believed cosmic acceleration concept [10][11][12][13].Interesting point to be noted is that, expansion velocity seems to depend on      This can be compared with other modern studies [5][6][7][8][9][10][11][12][13].Here, interesting point to be noted is that, cosmic angular velocity decreases with decreasing cosmic temperature and decreasing Hubble parameter.The first experimental evidence of the Universe rotation was done by Birch [5], evidently.According to Birch, there appears to be strong evidence that the Universe is anisotropic on a large scale, producing position angle offsets in the polarization and brightness distributions of radio sources.These can probably be explained on the basis of a rotation of the Universe with an angular velocity of approximately 13 10 rad/year.

About dark matter
Considering the very nature of Dark matter, new studies suggest that, a) Dark matter can be eliminated with emerging gravity concept [7].b) Dark matter can be considered as a Bose-Einstein condensate [8]. 3) Dark matter distribution can be understood through the distribution of intracluster light [9].3) Evidence for considering dark matter as a characteristic weakly interacting massive particle (WIMP) is geeting ruled out [23].4) In this critical situation, our proposal of considering dark matter as a kind of 'galactic foam' can be given some consideration.With further study, mystery of 'dark matter density ratio' can be explored with respect to different theoretically extended ideas of general theory of relativity or quantum cosmology.

Cosmic anisotropy
According to Shamik Ghosh et al [24] -The tantalizing possibility that the cosmological principle may be violated is indicated by many observations.The most prominent of these effects is the so-called Virgo alignment, which refers to a wide range of phenomena indicating a preferred direction pointing towards Virgo.The Square Kilometer Array has the capability to convincingly test several of these effects.These include the dipole anisotropy in radio polarization angles, the dipole in the number counts and sky brightness and in the polarized number counts and polarized flux.These observations may indicate that we need to go beyond the standard Big Bang cosmology.Alternatively they may be explained by preinflationary anisotropic and/or inhomogeneous modes.In either case, confirmation of this alignment effect is likely to revolutionize cosmology.

Conclusions
We would like appeal that, proposed decreasing trend of angular velocity, increasing trend of expanding speed (without dark energy), plotted graphs for understanding the smooth decreasing trend of density ratios of dark matter and ordinary matter, estimated noninflationary cosmic radius of 14.772 Gpc, early stage fast cooling and later stage slow cooling etc. seem to strengthen our proposed assumptions and semi empirical relations.With further study, big bang nucleosynthesis, inflation and cosmic time scales can be reviewed with respect to accelerating and rotating 'Planck-Hubble' universe.


Hubble parameter and pl H  Planck scale Hubble parameter.2) Ratio of ordinary matter density to critical density.4) Ratio of dark matter density to critical density.5)t  Cosmic angular velocity and pl   Planck scale angular velocity.6) Cosmic expansion velocity from and about the baby universe.


Total matter content = Total mass of evolving Planck ball.10) t R  Cosmic radius associated with t M = Radius of evolving Planck ball.11) t T  Cosmic temperature.12) t   Ratio of Hubble parameter to angular velocity. 13)  g t d  Galactic distance from and about the baby universe.Galactic receding speed from and about the baby universe.

( 3 )
Assumption 3 resembles Schwarzschild radius relation with denominator having two velocitiesc refers to initial expansion velocity and   exp t V time dependent increasing expansion velocity.(4) Assumptions 2 and 3 help in connecting cosmic expansion velocity and total matter density.(5) Assumption 4 may help in studying the nature of dark matter.


in view and guessing that, there exists   OM pl  and   DM pl  at Planck scale, we propose the following very simple 'model' relation.With further study, After 21.66 billion years of cosmic expansion, increment in expansion velocity seems to be     pl

Figure 2 :
Figure 2: Increasing trend of cosmic expansion velocity

Table 1 :
Current and Planck scale cosmic physical parameters

Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 11 March 2019 Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 11 March 2019 doi:10.20944/preprints201903.0117.v1
By considering a decreasing trend of ordinary matter and dark matter density, starting from the Planck scale, it is possible to get an expression for cosmic expansion velocity.It can be expressed as follows.