The Quasi Steady State Cosmology in a Radiation Dominated Phase

The Quasi Steady State Cosmology in a Radiation Dominated Phase Raj Bali* Department of Mathematics, University of Rajasthan, Jaipur-302004, India *Corresponding Author: Email: rbalijpr@gmail.com Abstract: Analytical solutions for radiation dominated phase of Quasi Steady State Cosmology in Friedmann-Robertson-Walkar models are obtained. We find that matter density is positive in all the cases (k = 0,-1,1). The nature of Hubble parameter (H) in [0,2] is discussed. The deceleration parameter (q) is marginally less than zero indicating accelerating universe. The scale factor (S) is graphically shown with time. The model represents oscillating universe between the above mentioned limits. Because of bounce in QSSC, the maximum density phase is still matter dominated. The models represent singularity free model. We also find that the models have event horizon i.e. no observer beyond the proper distance rH can communicate each other in FRW mdels for radiation dominated phase in the frame work of QSSC. The FRW models are special classes of Bianchi type I, V, IX space-times with zero, negative and positive curvatures respectively. Initially i.e. at  = 0, the model represents steady model. We have tried to show how a good fit can be obtained to the observations in the framework of QSSC during radiation dominated phase.


Introduction
In the early stages of the universe, the radiation was the dominant influence on the expansion of the universe because most of the energy was in the form of radiation.Thus examination of the radiation dominated expansion is essential for understanding the early universe.The main motivation to introduce QSSC is to have a universe without a singularity in which matter is created in an explosive way but physically understood (Narlikar, [1]).Any alternative cosmology must be more successful in explaining observations.In this cosmology the cosmological constant () is taken negative because we always get an oscillating universe whatever the curvature parameter.To understand the radiation dominated phase of universe, and QSSC, it is interesting to know about the Microwave Background Radiation (CMBR) and abundances of light nuclei in early universe.Between 1964 and1965, the steady state model received two near-fatal blows.Both came from considerations of issues of the early universe, (i) the discovery of microwave background (ii) the abundances of light nuclei.We discuss these briefly in order.
The cosmic microwave background is considered to be left over radiation from the big bang or the time when the universe began (Space.com).As mentioned by Narlikar [1], the case of radiation dominated universe differs from the matter dominated one where the pressure p of radiation makes a significant contribution to gravitational attraction and in this case, we have  = 3p (the speed of light is considered as c = 1 in gravitational unit).However, the turning point for cosmology came with the discovery of the microwave background radiation (Penzias and Wilson [2]).It confirmed the early universe scenario and taken together with the extended validity of Hubble's law.Also according to NASA observations, it is uniform temperature with small fluctuations visible with precise telescopes.Studying these fluctuations, cosmologists can learn about the origin and large scale structure of universe and can know how the early universe was formed.
The Gamow's ideas [3] on primordial nucleosynthesis had turned out to work for light nuclei only, producing mainly helium and small quantities of deuterium in stars and a few other light nuclei.For the majority of elements, stars provided the right setting for successive nucleosynthesis.This had led most astronomers to believe that stellar nucleosynthesis was the key process for all elements, since even helium was seen to be produced in stars.Apart from helium, the discovery of deuterium made the primordial version more credible since there was no known process for making even tiny quantities of deuterium in stars.So the steady state theory, which had no early hot era to make such light nuclei, faced difficulties in explaining their observed abundances.The case for the hot big bang become even stronger due to the discovery of microwave background.The steady state model had no natural process to maintain a radiation background at ~ 3K and it never quite recovered from these two blows.Nevertheless, the model made a comeback in a modified form in the 1990s.
In 1993, Hoyle, Burbidge and Narlikar introduced a new cosmology known as Quasi Steady State Cosmology (QSSC) which drew considerable interest on the earlier steady state cosmology.It also allows the possibility of evolution of universe on shorter time scale and arises from the consideration of Hoyle-Narlikar theory [4].Hoyle et al. [4,5] and Burbidge et al. [6] reviewed the progress of QSSC with the intention to bring a viable alternative to the standard hot big bang cosmology (HBBC).The HBBC has two versions: (i) the version in which the universe expands from a singularity in a radiation dominated phase which changes over to matter dominated one (ii) Post 1981 version in which there is a brief description of inflation very early in a radiation dominated phase.The later version was also called inflationary Big Bang Cosmology (IBBC) which was proposed to get rid of some of the conceptual defects of HBBC.While it was partially successful but it had problems of its own as explained by Narlikar and Padmanabhan [7].Using the field equations of QSSC, Sachs et al. [8] obtained the analytical solutions which relate with the observations.Some developments of quasi steady cosmology has been summarized by Narlikar [9].Riess et al. [10] and Perlmutter et al. [11] in their investigations used type Ia supernovae and have shown that the universe is accelerating.This then is a result which was predicted by QSSC and it has been shown by Banerjee et al. [12] that a good fit can be made to the observed data using QSSC.Burbidge [13] has pointed out that the decelerating parameter (q) is negative in quasi steady state cosmology.Thus this observational evidence confirms a real prediction in favour of QSSC.Narlikar et al. [14] have mentioned that cosmological observations support the accelerating models of the universe as driven by a cosmological constant or dark energy.It is also well established that the universe is expanding at an accelerating rate (Hawking and Mlodinow [15], [16], Krauss [17], Bali and Saraf [18,19] Bali and Singh [20].

The Metric and Field Equations
We consider homogeneous and isotropic space-time of Robertson-Walker in the form given by where S(t) is scale factor and k = 0, -1,1.
The modified Einstein's field equations for QSSC is considered in the orm where , is cosmological constant, f > 0 the coupling constant between matter and creation field in conventional unit.the constant  is the square of the reciprocal of the primary Planck particles and  > 0.
For the metric (1), the field equation (2) leads to

Solution of Field Equations
We assume that the universe is dominated by radiation phase.Thus, we have  = 3p which leads to where where  > 0, is constant of integration.Equation (8) leads to

Event Horizon
The coordinate distance to the horizon rH() is the maximum distance a null ray could have travelled at time  starting from the infinite past.Thus, we have In all the cases, we find that the models have event horizon i.e. no observer beyond the proper distance rH can communicate each other in FRW models in QSSC.

Discussion and Conclusion
The scale factor in all the cases (k = 0, 1, −1) is shown graphically which gives the nature of scale factor in QSSC.The deceleration parameter (q) is marginally < 0 which shows that the

For
the proper time  to (−) in the past because of the non-singular nature of the space-time.Now, we have model represents accelerating phase of universe.Thus the observational evidence as investigated by Riess et al. (1998) and Perlmutter et al. (1999) using type Ia supernovae confirms a real Preprints (www.preprints.org)| NOT PEER-REVIEWED | Posted: 19 November 2018 doi:10.20944/preprints201811.0473.v1prediction in favor of QSSC.The Hubble parameter (H) for k = 0, is initially zero at  = 0for k = 1, -1 may be discussed.Thus the models oscillate between these limits.Because of bounce in QSSC, the maximum density phase is still matter dominated.The bouncing universe is consistent with acceleration.Development of QSSC theory indicates that newly created particles have a mass .Such Planck particles are unstable over a time scale 10 -43 s (Hoyle et al. 1993).Presently, we are not in the radiative phase but it is interesting to study the Universe in radiative phase because in early stage of the Universe, most of the energy was in the form of radiation.Thus, examination of radiation dominated expansion is essential for understanding the early universe within QSSC in which matter is created in an explosive way (Narlikar 2012).The bouncing nature is involved in QSSC theory.The models represent singularity free space-times.The matter density () is positive in all cases.The present model initially i.e.  = 0 represents steady state model and at  = 0, ].The model has event horizon i.e. no observer beyond the proper distance rH can communicate each other in FRW models for radiation dominated phase in QSSC.
in creation field cosmology, we have assumed