Nonsingular cosmology with a time-dependent cosmological term

Abstract

The consequences of the cosmological constant snssts of Csrvslho, Lima, sad Wsgs (A 3PH + 37R ) sre investigated in an extension of the nonsingulsr Ozer-Tshs cosmology. The considered model describes a closed singularity-kee universe evolving through successive epochs of pure radiation, matter generation, and radiation and matter. The early phase of the last period is shown to be s concrete realization of the postslngulsrity radiation ers scenario of Freeze, Adams, Prieman, and Mottola. PACS number(s): 98.80. Cq, 98.80.Hw X. INTRODUCTION Carvalho, Lima, and Waga [1] have proposed the cosmological constant phenomenological ansatz where p and p are the cosmic energy density and pressure, respectively, and It the curvature index. Combining Eq. (3) and the differentiated form of Eq.(2) one has the energy (= E = pRs) equation II. NONSINGULAR MODELIn a Robertson-Walker»~averse with a perfect-Suid energy-moment»~tensor, Einstein's equations with a variable A give (n = 3/Sz G) a p=~-+ --A(t), (R) Rz 3(2) -" ('+")-R +R R where P and p are dimensionless numbers of the order of unity (natural units being used) R is the RobertsonWs&er scale factor, and H = R/R is Hubble's constant (an overdot denotes time &i&erentiation). Equation (1), a consequence of simple dimensional arguments consistent with quantum gravity [1], generalizes an earlier form, A oc R, suggested by Ozer and Taha [2] and also by Chen and Wu [3].Although the Ozer-Taha (OT) and Chen-Wu (CW) models postulate the same type of variation for A, the resulting cosmological scenarios are not similar. In one case (OT) one has a nonsingular universe with a cold beginning and an early phase transition, in the other (CW) a singular big-bang scenario. These differences are due to the model's difFerent initial conditions and the assignment of opposite signs to a certain integration constant.Carvslbo, Lima, and Waga [1] studied the modifications introduced by the P term in Eq. (1) on the cosmology of Chen and Wu. In this work we investigate the effect of this term in an extended Ozer-Taha cosmology. Also from Eqs. (1) and (2), I~' pp+ 1-In the radiation-(p = p/3) dominated (RD) universe Eqs. (1) -(3) yield (p g 2, p"= so. 'A, and Ao a constant) [1] g2 + + g~-2+4P 1 -2P (6)1-2P R +a(l -P)A R 4+~ ( 7) = ' P"R +PAR-1-2P For Ao & 0, p ( 1, the singular cosmological model based on these equations was studied by Car~&o, Lima, and Waga [1]. Here we investigate a scenario obtained by requiring Ao (0 and for which the model is nonsingular. For simplicity and physical relevance [4] we take p & 0 (tshing P = 0, Ao ( 0, P = h = 1 reProduces the nonsingular OT [2] model). A»mverse with a nonvanishing mi~~mum scale factor Ro at t = 0 arises Rom Eq. (6) if Ao ( 0, P ( z~, and k ( 2p. Then from Eq. (7), po -o.

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