Universe with Time Dependent Deceleration Parameter and Λ Term in General Relativity

Abstract

A new class of exact solutions of Einstein's field equations with perfect fluid for an LRS Bianchi type-I spacetime is obtained by using a time dependent deceleration parameter. We have obtained a general solution of the field equations from which three models of the universe are derived: exponential, polynomial and sinusoidal form respectively. The behaviour of these models of the universe are also discussed in the frame of reference of recent supernovae Ia observations.

A Generalized Solution of Bianchi Type-V Models with Time-Dependent G and Λ

“…It is clear that Equations (25), (38) and (39) are totally dependent on the value of a, which is yet to be determined. To complete the solution process, we substitute Equation (25) into Equation (23) so thatä…”

Plane symmetric inhomogeneous perfect fluid universe with electromagnetic field in Lyra geometry

“…On the other hand, Beesham (1988), Singh and Singh (1991a, 1991b, 1992, 1993, Singh and Desikan (1997) have studied FRW, Bianchi-type I, III, Kantowaski-Sachs spacetimes and obtained a new class of cosmological models with time dependent displacement field based on Lyra's geometry. In recent years, Pradhan and Vishwakarma (2004), Pradhan et al (2003Pradhan et al ( , 2005Pradhan et al ( , 2006Pradhan et al ( , 2007, Casama et al (2006), Rahaman et al (2005aRahaman et al ( , 2005b, Bali and Chandani (2008), Kumar and Singh (2008), Singh (2008) and Rao et al (2008) have studied cosmological models based on Lyra's geometry in various contexts.…”

A new class of bulk viscous universe with time dependent deceleration parameter and Λ-term

“…These models can be used to analyze aspects of the physical Universe which pertain to or which may be affected by anisotropy in the rate of expansion, for example, the cosmic microwave background radiation, nucleosynthesis in the early universe, and the question of the isotropization of the universe itself (MacCallum 1979). For simplification and description of the large scale behaviour of the actual universe, locally rotationally symmetric [henceforth referred as LRS] Bianchi I spacetime have widely studied (Hajj-Boutros and Sfeila 1987;Ram 1989;Mazumder 1994;Pradhan et al 2001aPradhan et al , 2001bPradhan and Vishwakarma 2000, 2004Chakrabarty and Pradhan 2001;Mohanty et al 2003). When the Bianchi I spacetime expands equally in two spatial directions it is called locally rotationally symmetric.…”

“…It is worth observing that most of the well-known models of Einstein's theory and Brans-Deke theory with curvature parameter k = 0, including inflationary models, are models with constant deceleration parameter. In earlier literature cosmological models with a constant deceleration parameter have been studied by Berman (1983), Gomide (1988), Johri andDesikan (1994), Singh and Desikan (1997), Maharaj and Naidoo (1993), Pradhan et al (2001b), Pradhan and Aotemashi (2002) and many others. But redshift magnitude test has had a chequered history.…”

“…Recently Pradhan and Otarod (2006) have studied the universe with time dependent deceleration parameter and -term in presence of perfect fluid. Motivated with the situation discussed above, in this paper we can focus upon the problem of establishing a formalism to study the relativistic evolution for a time dependent deceleration parameter in an expanding universe.…”