A New Class of Bianchi Type-I Cosmological Models in Scalar-Tensor Theory of Gravitation and Late Time Acceleration

Abstract

A new class of a spatially homogeneous and anisotropic Bianchi type-I cosmological models of the universe for perfect fluid distribution within the framework of scalar-tensor theory of gravitation proposed by Sáez and Ballester (Phys. Lett. 113:467, 1986) is investigated. To prevail the deterministic solutions we choose the different scale factors which yield time-dependent deceleration parameters (DP) representing models which generate a transition of the universe from the early decelerated phase to the recent accelerating phase. Three different physically viable models of the universe are obtained in which their anisotropic solutions may enter to some isotropic inflationary era. The modified Einstein's field equations are solved exactly and the models are found to be in good concordance with recent observations. Some physical and geometric properties of the models are also discussed.

Bianchi I model: an alternative way to model the present-day Universe

“…Given its importance for studying the possible effects of an anisotropy in the early universe on presentday observations, many researchers have investigated the BI model from different perspectives. Examples of these studies are, string theory (Alexeyev et al 2001;Rao et al 2008;Rathore & Mandawat 2009;Bali & Gupta 2010;Rikhvitsky et al 2012), dynamical properties (Salucci & Fabbri 1983;Chimento & Forte 2006;Ellis 2006;Akarsu & Kılınç 2010a,b;Adhav et al 2011;Singh & Chaubey 2012;Appleby & Linder 2012;Mostafapoor & Grøn 2013;Pradhan et al 2013;Singh & Chaubey 2013;Ali & Rahaman 2013;Kohli & Haslam 2013), the singularity problem (Bronnikov et al 2004;Khalatnikov et al 2003;Belinskij et al 1970), the spinor/scalar field (Saha 2001a,b;Fay 2005;Saha & Boyadjiev 2004;Saha 2005Saha , 2006Kucukakca et al 2012;Pradhan et al 2012;Saha 2013;Carloni et al 2013) and perturbations in the early phase of inflation (Gümrükçüoglu & Peloso 2007;Pereira et al 2007;Dong 2010;Bali 2011;Aluri & Jain 2012;Kofman et al 2011). Separately, Maartens et al (1995b) obtain evolution equations by which matter imposes anisotropies on freely propagating CMB radiation, leading to a new model independent way of using anisotropy measurements to limit the deviations of the Universe from a FRW geometry.…”

Anisotropic Bianchi Type-III Dark Energy Model with TimeDependent Deceleration Parameter in Saez-Ballester Theory

“…At = 0, all the spatial scale factors are zero which implies that the derived model has a point-type singularity at = 0 [29]. Equation (22) with the help of equation (18) yields a time-dependent deceleration parameter as = + 2 − 1 (27) We observe that > 0 for < − and < 0 for > − . For ≥ 3 and = 1, our model evolves from decelerating phase to accelerating phase.…”

“…Since the metric (4) is completely characterized by average scale factor therefore we consider following Amirhashchi et al [20], Pradhan et al [21][22][23] and Yadav [24] that average scale factor is an increasing function of time as following: = 1 (22) where and are positive constants.…”

“…So, in general, the DP is not a constant but time variable. Recently, Amirhashchi et al [20], Pradhan et al [21][22][23] and Yadav [24] investigated Bianchi type cosmological models with time-dependent deceleration parameter.…”

“…Motivated by the above works, in the present paper, we have examined an anisotropic Bianchi type-III dark energy model with variable EoS parameter in the framework of Saez-Ballester scalar-tensor theory of gravitation with the help of a variation law of scale factor [20][21][22][23][24] which yields a time-dependent deceleration parameter.…”