Abstract
In this work we study classical bouncing solutions in the context of f(mathsf{R},mathsf{T})=mathsf{R}+h(mathsf{T}) gravity in a flat FLRW background using a perfect fluid as the only matter content. Our investigation is based on introducing an effective fluid through defining effective energy density and pressure; we call this reformulation as the “effective picture”. These definitions have been already introduced to study the energy conditions in f(mathsf{R},mathsf{T}) gravity. We examine various models to which different effective equations of state, corresponding to different h(mathsf{T}) functions, can be attributed. It is also discussed that one can link between an assumed f(mathsf{R},mathsf{T}) model in the effective picture and the theories with generalized equation of state (EoS). We obtain cosmological scenarios exhibiting a nonsingular bounce before and after which the Universe lives within a de-Sitter phase. We then proceed to find general solutions for matter bounce and investigate their properties. We show that the properties of bouncing solution in the effective picture of f(mathsf{R},mathsf{T}) gravity are as follows: for a specific form of the f(mathsf{R,T}) function, these solutions are without any future singularities. Moreover, stability analysis of the nonsingular solutions through matter density perturbations revealed that except two of the models, the parameters of scalar-type perturbations for the other ones have a slight transient fluctuation around the bounce point and damp to zero or a finite value at late times. Hence these bouncing solutions are stable against scalar-type perturbations. It is possible that all energy conditions be respected by the real perfect fluid, however, the null and the strong energy conditions can be violated by the effective fluid near the bounce event. These solutions always correspond to a maximum in the real matter energy density and a vanishing minimum in the effective density. The effective pressure varies between negative values and may show either a minimum or a maximum.
Highlights
Today, the standard cosmological model (SCM) or the bigbang cosmology has become the most acceptable model which encompasses our knowledge of the Universe as a whole
It accounts for the expansion of the Universe (Hubble law), the black body nature of cosmic microwave background (CMB) within the framework of the SCM can be understood and the predictions of light-element abundances which were produced during the nucleosynthesis
In the present work we studied classical bouncing behavior of the Universe in the framework of f (R, T) = R + h(T) gravity theories
Summary
The standard cosmological model (SCM) or the bigbang cosmology has become the most acceptable model which encompasses our knowledge of the Universe as a whole. In the present section we review the field equations of f (R, T) gravity theories and rewrite them in terms of a conserved effective fluid This reformulation would allow us to better understand the properties of bouncing solutions as well as classifying them. Solving the differential equation leads to an h(T) function that conveys the specified property/relation In this way we can obtain a minimal f (R, T) model based on the conditions on energy density and pressure profiles of the effective fluid, instead of choosing the functionality of f (R, T) based on ad hoc mathematical terms. Let us begin with bouncing solutions which are obtained by assuming an effective fluid with constant pressure We show that these type of models lead to a de-Sitter era at late times [145]. A general solution of Eq (27) is obtained as aA (t )
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