Jerk Parameter and Modified Theory

Abstract

The accelerated expansion of the universe during recent times is well known in cosmology, whereas during early times, there was decelerated expansion. The ΛCDM model is consistent with most observations, but there are some issues with it. In addition, the transition from early deceleration to late-time acceleration cannot be explained by general relativity. Hence, it is worthwhile to examine modified gravity theories to explain this transition and to get a better understanding of dark energy. In this work, dark energy in modified f(R,T) gravity is investigated, where R is the Ricci scalar and T is the trace of the energy momentum tensor. Normally, the simplest form of f(R,T) is used, viz., f(R)=R+λT. In this work, the more complicated form f(R,T)=R+RT is investigated in Friedmann–Lemaître–Robertson–Walker spacetime. This form has not been well studied. Since the jerk parameter in general relativity is constant and j=1, in order to have as small a departure from general relativity as possible, the jerk parameter j=1 is also assumed here. This enables the complete solution for the scale factor to be found. One of these forms is used for a complete analysis and is compared with the usually studied form f(R,T)=R+RT. The solution can also be broken down into a power-law form at early times (deceleration) and an exponential form at late times (acceleration), which makes the analysis simpler. Surprisingly, each of these forms is also a solution to the differential equation j=1 (though they are not solutions to the general solution). The energy conditions are also studied, and plots are provided. It is shown that viable models can be obtained without the need for the introduction of a cosmological constant, which reduces to the ΛCDM at late times.