Constraining $$\boldsymbol{f(R,T)}$$ Gravity from the Dark Energy Density Parameter $$\boldsymbol{\Omega}_{\boldsymbol{\
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Constraining f (R, T ) Gravity from the Dark Energy Density Parameter ΩΛ Snehasish Bhattacharjee1* and P. K. Sahoo2** 1
2
Department of Astronomy, Osmania University, Hyderabad-500007, India Department of Mathematics, Birla Institute of Technology and Science-Pilani, Hyderabad Campus, Hyderabad-500078, India Received December 19, 2019; revised May 23, 2020; accepted May 25, 2020
Abstract—f (R, T ) gravity is a widely used extended theory of gravity introduced by Harko et al., which is a straightforward generalization of f (R) gravity. The action in this extended theory of gravity incorporates well-motivated functional forms of the Ricci scalar R and the trace of the energy momentum tensor T . The present manuscript aims at constraining the most widely used f (R, T ) gravity model of the form f (R + 2λT ) to understand its coherency and applicability in cosmology. We communicate here a novel method to find a lower bound on the model parameter λ −1.9 × 10−8 through the equation relating the cosmological constant (Λ) and the critical density of the universe (ρcr ). DOI: 10.1134/S0202289320030032
1. INTRODUCTION The cosmological constant (Λ) problem is one of the major unsolved mysteries concerned with the dissimilarity between the tiny observed value of the cosmological constant and the extremely large value of zero point energy. Based on the Planck energy cutoff along with other factors, the disaccord is as high as 120 orders of magnitude [1], a predicament often quoted as [2] “the worst theoretical prediction in the history of physics.” After the discovery of the expansion of the universe by E. Hubble in 1929 [3], it was expected that the rate of expansion must be slowing down owing to the attractive nature of gravity. Nonetheless, measurements of the intrinsic brightness of distant Type Ia supernovae [4, 5] showed that the expansion is in fact accelerating. This mysterious component which fuels the expansion at an ever increasing rate accounts for nearly 70% of the energy budget of the universe and is termed Dark Energy (DE). There are three different kinds of DE models. These are: quintessence (−1 < ω < 0), phantom energy (ω < −1) and the cosmological constant (ω = −1), where ω represents the equation-of-state (EoS) parameter. Current observations suggest ω ≈ −1 [6]. Due to the lack of any observational evidence for the existence of any DE candidates (for a detailed reference of various DE candidates, one may refer * **
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to [7]), researchers were inspired to modify the geometric sector of the field equations, where the Ricci scalar R in the action is replaced by various generic functions of f (R) [8], f (T ) [9], where T is the torsion scalar, f (R, T ) [10] where T is the trace of the energymomentum tensor, and f (G) [11], where G is the Gauss–Bonnet invariant. Due to some fascinating features of f (R, T ) gravity and robustness is solving the cosmological issues, it is often employed in the literature [12]. f (R, T ) gravi
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