Consequences of energy conservation violation: late time solutions of $$\Lambda (\mathsf{T}) \mathsf{CDM}$$ Λ ( T ) CDM subclass of $$f(\mathsf{R},\mathsf{T})$$ f ( R , T ) gravity using dynamical system approach

Abstract

Very recently, Josset and Perez (Phys. Rev. Lett. 118:021102, 2017) have shown that a violation of the energymomentum tensor (EMT) could result in an accelerated expansion state via the appearance of an effective cosmological constant, in the context of unimodular gravity. Inspired by this outcome, in this paper we investigate cosmological consequences of a violation of the EMT conservation in a particular class of f (R, T) gravity when only the pressureless fluid is present. In this respect, we focus on the late time solutions of models of the type f (R, T) = R + β (−T). As the first task, we study the solutions when the conservation of EMT is respected, and then we proceed with those in which violation occurs. We have found, provided that the EMT conservation is violated, that there generally exist two accelerated expansion solutions of which the stability properties depend on the underlying model. More exactly, we obtain a dark energy solution for which the effective equation of state depends on the model parameters and a de Sitter solution. We present a method to parametrize the (−T) function, which is useful in a dynamical system approach and has been employed in the model. Also, we discuss the cosmological solutions for models with (−T) = 8π G(−T) α in the presence of ultra-relativistic matter.

Cosmic acceleration in a dust only universe via energy-momentum powered gravity

“…In the context of late-time acceleration, the violation of energy conservation is not uncommon in the literature [49,50].…”

Late-time cosmological evolution of a general class of $$f(\mathsf{R},\mathsf{T})$$ f ( R , T ) gravity with minimal curvature-matter coupling

“…The application of this approach to explain the late time cosmological acceleration has been introduced in [54] in the framework of f (R) gravity models. It has also been used in f (R, T) = R + α √ T as the only case which respects the conservation of EMT [20] and within the framework of f (R, T) = R + αΛ(T) gravity [31], to extract cosmological solutions. Therefore, the current study may be regarded as an attempt to complete the previous in-vestigations on the cosmological late time behavior of the minimally coupled f (R, T) gravity models.…”

“…A particular case has occurred; the coordinates of the DE fixed point and its eigenvalues (see the results given in (58)) are singular for n = −3/2. In [31], we have discussed in detail the cosmological behavior of this case by algebraic treatments and have shown that in this case the late time solution corresponds to a de Sitter era. As a final remark, we point out that, from 2015 Planck data [4] which has determined the present value of the EoS of DE as −1.051 < w (DE) 0 < −0.961, we may conclude that power law models can be admissible only for m → 0 + and −1.025 < n < −0.980 which corresponds to −0.024 < α < 0.02.…”

Bouncing cosmological solutions from $$f(\mathsf{R,T})$$ f ( R , T ) gravity

“…Equation 14tells us that the conservation of EMT is not generally respected in f (R, T) gravity theories. There is Only a narrow class of solutions for which the conservation of energy is still preserved [137]. In this work we consider a specific class of models for which the Lagrangian is written as a minimal coupling between the Ricci curvature scalar and a function of trace of EMT, i.e.,…”

“…In the present work we study the existence of the bouncing solutions in the context of f (R, T) gravity. These type of theories have been firstly introduced in [125] and later, their different aspects have been carefully studied and analyzed in [126][127][128][129][130][131][132][133][134][135][136][137][138][139][140][141][142][143][144]. In the current work we use an effective approach that we have introduced previously in [145].…”