Cosmological and Solar System Consequences of f(R,T) Gravity Models

Abstract: To find more deliberate f(R,T) cosmological solutions, we proceed our previous paper further by studying some new aspects of the considered models via investigation of some new cosmological parameters/quantities to attain the most acceptable cosmological results. Our investigations are performed by applying the dynamical system approach. We obtain the cosmological parameters/quantities in terms of some defined dimensionless parameters that are used in constructing the dynamical equations of motion. The investigated parameters/quantities are the evolution of the Hubble parameter and its inverse, the "weight function", the ratio of the matter density to the dark energy density and its time variation, the deceleration, the jerk and the snap parameters, and the equation-of-state parameter of the dark energy. We numerically examine these quantities for two general models $R+\alpha R^{-n}+\sqrt{-T}$ and $R\log{[\alpha R]}^{q}+\sqrt{-T}$. All considered models have some inconsistent quantities (with respect to the available observational data), except the model with n=-0.9 which has more consistent quantities than the other ones. By considering the ratio of the matter density to the dark energy density, we find that the coincidence problem does~not refer to a unique cosmological event, rather, this coincidence also occurred in the early universe. We also present the cosmological solutions for an interesting model $R+c_{1}\sqrt{-T}$ in the non--flat FLRW metric. We show that this model has an attractor solution for the late times, though with $w^{(\textrm{DE})}=-1/2$. This model indicates that the spatial curvature density parameter gets negligible values until the present era, in which it acquires the values of the order $10^{-4}$ or $10^{-3}$. As the second part of this work, we consider the weak-field [It continues ...]

An Overview of the Cosmological and Solar System Consequences of $f(R,T)$ Gravity Models

The paper "Cosmological and Solar System Consequences of $f(R,T)$ Gravity Models" by Hamid Shabani and Mehrdad Farhoudi presents an analytical exploration of $f(R,T)$ gravity theories, which extend the traditional $f(R)$ gravity models by incorporating the trace of the energy-momentum tensor (T) alongside the Ricci scalar (R). This extension aims to address the enigmatic nature of dark energy and dark matter while ensuring compatibility with observed cosmic acceleration.

Key Objectives and Methodology

The primary focus is on acquiring viable cosmological models within the $f(R,T)$ framework and evaluating their implications through the dynamical system approach. The paper examines several cosmological parameters such as the Hubble, deceleration, jerk, and snap parameters, alongside the ratio of matter to dark energy density, to identify the most consistent models with observational data. Two specific models are scrutinized: $R+\alpha R^{-n}+\sqrt{-T}$ and $R\log{[\alpha R]}^{q}+\sqrt{-T}$, with particular interest in the model where $n=-0.9$ for its pronounced alignment with empirical observations.

Significant Findings

• Cosmological Consistency: The model with $n=-0.9$ from the $R+\alpha R^{-n}+\sqrt{-T}$ class shows a better match with cosmological observations. It sustains a consistent sequence of eras: radiation-dominated, matter-dominated, and an accelerated expansion phase.
• Coincidence Problem Insights: The paper highlights a novel perspective that the ratio of matter to dark energy, considered a mystery in the current epoch, has a conceivable explanation by noting that a similar ratio was prevalent in the universe's early stage too.
• PPN Parameters: For the weak-field limit of these models in a solar system context, the paper provides a parametrized post-Newtonian (PPN) framework showing that the theory can admit values within experimental measurement ranges. This underscores the potential compatibility of $f(R,T)$ gravity with solar system experiments, differing from some $f(R)$ models that struggle with such constraints.

Implications for Cosmology and Solar System Dynamics

The findings assert the relevance of $f(R,T)$ models in generating cosmological solutions that cater to the unexplained phenomena attributed to dark energy and dark matter. By retaining terms dependent on the trace of the energy-momentum tensor, these models potentially introduce gravitational effects that are absent in standard $f(R)$ models, offering new pathways for resolving dark fluid dynamics.

The investigation into the PPN parameters further marks a significant development, reflecting that modified theories of gravity can be consistent with precision solar system tests, opening doors for these theories to be explored further in both cosmological and astrophysical settings.

Future Directions

While this research establishes foundational steps in understanding the viability of $f(R,T)$ gravity, future efforts might concentrate on performing more extensive numerical simulations and observational data analysis. Enhanced precision in estimating cosmological parameters would ascertain the robustness of $f(R,T)$ predictions over continued large-scale sky surveys and could potentially verify the nature of dark energy and its linkage to modified gravity theories.

In summation, this paper presents a compelling investigation into extended gravity models, demonstrating their prowess and limitations within both cosmic scale dynamics and localized gravitational systems. It paves the way for subsequent explorations in the quest for a unified theory accommodating the complex interplay of gravitation, geometry, and cosmic evolution.