## Exploring Cosmological Features of $mathcal{F}(R,L_m,T)$ Theory

arXiv:2404.03682v1 Announce Type: new

Abstract: The present work is devoted to explore some interesting cosmological features of a newly proposed theory of gravity namely $mathcal{F}(R,L_m,T)$ theory, where $R$ and $T$ represent the Ricci scalar and trace of energy momentum-tensor, respectively. Firstly, a non-equilibrium thermodynamical description is considered on the apparent horizon of the Friedmann’s cosmos. The Friedmann equations are demonstrated to be equivalent to the first law of thermodynamics, i.e., ${T_{Ah}dvarepsilon_{h}^prime+T_{Ah}d_{i}varepsilon_{h}^prime=-dhat{E}+hat{W}dV}$, where ${d_{i}varepsilon_{h}^prime}$ refers to entropy production term. We also formulate the constraint for validity of generalized second law of thermodynamics and check it for some simple well-known forms of generic function $mathcal{F}(R,L_m,T)$. Next, we develop the energy bounds for this framework and constraint the free variables by finding the validity regions for NEC and WEC. Further, we reconstruct some interesting cosmological solutions namely power law, $Lambda$CDM and de Sitter models in this theory. The reconstructed solutions are then examined by checking the validity of GSLT and energy bounds. Lastly, we analyze the stability of all reconstructed solutions by introducing suitable perturbations in the field equations. It is concluded that obtained solutions are stable and cosmologically viable.

Recently, there has been a proposal for a new theory of gravity called $mathcal{F}(R,L_m,T)$ theory. In this article, we aim to explore the various cosmological features of this theory and analyze its implications. The following conclusions can be drawn from our study:

## Non-equilibrium thermodynamics and the Friedmann equations

In our investigation, we have considered a non-equilibrium thermodynamical description on the apparent horizon of the Friedmann’s cosmos. Surprisingly, we have discovered that the Friedmann equations can be represented as the first law of thermodynamics. This equivalence is expressed as ${T_{Ah}dvarepsilon_{h}^prime+T_{Ah}d_{i}varepsilon_{h}^prime=-dhat{E}+hat{W}dV}$, where ${d_{i}varepsilon_{h}^prime}$ denotes the entropy production term.

## Validity of generalized second law of thermodynamics

We have also formulated a constraint to determine the validity of the generalized second law of thermodynamics in the context of the $mathcal{F}(R,L_m,T)$ theory. By applying this constraint to some well-known forms of the generic function $mathcal{F}(R,L_m,T)$, we have been able to verify its validity.

## Energy bounds and constraints

Next, we have developed energy bounds for the $mathcal{F}(R,L_m,T)$ theory and constrained the free variables by identifying regions where the null energy condition (NEC) and weak energy condition (WEC) hold. This analysis provides important insights into the behavior of the theory.

## Reconstruction of cosmological solutions

We have reconstructed several interesting cosmological solutions, including power law, $Lambda$CDM, and de Sitter models, within the framework of $mathcal{F}(R,L_m,T)$ theory. These reconstructed solutions have been carefully examined to ensure the validity of the generalized second law of thermodynamics and energy bounds.

## Stability analysis of reconstructed solutions

Finally, we have analyzed the stability of all the reconstructed solutions by introducing suitable perturbations in the field equations. Our findings indicate that the obtained solutions are stable and cosmologically viable.

**Roadmap for readers:**

- Introduction to $mathcal{F}(R,L_m,T)$ theory and its cosmological features
- Explanation of the equivalence between the Friedmann equations and the first law of thermodynamics
- Constraint formulation for the validity of the generalized second law of thermodynamics
- Analysis of energy bounds and constraints, including NEC and WEC
- Reconstruction of cosmological solutions in $mathcal{F}(R,L_m,T)$ theory
- Evaluation of the validity of the generalized second law of thermodynamics and energy bounds for the reconstructed solutions
- Stability analysis of the reconstructed solutions through perturbations
- Conclusion and implications of the study

**Potential challenges:**

- Understanding the mathematical formulation of the $mathcal{F}(R,L_m,T)$ theory
- Navigating through the thermodynamical concepts and their implications in cosmology
- Grasping the reconstruction process of cosmological solutions within the framework of $mathcal{F}(R,L_m,T)$ theory
- Applying perturbation analysis to evaluate the stability of the solutions

**Potential opportunities:**

- Exploring a new theory of gravity and its implications for cosmology
- Gaining a deeper understanding of the connection between thermodynamics and gravitational theories
- Deriving and examining new cosmological solutions beyond the standard models
- Contributing to the stability analysis of cosmological solutions in alternative theories of gravity