Cosmic and Thermodynamic Aspects of $f(R,A)$ Gravity

In this study, we explore the recently proposed $f(R,A)$ gravity, a novel extension of modified gravity theories, where R represents the Ricci scalar and A denotes the anticurvature scalar. The addition of anticurvature term might play a role in softening or avoiding singularities, offering smoother transitions in regions of high curvature, such as near black holes or during cosmic inflation [Amendola, et al. (2020)]. We also incorporate well-established cosmological bouncing scenarios, including the symmetric bounce, oscillatory bounce, matter bounce, little rip, and super bounce, to examine their implications within the framework of underlying gravity theory. In this context, we investigate the some cosmic and thermodynamics aspects for flat FRW universe. We analyze the effective equation of state parameter ωeff, which exhibits a transition from quintessence to phantom regimes across different bouncing cosmologies. The stability of the models is examined through the squared speed of sound parameter vₛ², confirming stability in certain bouncing scenarios. The validity of the generalized second law of thermodynamics is verified by ensuring the positivity of total entropy production Ṡₜₒₜ. Additionally, the ωeff-ω'eff plane exhibits the thawing as well as the freezing regions. Our findings demonstrate that the chosen bouncing models provide viable cosmic and thermodynamic behavior, supporting their relevance in modified gravity theories.