Cosmic and thermodynamic aspects of f ( R , A ) gravity

Abstract 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 (Amendol et al 2020 Phys. Lett . B 811 135923). 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 some cosmic and thermodynamic aspects of flat FRW universe. We analyze the effective equation of state parameter ω eff , 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 v s 2 , 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 S ̇ tot . Additionally, the ω eff − 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.