First law of thermodynamics and entropy of FLRW universe in modified gravity

Bouncing Cosmology in f(R,G)$f(R,\mathcal {G})$ Gravity with Thermodynamic Analysis

“…Many authors have worked on the f (R, 𝒢) theory of gravity and proposed various dark energy models. [25][26][27][28][29][30][31][32][33][34][35][36] The bouncing cosmology model, rooted in theoretical physics and cosmology, questions the traditional understanding of the universe's origin and evolution. This model suggests that our universe experiences a cycle of expansions and contractions, each ending in a "big bounce", rather than the traditional "big bang" or "big crunch" scenarios proposed by standard cosmology.…”

“…Many authors have worked on the $$ f(R,\mathcal {G})$$ theory of gravity and proposed various dark energy models. [ 25–36 ]…”