Inflation and cosmological evolution with $F(R,G)$ gravity theory

In the last decade Planck PR4 data together with ground-based experimental data such as, BK18, BAO and CMB lensing, tightened constraint of the tensor to scalar ratio, starting form $r < 0.14$ to $r < 0.032$, while the spectral index lies within the range $0.9631 < n_s < 0.9705$. Viability of modified gravity theories, proposed as alternatives to the dark-energy issue, should therefore be tested in the light of such new result. Here, we explore $F(R,G)$ gravity theory in regard of the early universe and have shown that, it is not compatible with newly released constraints on $r$ and $n_s$ simultaneously. Further, it also fails to produce a feasible radiation dominated era. It therefore questions the justification of using the model for resolving the cosmic puzzle.