Reconstructing cosmic expansion in f(R,G) gravity using a log-periodic deceleration model

Abstract

We study the late-time cosmology in $f(R,G)=R+\alpha R^2+\beta e^{\gamma G}$, using a logarithmic parametrization of the deceleration parameter $q\left(z\right)=q_0+q_{1}sin\left[log(1+z)\right]$. The Hubble parameter $H\left(z\right)$ is reconstructed and model parameters are constrained via MCMC analysis using CC (31), BAO 15+DESI DR2 BAO and Pantheon+SHOES (1701) datasets. Our results yield a Hubble constant in the range $H_0=71.7$–72.8 km/s/Mpc, consistent with late-time observations. The present deceleration parameter is found to be $q_0=-0.484$ to $-0.517$, while the evolution parameter $q_1\approx 1$, indicating increasing acceleration. The transition redshift shifts from $z_{tr}=0.879$ (CC) to 0.744 (CC+BAO+Pantheon+SHOES), supporting a dynamic acceleration phase. The model reproduces early radiation behavior with $\omega (z>>1)\approx 0.33$ and predicts present-day values ${\omega }_0\approx -0.49$. Energy conditions NEC and DEC are satisfied, while SEC is violated at late times. The statefinder parameters $\{r_0,s_0\}=(0.866,0.046)$ lie near the $\Lambda$CDM point. Estimated age of the Universe ranges from 13.01 to 13.59 Gyr. Thermodynamic analysis confirms consistency with the generalized second law. Furthermore, linear perturbation analysis of the energy density and Hubble parameter demonstrates that fluctuations remain bounded across the cosmic timeline, which ensures the dynamical stability of the model. Overall, the framework provides a viable, stable, and observationally consistent description of cosmic acceleration.