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In the present paper, we observationally constrain scalar field assisted f ( G ) gravity with f ( G ) = f 0 G β , at both the background and perturbation levels using Type Ia supernovae from the Pantheon Plus (PP) sample, cosmic chronometer (CC) data, redshift space distortion measurements (RSD) and the recent Baryon Acoustic Oscillation (BAO) measurements released by DESI. For the analysis, we consider three combinations of datasets: (i) PP + CC, ii) CC+DESI BAO and (iii) CC + RSD. In each case, we determine the best-fit parameters by numerically solving the modified Friedmann and perturbation equations. This is achieved through Markov Chain Monte Carlo (MCMC) simulations. To assess the statistical significance of the scalar field assisted f ( G ) model, we employ the Akaike Information Criterion (AIC), Deviance information criterion (DIC) and the Bayesian Information Criterion (BIC), as well as their relative differences Δ AIC , Δ DIC and Δ BIC . It can be observed that GR is recovered for m = 0 , β = 1 . After constraining the considered f ( G ) models using different data sets, the best fit parameters were obtained, such as Ω m = 0.2566 ± 0.0551 and H 0 = 69.1315 ± 1.6443 at the background level and H 0 = 69.6939 ± 1.6851 and σ 8 = 0.8271 ± 0.2787 for the perturbation level, which may potentially alleviate both Hubble and σ 8 tensions. Overall, our results provide strong evidence that the scalar field assisted f ( G ) gravity framework can serve as a viable alternative to ΛCDM in describing the dynamics of the universe without invoking the dark energy hypothesis.
Dhankar et al. (Sat,) studied this question.