The cosmology of f(R, Lm) gravity: constraining the background and perturbed dynamics

Abstract

This paper delves into the late-time accelerated expansion of the universe and the evolution of cosmic structures within the context of a specific f (R, Lm) gravity model, formulated as f (R, Lm) = λR + βLα m + η. To study the cosmological viability of the model, we employed the latest cosmic measurement datasets: (i) 57 observational Hubble parameter data points (OHD); (ii) 1048 distance moduli data points (SNIa); (iii) a combined dataset (OHD+SNIa); and large scale structure datasets, including (iv) 14 growth rate data points (f); and (v) 30 redshift space distortion data points (fσ8). These datasets facilitated the constraint of the f (R, Lm)-gravity model via MCMC simulations, followed by a comparative analysis with the ΛCDM model. A comprehensive statistical analysis has been conducted to evaluate the f (R, Lm)-gravity model's efficacy in explaining both the accelerated expansion of the universe and the growth of cosmic structures. Using large-scale structure data, we find the best-fit values of Ωm = 0.242+0.016 −0.032, α = 1.15+0.20 −0.20, β = 1.12+0.13 −0.30, λ = 0.72+0.30 −0.13 and γ = 0.555 ± 0.014 using f-data and Ωm = 0.284+0.035 −0.049, σ8 = 0.799+0.045 −0.086, α = 0.766+0.026 −0.064, β = 1.08+0.40 −0.16, and λ = 0.279+0.078 −0.11 using fσ8-data at the 1σ and 2σ confidence levels, respectively, with the model showing substantial observational support based on ΔAIC values but less observational support based on the ΔBIC values on Jeffreys' statistical criteria. On the other hand, from the joint analysis of the OHD+SNIa data, we obtain α = 1.091+0.035 −0.042, β = 1.237+0.056 −0.16 and ae-mails: shambel.sahlu@nithecs.ac.za; sahlushambel@gmail.com (corresponding author) be-mail: aaalnadhief@imamu.edu.sa ce-mail: amare.abebe@nithecs.ac.za λ = 0.630+0.031 −0.050 with the Jeffreys' scale statistical criteria showing the f (R, Lm) model having substantial support when using OHD data, less observational support with the joint analysis OHD+SNIa, and rejected using SNIa data, compared with ΛCDM at the background level.