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

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) f ( R , L m ) gravity model, formulated as f(R, Lₘ) = λ R + β Lₘ^α + η f ( R , L m ) = λ R + β L m α + η . To study the cosmological viability of the model, we employed the latest cosmic measurement datasets: (i) 57 observational Hubble parameter data points (); (ii) 1048 distance moduli data points (); (iii) a combined dataset (); and large scale structure datasets, including (iv) 14 growth rate data points (); and (v) 30 redshift space distortion data points ( σ ₈ σ 8 ). These datasets facilitated the constraint of the f(R, Lₘ) f ( R , L m ) -gravity model via MCMC simulations, followed by a comparative analysis with the Λ CDM model. A comprehensive statistical analysis has been conducted to evaluate the f(R, Lₘ) f ( R , L m ) -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 ₘ = 0.242+0.016-0.032 Ω m = 0 . 242 - 0.032 + 0.016 , α = 1.15+0.20-0.20 α = 1 . 15 - 0.20 + 0.20 , β = 1.12+0.13-0.30 β = 1 . 12 - 0.30 + 0.13 , λ = 0.72+0.30-0.13 λ = 0 . 72 - 0.13 + 0.30 and γ = 0.555± 0.014 γ = 0.555 ± 0.014 using -data and ₘ = 0.284+0.035-0.049 Ω m = 0 . 284 - 0.049 + 0.035 , σ ₈ = 0.799+0.045-0.086 σ 8 = 0 . 799 - 0.086 + 0.045 , α = 0.766+0.026-0.064 α = 0 . 766 - 0.064 + 0.026 , β = 1.08+0.40-0.16 β = 1 . 08 - 0.16 + 0.40 , and λ = 0.279+0.078-0.11 λ = 0 . 279 - 0.11 + 0.078 using σ ₈ σ 8 -data at the 1σ 1 σ and 2σ 2 σ confidence levels, respectively, with the model showing substantial observational support based on Δ AIC values but less observational support based on the Δ BIC values on Jeffreys’ statistical criteria. On the other hand, from the joint analysis of the data, we obtain α = 1.091+0.035-0.042 α = 1 . 091 - 0.042 + 0.035 , β = 1.237+ 0.056-0.16 β = 1 . 237 - 0.16 + 0.056 and λ = 0.630+0.031-0.050 λ = 0 . 630 - 0.050 + 0.031 with the Jeffreys’ scale statistical criteria showing the f(R, Lₘ) f ( R , L m ) model having substantial support when using data, less observational support with the joint analysis , and rejected using data, compared with Λ CDM at the background level.