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) f (R, L m) gravity model, formulated as f (R, Lₘ) = R + Lₘ^ + 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 (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, = 1. 15^+0. 20-₀. ₂₀ α = 1. 15 - 0. 20 + 0. 20, = 1. 12^+0. 13-₀. ₃₀ β = 1. 12 - 0. 30 + 0. 13, = 0. 72^+0. 30-₀. ₁₃ λ = 0. 72 - 0. 13 + 0. 30 and = 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, ₈ = 0. 799^+0. 045-₀. ₀₈₆ σ 8 = 0. 799 - 0. 086 + 0. 045, = 0. 766^+0. 026-₀. ₀₆₄ α = 0. 766 - 0. 064 + 0. 026, = 1. 08^+0. 40-₀. ₁₆ β = 1. 08 - 0. 16 + 0. 40, and = 0. 279^+0. 078-₀. ₁₁ λ = 0. 279 - 0. 11 + 0. 078 using ₈ σ 8 -data at the 1 1 σ and 2 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 = 1. 091^+0. 035-₀. ₀₄₂ α = 1. 091 - 0. 042 + 0. 035, = 1. 237^+ 0. 056-₀. ₁₆ β = 1. 237 - 0. 16 + 0. 056 and = 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.