The cosmology of $$f(R, L_m)$$ f ( R , L m ) gravity: constraining the background and perturbed dynamics

Abstract

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 $$ f(R, L_m) $$ f ( R , L m ) gravity model, formulated as $$ f(R, L_m) = \lambda R + \beta L_m^\alpha + \eta $$ 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 (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 (f $$\sigma _8$$ σ 8 ). These datasets facilitated the constraint of the $$ f(R, L_m) $$ f ( R , L m ) -gravity model via MCMC simulations, followed by a comparative analysis with the $$\varLambda $$ Λ CDM model. A comprehensive statistical analysis has been conducted to evaluate the $$ f(R, L_m) $$ 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 $$\varOmega _m = 0.242^{+0.016}_{-0.032}$$ Ω m = 0 . 242 - 0.032 + 0.016 , $$\alpha = 1.15^{+0.20}_{-0.20}$$ α = 1 . 15 - 0.20 + 0.20 , $$\beta = 1.12^{+0.13}_{-0.30}$$ β = 1 . 12 - 0.30 + 0.13 , $$\lambda = 0.72^{+0.30}_{-0.13}$$ λ = 0 . 72 - 0.13 + 0.30 and $$\gamma = 0.555\pm {0.014}$$ γ = 0.555 ± 0.014 using f-data and $$\varOmega _m = 0.284^{+0.035}_{-0.049}$$ Ω m = 0 . 284 - 0.049 + 0.035 , $$\sigma _8 = 0.799^{+0.045}_{-0.086}$$ σ 8 = 0 . 799 - 0.086 + 0.045 , $$\alpha = 0.766^{+0.026}_{-0.064}$$ α = 0 . 766 - 0.064 + 0.026 , $$\beta = 1.08^{+0.40}_{-0.16}$$ β = 1 . 08 - 0.16 + 0.40 , and $$\lambda = 0.279^{+0.078}_{-0.11}$$ λ = 0 . 279 - 0.11 + 0.078 using f $$\sigma _8$$ σ 8 -data at the $$1\sigma $$ 1 σ and $$2\sigma $$ 2 σ confidence levels, respectively, with the model showing substantial observational support based on $$\varDelta $$ Δ AIC values but less observational support based on the $$\varDelta $$ Δ BIC values on Jeffreys’ statistical criteria. On the other hand, from the joint analysis of the OHD+SNIa data, we obtain $$\alpha = 1.091^{+0.035}_{-0.042}$$ α = 1 . 091 - 0.042 + 0.035 , $$\beta = 1.237^{+ 0.056}_{-0.16}$$ β = 1 . 237 - 0.16 + 0.056 and $$\lambda = 0.630^{+0.031}_{-0.050}$$ λ = 0 . 630 - 0.050 + 0.031 with the Jeffreys’ scale statistical criteria showing the $$ f(R, L_m) $$ f ( R , L m ) model having substantial support when using OHD data, less observational support with the joint analysis OHD+SNIa, and rejected using SNIa data, compared with $$\varLambda $$ Λ CDM at the background level.