Constraining a $f(R, L_m)$ Gravity Cosmological Model with Observational Data

G. K. Goswami; Anirudh Pradhan; Syamala Krishnannair

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arXiv · 2505.18226

Constraining a $f(R, L_m)$ Gravity Cosmological Model with Observational Data

G. K. Goswami·Anirudh Pradhan·Syamala Krishnannair

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Abstract

We investigate a spatially flat FLRW cosmological model in the framework of modified gravity described by the function $ f(R, L_m) = \alpha R + L_m^\beta + \gamma $, where $ L_m $ is the matter Lagrangian density. The modified Friedmann equations yield the Hubble parameter as $ H(z) = H_0 \sqrt{(1 - \lambda) + \lambda (1 + z)^{3(1 + w)}},$ with the parameters $ \lambda = \frac{\gamma}{6\alpha H_0^2} + 1 $ and $ w = \frac{\beta(n - 2) + 1}{2\beta - 1} $. Using a Bayesian Markov Chain Monte Carlo (MCMC) approach, we constrain the model parameters with recent observational data, including cosmic chronometers, the Pantheon+ Supernovae dataset, Baryon Acoustic Oscillations (BAO), and Cosmic Microwave Background (CMB) shift parameters. The best-fit values are found to be $ H_0 = 72.773^{+0.148}_{-0.152} $ km/s/Mpc, $ \lambda = 0.289^{+0.007}_{-0.007} $, and $ w = -0.002^{+0.002}_{-0.002} $, all quoted at the 1$\sigma$ confidence level.This model predicts a transition redshift of $ z_t \approx 0.76 $ for the onset of cosmic acceleration and an estimated universe age of 13.21 Gyr. The higher inferred value of $ H_0 $ compared to the Planck 2018 result offers a potential resolution to the Hubble tension. Additionally, using $ \rho_0 = 0.534 \times 10^{-30} \, \text{g/cm}^3 $ and assuming $ n = 1 $, we derive the model constants as $ \beta = 1.00201 $, $ \alpha = 512247 $, and $ \gamma = -1.215 \times 10^{-29} $. We also evaluate the Bayesian Information Criterion (BIC) to compare the model's performance with that of the standard $\Lambda$CDM model. The small BIC difference ($ \Delta \text{BIC} = 0.16 $) indicates comparable statistical support for both models. Thus, the $ f(R, L_m) $ gravity scenario serves as a consistent and viable alternative to $\Lambda$CDM, potentially addressing open questions in late-time cosmology.

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G. K. Goswami, Anirudh Pradhan, Syamala Krishnannair. 2025-05-23. Constraining a $f(R, L_m)$ Gravity Cosmological Model with Observational Data. https://arxiv.org/abs/2505.18226

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