Unveiling a universal relationship between the f(R) parameter and neutron star properties

In recent years, modified gravity theories have gained significant attention as potential replacements for the general theory of relativity. Neutron stars, which are dense compact objects, provide ideal astrophysical laboratories for testing these theories. However, understanding the properties of neutron stars within the framework of modified gravity theories requires careful consideration of the presently known uncertainty of equations of state (EoS) that describe the behavior of matter at extreme densities. In this study, we investigate three realistic EoS generated using a relativistic mean field framework, which covers the currently known uncertainties in the stiffness of neutron star matter. We then employ a Bayesian approach to statistically analyze the posterior distribution of the free parameter $\alpha$ of the $f(R)$ gravity model, specifically $f(R) = R + \alpha R^2$. By using this approach, we are able to account for our limited understanding of the interiors of neutron stars as well as the uncertainties associated with the modified gravity theory. We impose observational constraints on our analysis, including the maximum mass, and the radius of a neutron star with a mass of $1.4 M_{\odot}$ and $2.08 M_{\odot}$, which are obtained from X-ray NICER observations. By considering these constraints, we are able to robustly investigate the relationship between the $f(R)$ gravity model parameter $\alpha$ and the maximum mass of neutron stars. Our results reveal a universality relationship between the $f(R)$ gravity model parameter $\alpha$ and the maximum mass of neutron stars. This relationship provides insights into the behavior of neutron stars in modified gravity theories and helps us understand the degeneracies arising from our current limited knowledge of the interiors of neutron stars and the free parameter $\alpha$ of the modified gravity theory.