Tidal deformability of neutron stars with exotic particles within a density dependent relativistic mean field model in R-squared gravity

There is a growing interest in investigating modified theories of gravity, primarily, with the aim explaining universe's accelerated expansion, which has been confirmed by several independent observations. Compact objects, like neutron stars, exhibit strong gravity effects and therefore are used to study theories. We use $f(R)=R+aR^2$ model, where R Ricci scalar $a$ free parameter. This model studied both perturbatively non-perturbatively. However, it was found that perturbative methods results nonphysical solutions for stars. In this paper, we examine star properties, such as mass, radius, tidal deformability non-perturbative $f(R)$ density dependant relativistic equation state different particle compositions. The strange particles core NS form ${\bf \Lambda}$ hyperons, $K^-$ condensate, quarks considered. have observed while mass-radius relation allows wide range parameter $a$, when considered, constrained down one order.