Boson stars in Palatini f(R) gravity

We explore equilibrium solutions of spherically symmetric boson stars in the Palatini formulation $f(\mathcal{R})$ gravity. account for modifications introduced gravitational sector by using a recently established correspondence between modified gravity with scalar matter and general relativity matter. focus on quadratic theory $f(\mathcal{R})=R+\xi R^2$ compare its those found relativity, exploring both positive negative values coupling parameter $\xi$. As source, complex, massive field without self-interaction terms is considered. Our results show that existence curves are fairly similar to relativity. Major differences observed which repulsive component high enough density distributions. Adding self-interactions makes degeneracy even more pronounced, leaving very little room observational discrimination two theories.