Boson stars in Palatini $f(\mathcal{R})$ gravity

TL;DR

This paper investigates boson star solutions within Palatini $f( ext{R})$ gravity, finding that their properties closely resemble those in general relativity, with notable differences emerging for negative coupling parameters.

Contribution

It provides the first detailed comparison of boson stars in Palatini $f( ext{R})$ gravity with those in general relativity, highlighting the effects of the quadratic $f( ext{R})$ model and matter self-interactions.

Findings

Solutions are similar to GR for positive coupling values.

Negative coupling introduces repulsive gravity effects.

Self-interactions increase degeneracy with GR solutions.

Abstract

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