Chameleon scalar fields in relativistic gravitational backgrounds

TL;DR

This paper analytically and numerically investigates chameleon scalar fields in relativistic gravitational backgrounds, demonstrating the existence of thin-shell solutions and their dependence on gravitational potential, relevant for understanding scalar field screening near compact objects.

Contribution

The paper derives analytical thin-shell solutions for chameleon fields in relativistic backgrounds and confirms their existence through numerical simulations, clarifying conditions for screening effects.

Findings

Thin-shell solutions exist if gravitational potential < 0.3.

Analytical solutions help set boundary conditions for numerical models.

Chameleon mechanism effectively reduces coupling in relativistic regimes.

Abstract

We study the field profile of a scalar field $\phi$ that couples to a matter fluid (dubbed a chameleon field) in the relativistic gravitational background of a spherically symmetric spacetime. Employing a linear expansion in terms of the gravitational potential $\Phi_c$ at the surface of a compact object with a constant density, we derive the thin-shell field profile both inside and outside the object, as well as the resulting effective coupling with matter, analytically. We also carry out numerical simulations for the class of inverse power-law potentials $V(\phi)=M^{4+n} \phi^{-n}$ by employing the information provided by our analytical solutions to set the boundary conditions around the centre of the object and show that thin-shell solutions in fact exist if the gravitational potential $\Phi_c$ is smaller than 0.3, which marginally covers the case of neutron stars. Thus the chameleon mechanism is present in the relativistic gravitational backgrounds, capable of reducing the effective coupling. Since thin-shell solutions are sensitive to the choice of boundary conditions, our analytic field profile is very helpful to provide appropriate boundary conditions for $\Phi_c \lesssim O(0.1)$.