Screenings in modified gravity: a perturbative approach

¹ Consejo Nacional de Ciencia y Tecnología, Av. Insurgentes Sur 1582, Colonia Crédito Constructor, Del. Benito Jurez 03940, Ciudad de México, Mexico
² Departamento de Física, Instituto Nacional de Investigaciones Nucleares, Apartado Postal 18-1027, Col. Escandon, Ciudad de México 11801, Mexico
³ Institute Of Theoretical Astrophysics, University of Oslo, 0315 Oslo, Norway
e-mail: d.f.mota@astro.uio.no

Received: 5 October 2018
Accepted: 29 November 2018

Abstract

We present a formalism to study screening mechanisms in modified theories of gravity through perturbative methods in different cosmological scenarios. We consider Einstein-frame posed theories that are recast as Jordan-frame theories, where a known formalism is employed, although the resulting nonlinearities of the Klein–Gordon equation acquire an explicit coupling between matter and the scalar field, which is absent in Jordan-frame theories. The obtained growth functions are then separated into screening and non-screened contributions to facilitate their analysis. This allows us to compare several theoretical models and to recognize patterns that can be used to distinguish models and their screening mechanisms. In particular, we find anti-screening features in the symmetron model. In contrast, chameleon-type theories in both the Jordan and Einstein frames always present a screening behaviour. Up to third order in perturbation, we find no anti-screening behaviour in theories with a Vainshtein mechanism, such as the Dvali Gabadadze Porrati braneworld model and the cubic Galileon.