Restricted Galileons

TL;DR

This work investigates Restricted Galileons (ReG), a ghost-free massive gravity subclass where the helicity-0 mode decouples from the tensor sector and couples to matter with a fixed coefficient. The authors show that for the physically viable sign $\alpha>0$, there are no static, stable solutions that interpolate between the Vainshtein region and asymptotically flat space; instead, the Vainshtein region must connect to a cosmological background with stable, sub-luminal fluctuations. They analyze the exact static solution and its observational implications, finding that a graviton mass of order the Hubble parameter is consistent with data due to the large Vainshtein screening and cosmological matching. The paper also discusses nonperturbative Solar-System effects and quantum corrections, arguing that current laboratory and solar-system constraints do not rule out $m \sim H_0$ and that de-mixing cosmological solutions can occur in this framework, enriching the landscape of viable modified gravity models.

Abstract

We study Galileon theories that emerge in ghost-free massive gravity. In particular, we focus on a sub-class of these theories where the Galileons can be completely decoupled from the tensor Lagrangian. These Galileons differ from generic ones -- they have interrelated coefficients of the cubic and quartic terms, and most importantly, a non-standard coupling to external stress-tensors, governed by the same coefficient. We show that this theory has no static stable spherically symmetric solutions that would interpolate from the Vainshtein region to flat space; these two regions cannot be smoothly matched for the sign of the coefficient for which fluctuations are stable. Instead, for this sign choice, a solution in the Vainshtein domain is matched onto a cosmological background. Small fluctuations above this solution are stable, and sub-luminal. We discuss observational constraints on this theory, within the quantum effective Lagrangian approach, and argue that having a graviton mass of the order of the present-day Hubble parameter, is consistent with the data. Last but not least, we also present a general class of cosmological solutions in this theory, some of which exhibit the de-mixing phenomenon, previously found for the self-accelerated solution.