The nonlinear dynamical stability of infrared modifications of gravity

TL;DR

This paper investigates the stability and dynamics of the Vainshtein screening mechanism in modified gravity theories, revealing stable behavior, oscillations, and efficient higher multipole screening, with implications for gravitational collapse.

Contribution

It provides a detailed analysis of the dynamical stability and behavior of screening solutions in scalar-tensor theories of gravity, including new insights into their oscillations and multipolar structure.

Findings

Screening solutions are stable and oscillate before settling.

Late-time decay of solutions follows a power-law consistent with analytical predictions.

Higher multipoles are more efficiently screened than the monopole.

Abstract

Scalar forces "screened" by the Vainshtein mechanism may hold the key to understanding the cosmological expansion of our universe, while predicting new and exciting features in the interaction between massive bodies. Here we explore the dynamics of the Vainshtein screening mechanism, focusing on the decoupling limit of the DGP braneworld scenario and dRGT massive gravity. We show that there is a vast set of initial conditions whose evolution is well defined and which are driven to the static, screening solutions of these theories. Screening solutions are stable and behave coherently under small fluctuations: they oscillate and eventually settle to an equilibrium configuration, the timescale for the oscillations and damping being dictated by the Vainshtein radius of the screening solutions. At very late times, a power-law decay ensues, in agreement with known analytical results. However, we also conjecture that physically interesting processes such as gravitational collapse of compact stars may not possess a well-posed initial value problem. Finally, we construct solutions with nontrivial multipolar structure describing the screening field of deformed, asymmetric bodies and show that higher multipoles are screened more efficiently than the monopole component.