Nonlinear dynamical stability of infrared modifications of gravity
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 time scale for the oscillations and damping being dictated by the Vainshtein radius of the screening solutions. At very late times, a powerlaw decay ensues, in agreement with known analytical results. However, we also conjecture that physically interesting processes such as the gravitational collapse of compact stars may not possess a wellposed 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.
 Publication:

Physical Review D
 Pub Date:
 December 2014
 DOI:
 10.1103/PhysRevD.90.124035
 arXiv:
 arXiv:1409.0886
 Bibcode:
 2014PhRvD..90l4035B
 Keywords:

 04.50.Kd;
 04.25.Nx;
 04.70.s;
 11.10.Lm;
 Modified theories of gravity;
 PostNewtonian approximation;
 perturbation theory;
 related approximations;
 Physics of black holes;
 Nonlinear or nonlocal theories and models;
 High Energy Physics  Theory;
 Astrophysics  Cosmology and Nongalactic Astrophysics;
 General Relativity and Quantum Cosmology
 EPrint:
 24 pages, 18 figures