Perturbations of Self-Accelerated Universe

TL;DR

This work analyzes perturbations around the self-accelerated DGP solution and argues that stability cannot be decided from linearized perturbations alone. It shows that empty-background perturbations can be ghost-free and that conformal sources remain stable, while non-conformal sources trigger ghost-like behavior only within a regime where nonlinear dynamics must be considered. Global Euclidean constraints further underscore the need for nonlinear 5D analysis to assess stability, as linear results can be misleading near sources where a Vainshtein halo forms. The truncated linear theory with sources illustrates delicate boundary conditions and pole structures that Solar System tests already constrain, highlighting that a full nonlinear treatment is essential for viability.

Abstract

We discuss small perturbations on the self-accelerated solution of the DGP model, and argue that claims of instability of the solution that are based on linearized calculations are unwarranted because of the following: (1) Small perturbations of an empty self-accelerated background can be quantized consistently without yielding ghosts. (2) Conformal sources, such as radiation, do not give rise to instabilities either. (3) A typical non-conformal source could introduce ghosts in the linearized approximation and become unstable, however, it also invalidates the approximation itself. Such a source creates a halo of variable curvature that locally dominates over the self-accelerated background and extends over a domain in which the linearization breaks down. Perturbations that are valid outside the halo may not continue inside, as it is suggested by some non-perturbative solutions. (4) In the Euclidean continuation of the theory, with arbitrary sources, we derive certain constraints imposed by the second order equations on first order perturbations, thus restricting the linearized solutions that could be continued into the full nonlinear theory. Naive linearized solutions fail to satisfy the above constraints. (5) Finally, we clarify in detail subtleties associated with the boundary conditions and analytic properties of the Green's functions.