Perturbations of Self-Accelerated Universe

TL;DR

This paper analyzes small perturbations in the self-accelerated DGP universe, arguing that previous claims of instability based on linearized calculations are unwarranted due to the complexities of sources, nonlinear effects, and boundary conditions.

Contribution

It provides a detailed critique of linearized instability claims, emphasizing the importance of nonlinear effects and boundary conditions in the self-accelerated DGP model.

Findings

Small perturbations of an empty background can be quantized without ghosts.

Conformal sources do not induce instabilities.

Non-conformal sources invalidate linear approximation and may lead to ghosts.

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.