Perturbations of the self-accelerated Universe

Abstract

We discuss small perturbations on the self-accelerated solution of the Dvali–Gabadadze–Porratimodel, and argue that claims of instability of the solution that are based on linearizedcalculations are unwarranted because of the following. (1) Small perturbations of an emptyself-accelerated background can be quantized consistently without yielding ghosts. (2)Conformal sources, such as radiation, do not give rise to instabilities either. (3) A typicalnon-conformal source could introduce ghosts in the linearized approximation andbecome unstable; however, it also invalidates the approximation itself. Such a sourcecreates a halo of variable curvature that locally dominates over the self-acceleratedbackground and extends over a domain in which the linearization breaks down.Perturbations that are valid outside the halo may not continue inside, as is suggested bysome non-perturbative solutions. (4) In the Euclidean continuation of the theory,with arbitrary sources, we derive certain constraints imposed by the second orderequations on first order perturbations, thus restricting the linearized solutions thatcould be continued to the full non-linear theory. Naive linearized solutions fail tosatisfy the above constraints. (5) Finally, we clarify in detail subtleties associatedwith the boundary conditions and analytic properties of the Green’s functions.