Gravitational instability of de Sitter compactifications

Abstract

We consider warped compactifications in(4 + d)-dimensional theories, with four-dimensional (4d) de SitterdS4 vacua (withHubble parameter H) and with a compact internal space. After introducing a gauge-invariant formalism for the genericmetric perturbations of these backgrounds, we focus on modes which are scalar with respect todS4. The physical eigenmasses of these modes acquire a large universal tachyonic contribution−12d/(d + 2)H2, independently of the stabilization mechanism for the compact space, in additionto the usual KK masses, which instead encode the effects of the stabilization.General arguments, as well as specific examples, lead us to conjecture that, forsufficiently large dS curvature, the compactified geometry becomes gravitationallyunstable due to the tachyonic growth of the scalar perturbations. This meansthat for any stabilization mechanism the curvature of the dS geometry cannotexceed some critical value. We relate this effect to the anisotropy of the bulkgeometry and suggest the end points of the instability. Of relevance for inflationarycosmology, the perturbations of the bulk metric inevitably induce a new modulusfield, which describes the conformal fluctuations of the 4d metric. If this modeis light during inflation, the induced conformal fluctuations will be amplifiedwith a scale free spectrum and with an amplitude which is disentangled from thestandard result of slow-roll inflation. The conformal 4d metric fluctuations giverise to a very generic realization of the mechanism of modulated cosmologicalfluctuations, related to spatial variation of couplings during (p)reheating after inflation.