Can superhorizon cosmological perturbations explain the acceleration of the universe?

We investigate the recent suggestions by Barausse et al. and Kolb et al. that the acceleration of the universe could be explained by large superhorizon fluctuations generated by inflation. We show that no acceleration can be produced by this mechanism. We begin by showing how the application of Raychaudhuri equation to inhomogeneous cosmologies results in several “no go” theorems for accelerated expansion. Next we derive an exact solution for a specific case of initial perturbations, for which application of the Kolb et al. expressions leads to an acceleration, while the exact solution reveals that no acceleration is present. We show that the discrepancy can be traced to higher-order terms that were dropped in the Kolb et al. analysis. We proceed with the analysis of initial value formulation of general relativity to argue that causality severely limits what observable effects can be derived from superhorizon perturbations. By constructing a Riemann normal coordinate system on initial slice we show that no infrared divergence terms arise in this coordinate system. Thus any divergences found previously can be eliminated by a local rescaling of coordinates and are unobservable. We perform an explicit analysis of the variance of the deceleration parameter for the case of single-field inflation using usual coordinates and show that the infrared-divergent terms found by Barausse et al. and Kolb et al. cancel against several additional terms not considered in their analysis. Finally, we argue that introducing isocurvature perturbations does not alter our conclusion that the accelerating expansion of the universe cannot be explained by superhorizon modes.

Figure 1

The regions of spacetime described in the text. Initial data are supplied on the Cauchy hypersurface $\Sigma$. Causality implies that the observables seen by observer $\mathcal{O}$ can depend only on the initial data within the shaded region $\Sigma \cap J^{-}(\mathcal{O})$. Within the context of perturbation theory around an FRW spacetime, the perturbations to the observables can be determined given initial data within any open set $\mathcal{U}$ containing $\Sigma \cap J^{-}(\mathcal{O},\mathrm{FRW})$. Superhorizon perturbations can only be observed to the extent that they affect the initial data inside $\mathcal{U}$.