Causality and the Power Spectrum

Abstract

We find constraints on the generation of super-causal-horizon energy perturbations from a smooth initial state, under a simple physical scheme. We quantify these constraints by placing the upper limit $\lambda_c = 3.0 d_H$ on the wavelength at which the power spectrum turns over to $k^4$ behavior. This means that sub-horizon processes can generate significant power on scales further outside the horizon than one might naively expect. The existence of this limit may have important implications for the interpretation of the small scale power spectrum of the Cosmic Microwave Background.