On the soft limit of the large scale structure power spectrum: UV dependence
Abstract
We derive a nonperturbative equation for the large scale structure power spectrum of longwavelength modes. Thereby, we use an operator product expansion together with relations between the threepoint function and power spectrum in the soft limit. The resulting equation encodes the coupling to ultraviolet (UV) modes in two timedependent coefficients, which may be obtained from response functions to (anisotropic) parameters, such as spatial curvature, in a modified cosmology. We argue that both depend weakly on fluctuations deep in the UV. As a byproduct, this implies that the renormalized leading order coefficient(s) in the effective field theory (EFT) of large scale structures receive most of their contribution from modes close to the nonlinear scale. Consequently, the UV dependence found in explicit computations within standard perturbation theory stems mostly from counterterm(s). We confront a simplified version of our nonperturbative equation against existent numerical simulations, and find good agreement within the expected uncertainties. Our approach can in principle be used to precisely infer the relevance of the leading order EFT coefficient(s) using small volume simulations in an `anisotropic separate universe' framework. Our results suggest that the importance of these coefficient(s) is a ~ 10% effect, and plausibly smaller.
 Publication:

Journal of Cosmology and Astroparticle Physics
 Pub Date:
 November 2015
 DOI:
 10.1088/14757516/2015/11/032
 arXiv:
 arXiv:1508.06306
 Bibcode:
 2015JCAP...11..032G
 Keywords:

 Astrophysics  Cosmology and Nongalactic Astrophysics;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Phenomenology;
 High Energy Physics  Theory
 EPrint:
 25+5 pages, 10 figures, comments added, matches published version