A Comment on the Path Integral Approach to Cosmological Perturbation Theory
Oliver J. Rosten (Dublin Inst.)
TL;DR
This paper critiques the application of the exact renormalization group approach to cosmological perturbation theory, clarifying its mischaracterization and connecting it to the path integral formulation and generating functional responses.
Contribution
It clarifies that the so-called renormalization group approach is actually a path integral response analysis, correcting a misnomer in prior work.
Findings
The evolution equation is a special case of generating functional variations.
The approach is misnamed as an exact renormalization group method.
Path integral formulation provides insight into cosmological perturbation evolution.
Abstract
It is pointed out that the exact renormalization group approach to cosmological perturbation theory, proposed in Matarrese and Pietroni, JCAP 0706 (2007) 026, arXiv:astro-ph/0703563 and arXiv:astro-ph/0702653, constitutes a misnomer. Rather, having instructively cast this classical problem into path integral form, the evolution equation then derived comes about as a special case of considering how the generating functional responds to variations of the primordial power spectrum.
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