FRW cosmologies and hyperscaling-violating geometries: higher curvature corrections, ultrametricity, Q-space/QFT duality, and a little string theory

TL;DR

This paper explores the connections between FRW cosmologies, hyperscaling-violating geometries, and holographic dualities, revealing simplified higher curvature corrections, proposing a Q-space/QFT duality, and analyzing ultrametric structures and their relation to little string theory.

Contribution

It introduces a novel perspective on scale covariance in cosmologies, proposes a Q-space/QFT duality extending dS/CFT, and links ultrametric structures to little string theory.

Findings

Higher curvature corrections are simplified via scale covariance.

A conjectured Q-space/QFT duality extends holographic principles.

Ultrametric structures become sharper in slower accelerated cosmologies.

Abstract

We analyze flat FRW cosmologies and hyperscaling-violating geometries by emphasizing the analytic continuation between them and their scale covariance. We exhibit two main calculations where this point of view is useful. First, based on the scale covariance, we show that the structure of higher curvature corrections to Einstein's equation is very simple. Second, in the context of accelerated FRW cosmologies, also known as Q-space, we begin by calculating the Bunch-Davies wavefunctional for a massless scalar field and considering its interpretation as a generating functional of correlation functions of a holographic dual. We use this to conjecture a Q-space/QFT duality, a natural extension of dS/CFT, and argue that the Euclidean dual theory violates hyperscaling. This proposal, when extended to epochs in our own cosmological history like matter or radiation domination, suggests a holographically dual description via RG phases which violate hyperscaling. We further use the wavefunctional to compute Anninos-Denef overlaps and show that the ultrametric structure discovered for de Sitter becomes sharper in accelerated FRW cosmologies as the acceleration slows. The substitution $d --> d_{eff}=d-\theta$ permeates and illuminates the discussion of wavefunctionals and overlaps in FRW cosmologies, allowing one to predict the sharpened structure. We try to find an alternate manifestation of this ultrametric structure by studying the connection of the $\theta --> -\infty$ background to little string theory.