Towards a Gravity Dual for the Large Scale Structure of the Universe

TL;DR

This paper proposes a holographic gravity dual model for the universe's large-scale structure, linking Lifshitz symmetry in the bulk to observable growth rates and fixed points in the universe's evolution.

Contribution

It introduces a six-dimensional spacetime framework with Lifshitz symmetry as a dual to the universe's large-scale structure, connecting bulk symmetries to cosmological observations.

Findings

The preferred Lifshitz exponent matches a fixed point with enhanced symmetry.

The RGE flow in the dual system correlates with the growth rate of large-scale structure.

Qualitative agreement with observational data on structure growth.

Abstract

The dynamics of the large-scale structure of the universe enjoys at all scales, even in the highly non-linear regime, a Lifshitz symmetry during the matter-dominated period. In this paper we propose a general class of six-dimensional spacetimes which could be a gravity dual to the four-dimensional large-scale structure of the universe. In this set-up, the Lifshitz symmetry manifests itself as an isometry in the bulk and our universe is a four-dimensional brane moving in such six-dimensional bulk. After finding the correspondence between the bulk and the brane dynamical Lifshitz exponents, we find the intriguing result that the preferred value of the dynamical Lifshitz exponent of our observed universe, at both linear and non-linear scales, corresponds to a fixed point of the RGE flow of the dynamical Lifshitz exponent in the dual system where the symmetry is enhanced to the Schrodinger group containing a non-relativistic conformal symmetry. We also investigate the RGE flow between fixed points of the Lifshitz dynamical exponent in the bulk and observe that this flow is reflected in a growth rate of the large-scale structure, which seems to be in qualitative agreement with what is observed in current data. Our set-up might provide an interesting new arena for testing the ideas of holography and gravitational duals.