Towards a gravity dual for the large scale structure of the universe

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 sixdimensional 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 Schrödinger 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.

The stable clustering ansatz, consistency relations and gravity dual of large-scale structure

“…These generalizes the results derived in ref. [26] to arbitrary dimension. We will use the following forms for the potential V (φ) and gauge coupling W (φ):…”

“…The gravity dual of the large scale structure (LSS) has recently been introduced in [26]. In this scenario, the Universe, is pictured as a four-dimensional brane immersed in a six-dimensional bulk.…”