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