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We analyze flat FRW cosmologies and hyperscaling-violating geometries byemphasizing 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 curvaturecorrections to Einstein's equation is very simple. Second, in the context ofaccelerated FRW cosmologies, also known as Q-space, we begin by calculating theBunch-Davies wavefunctional for a massless scalar field and considering itsinterpretation as a generating functional of correlation functions of aholographic dual. We use this to conjecture a Q-space/QFT duality, a naturalextension of dS/CFT, and argue that the Euclidean dual theory violateshyperscaling. This proposal, when extended to epochs in our own cosmologicalhistory like matter or radiation domination, suggests a holographically dualdescription via RG phases which violate hyperscaling. We further use thewavefunctional to compute Anninos-Denef overlaps and show that the ultrametricstructure discovered for de Sitter becomes sharper in accelerated FRWcosmologies as the acceleration slows. The substitution $d -->d_{eff}=d-\theta$ permeates and illuminates the discussion of wavefunctionalsand overlaps in FRW cosmologies, allowing one to predict the sharpenedstructure. We try to find an alternate manifestation of this ultrametricstructure by studying the connection of the $\theta --> -\infty$ background tolittle string theory.

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