Cosmological Evolution as a Renormalization Group Flow

This work investigates a possible microscopic interpretation of the cosmological renormalization group (RG) framework introduced in the companion paper Cosmological Evolution as a Renormalization Group Flow: Entropy Growth and the Hierarchy of Cosmic Scales. Starting from the formulation in which the expansion history of the Universe can be interpreted as a renormalization group trajectory in theory space, we explore how this structure may arise from the RG dynamics of an underlying conformal field theory. In particular, we show that conformal field theories deformed by nearly marginal operators naturally generate beta functions of the formβ (φ) = −εφ + bφ², which reproduce the cosmological RG flow governing the evolution of the Hubble parameter. Within this framework the cosmological history corresponds to a renormalization group trajectory connecting two quasi–conformal regimes: an ultraviolet fixed point associated with inflation and an infrared fixed point corresponding to the late-time dark-energy dominated phase. The hierarchy between the inflationary and present Hubble scales is determined by the RG length of the trajectory, LRG = 2 ln (HUV / HIR), which can also be interpreted as the logarithmic growth of cosmological horizon entropy. We further discuss possible microscopic realizations of this structure in large-N Chern–Simons matter theories and ABJM-type conformal field theories, and explore the implications for cosmological observables and the thermodynamic arrow of time. This work should be viewed as a conceptual extension of the cosmological RG framework and as a step toward identifying possible microscopic origins of cosmological evolution.