Coarse-Graining and Renormalization Group in the Einstein Universe

TL;DR

This paper applies the renormalization group approach to a scalar field coupled with gravity in an Einstein universe, revealing how curvature influences the flow of coupling constants and identifying new effective interactions.

Contribution

It extends the Kadanoff-Wilson renormalization group method to curved spacetime, explicitly computing the average potential and analyzing coupling flows in an Einstein universe.

Findings

Curvature dominates the crossover scale in the potential.

Renormalized trajectories match perturbative results near the UV fixed point.

New effective interactions between gravity and matter are identified.

Abstract

The Kadanoff-Wilson renormalization group approach for a scalar self-interacting field theor generally coupled with gravity is presented. An average potential that monitors the fluctuations of the blocked field in different scaling regimes is constructed in a nonflat background and explicitly computed within the loop-expansion approximation for an Einstein universe. The curvature turns out to be dominant in setting the crossover scale from a double-peak and a symmetric distribution of the block variables. The evolution of all the coupling constants generated by the blocking procedure is examined: the renormalized trajectories agree with the standard perturbative results for the relevant vertices near the ultraviolet fixed point, but new effective interactions between gravity and matter are present. The flow of the conformal coupling constant is therefore analyzed in the improved scheme and the infrared fixed point is reached for arbitrary values of the renormalized parameters.