Dynamical RG and critical phenomena in de Sitter space

Abstract

Perturbative quantum field theory in de Sitter space is known to give rise to a variety of contributions that diverge with time (secular terms). Despite significant progress, a complete understanding of the physical origin of these divergences remains an outstanding problem. In this paper, we will study the origin of secular divergences in de Sitter space for interacting theories that are near attractive conformal fixed points. We show that the secular divergences are determined by the anomalous dimensions of the same theory in flat space and can be re-summed using the dynamical renormalization group. This behavior is mandatory at the conformal fixed point but we show that it holds away from the fixed point as well. We analyze this problem in general using conformal perturbation theory and study conformally coupled scalar fields in four and 4 − dimensions as examples.

Soft de Sitter Effective Theory

“…We will show how this simple consequence of power counting and symmetries underlies the all orders conservation of ζ and gravitational waves. For contrast, in the case of light scalars in dS, there can be marginal operators, which result in non-trivial DRG flow, as was also suggested previously [23,64,65], see also [31,[35][36][37][38]66] for related recent work. This RG can be converted to the formalism for stochastic inflation [15,16].…”

“…As discussed in detail in [38] for α = 1 (a conformally coupled scalar), this operator will acquire a one-loop anomalous scaling. However, as we just showed, one-loop corrections to the two-point function of ϕ + vanishes.…”

“…In particular, α and β can be changed through integrating out the short distance modes, for example though a correction to the effective mass of φ or an anomalous dimension, see e.g. [38]. To this end, our first goal towards understanding the bottom-up structure is to show that we can derive this fact within the EFT, which implies it cannot be altered by matching or running effects.…”

“…See e.g. [38,96] for further discussions. 20 In fact, this scaling behavior is in exact analogy with integrating out a heavy particle in a relativistic theory, whose influence follows a Yukawa potential which drops off exponentially fast.…”

Critical Reflections on Asymptotically Safe Gravity

“…A correlator evaluated at the fixed point can be related to a CFT correlator in flat space by a Weyl transformation. Then, the late time powerlike behavior of correlators can be obtained as a resummation of secular terms controlled by the anomalous dimensions in flat space, with an RG improvement at the renormalization scale µ = H [380], where the Hubble scale H of the de Sitter background is the only non-trivial scale in the problem.…”