Manifestly causal in-in perturbation theory about the interacting vacuum

Abstract

In-In perturbation theory is a vital tool for cosmology and nonequilibrium physics. Here, we reconcile an apparent conflict between two of its important aspects with particular relevance to De Sitter/inflationary contexts: (i) the need to slightly deform unitary time evolution with an iϵ prescription that projects the free (“Bunch-Davies”) vacuum onto the interacting vacuum and renders vertex integrals well-defined, and (ii) Weinberg’s “nested commutator” reformulation of in-in perturbation theory which makes manifest the constraints of causality within expectation values of local operators, assuming exact unitarity. We show that a modified iϵ prescription maintains the exact unitarity on which the derivation of (ii) rests, while nontrivially agreeing with (i) to all orders of perturbation theory.

From locality and unitarity to cosmological correlators

“…In the past few years, our understanding of how fundamental principles constrain primordial correlators has dramatically improved. Much information has emerged from improvements in perturbative calculations [1][2][3][4][5][6][7][8][9][10][11][12]. At the same time, it has become clear that very powerful results can be bootstrapped directly from fundamental principles taking advantage of the restrictive symmetries of de Sitter spacetime [13][14][15][16][17][18][19][20][21][22][23][24][25][26].…”

Cosmological Cutting Rules

“…Similarly, when restricting to the most symmetric spacetime relevant for cosmology, namely de Sitter, very general results can be obtained, as for example various combinations of scalar and graviton correlators [26][27][28][29][30][31][32][33][34][35][36]. When combined with much progress on the front of perturbative calculations [14,17,[37][38][39][40][41][42][43], these powerful symmetry-based results have given us a much better understanding of general structures that appear in the wavefunction coefficients, such as singularities and the analytic structure. At the same, if we want to make connection with observations we absolutely need a "boostless" bootstrap approach where we relax the requirement of invariance under de Sitter boosts, since such symmetries are incompatible with large non-Gaussianity in single field inflation [44].…”

Stochastic Inflation at NNLO

“…Stochastic Inflation, and corrections to it, are the consequence of quantum field theory in dS for scalar particles with masses m 2 H 2 . This can be seen directly at leading order, where a variety of methods have been used to derive the Fokker-Planck equation [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35]. However, many of these methods become cumbersome beyond leading order and often obscure how corrections arise.…”

“…This result also provides the map between SdSET and refs. [31,35], which derived the soft behavior by explicitly expanding the UV in-in correlator in the superhorizon limit. The tree-like structure they observe is a consequence of our power counting as only c n,1 is marginal and hence interactions only include a single factor of ϕ − .…”

“…Stochastic Inflation [21][22][23] is a framework for treating the IR dynamics of a massless scalar field in a dS background, and has long been suspected to provide the non-perturbative resolution to the IR issues associated with massless fields in dS [24][25][26][27][28][29][30][31][32][33][34][35]. The idea is to reframe the problem in terms of the probability distribution for the scalar field as a function of time, resulting in a Fokker-Planck equation that depends on the scalar field potential.…”