Effective field theory during inflation. II. Stochastic dynamics and power spectrum suppression

Abstract

We obtain the non-equilibrium effective action of an inflaton like scalar field -the system-by tracing over sub Hubble degrees of freedom of "environmental" light scalar fields. The effective action is stochastic leading to effective Langevin equations of motion for the fluctuations of the inflaton-like field, with self-energy corrections and stochastic noise correlators that obey a de Sitter space-time analog of a fluctuation dissipation relation. We solve the Langevin equation implementing a dynamical renormalization group resummation of the leading secular terms and obtain the corrections to the power spectrum of super Hubble fluctuations of the inflaton field, P(k; η) = P 0 (k) e −γ(k;η) where P 0 (k) is the nearly scale invariant power spectrum in absence of coupling. γ(k; η) > 0 describes the suppression of the power spectrum, it features Sudakov-type double logarithms and entails violations of scale invariance. We also obtain the effective action for the case of a heavy scalar field of mass M ≫ H, this case yields a local "Fermi" limit with a very weak self-interaction of the inflaton-like field and dissipative terms that are suppressed by powers of H/M . We conjecture on the possibility that the large scale anomalies in the CMB may originate in dissipative processes from inflaton coupling to sub-Hubble degrees of freedom.

Hot cosmic qubits: late-time de Sitter evolution and critical slowing down

“…(B.2) 14 We replace sinh( as 2 ) − i We find no way to analytically compute (B.10) here, although this form is easier to use for numerical integration with computer algebra systems. Numerical investigation reveal the logarithmic -dependences (in terms of H 1 or ω 1) given in Table 2 (differentiating these forms with respect to ω leads to the -divergences for ∆ BD ).…”

“…Similarities between the physics of quantum systems in gravitational spacetimes (especially with horizons) and open systems [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] show that this assumption is actually unlikely to be true. The problem is that open systems (by definition) always have an 'environment' whose properties are not measured (in this case, perhaps, the degrees of freedom behind the horizon).…”

Hot accelerated qubits: decoherence, thermalization, secular growth and reliable late-time predictions

“…for all t. This differential relation is sufficient to justify (1.2), and perturbation theory is then simply used to derive the value of the coefficient Γ. An argument similar in spirit to this -though different in detail -is also often available for computing the late-time limit of open systems [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40]. We argue here that for many OpenEFT applications it is the Lindblad equation [41,42] that is the desired evolution equation for these purposes.…”

Open EFTs, IR effects & late-time resummations: systematic corrections in stochastic inflation

“…This was done in refs. [78][79][80] Our conclusions are briefly summarized in section 4, with a short outline of possible future directions. Various appendixes contain technical details and extensions of the arguments used in the main text.…”