Effective theories of single field inflation when heavy fields matter

Abstract

We compute the low energy effective field theory (EFT) expansion for singlefield inflationary models that descend from a parent theory containing multiple other scalar fields. By assuming that all other degrees of freedom in the parent theory are sufficiently massive relative to the inflaton, it is possible to derive an EFT valid to arbitrary order in perturbations, provided certain generalized adiabaticity conditions are respected. These conditions permit a consistent low energy EFT description even when the inflaton deviates off its adiabatic minimum along its slowly rolling trajectory. By generalizing the formalism that identifies the adiabatic mode with the Goldstone boson of this spontaneously broken time translational symmetry prior to the integration of the heavy fields, we show that this invariance of the parent theory dictates the entire non-perturbative structure of the descendent EFT. The couplings of this theory can be written entirely in terms of the reduced speed of sound of adiabatic perturbations. The resulting operator expansion is distinguishable from that of other scenarios, such as standard single inflation or DBI inflation. In particular, we re-derive how certain operators can become transiently strongly coupled along the inflaton trajectory, consistent with slow-roll and the validity of the EFT expansion, imprinting features in the primordial power spectrum, and we deduce the relevant cubic operators that imply distinct signatures in the primordial bispectrum which may soon be constrained by observations.

Inflation and String Theory

“…1 These fields fluctuation quantum-mechanically during inflation and therefore have to be included in the computation of the primordial perturbations. The phenomenology of these models of quasisingle-field inflation [490] has been explored in [118,207,208,239,255,265,267,[491][492][493][494][495][496][497].…”

“…As discussed in §2.1.5, a heavy mode of frequency ω can be integrated out in this way only when the adiabatic conditionω/ω 2 < 1 holds: more rapid evolution leads to excitation of the heavy modes. (Analyses of the effects of heavy fields include [493,496,505,506]. See also the discussion of resonance in §5.…”

Effective field theory in time-dependent settings

“…Some effort has already been made to apply the ideas of effective field theories to inflationary backgrounds [17][18][19][20]. And some works too have specifically examined the influence of a heavy field on the correlation functions of the inflaton [21][22][23][24], using classical field theory. The picture that is emerging is a very intriguing one.…”

Constraining $ \mathcal{N} $ = 1 supergravity inflationary framework with non-minimal Kähler operators

“…We will assume that these two fields are coupled gravitationally. In past such a scenario has been considered by many authors, where the heavy field leaves interesting imprints in the dynamics of a low scale inflation [23][24][25][26][27][28][29][30][31][32][33][34][35]. Broadly speaking there are two possible scenarios which one can envisage:…”