Spinodal Instabilities and Super-Planckian Excursions in Natural Inflation

Abstract

Models such as Natural Inflation that use pseudo-Nambu-Goldstone bosons as the inflaton are attractive for many reasons. However, they typically require trans-Planckian field excursions ΔΦ > M Pl , due to the need for an axion decay constant f > M Pl to have both a sufficient number of e-folds and values of n s ; r consistent with data. Such excursions would in general require the addition of all other higher dimension operators consistent with symmetries, thus disrupting the required flatness of the potential and rendering the theory nonpredictive. We show that in the case of Natural Inflation, the existence of spinodal instabilities (modes with tachyonic masses) can modify the inflaton equations of motion to the point that versions of the model with f < M Pl can still inflate for the required number of e-folds. The instabilities naturally give rise to two separate phases of inflation with different values of the Hubble parameter H, one driven by the zero mode, the other by the unstable fluctuation modes. The values of n s and r typically depend on the initial conditions for the zero mode, and, at least for those examined here, the values of r tend to be unobservably small.

Cosmic fluctuations from a quantum effective action

“…Also ref. [6] suggests a partial insensitivity of observables from the choice of initial conditions. This is again due to the selected observables and restricted initial conditions.…”

“…We undertake here first steps within the conceptual framework of the quantum effective action. This allows us to discuss interacting fields and to go beyond investigations [1][2][3][4][5][6][7] of free fields in a pure quantum state. Interactions are crucial for possible symmetrization and equilibration processes.…”

Spinodal backreaction during inflation and initial conditions

“…In [11], the choice was made not to call upon a condensation of all the unstable modes in a classical diakyon-like field, in favor of a cutoff in q-space. Using mode equations, however, one needs to make choices in order to comply with numerical limitations while still accounting for most of the effect due to the presence of tachyonic modes.…”

The two-field regime of natural inflation

“…For example, even if these additional fields are very heavy with respect to the energy scale of inflation, they can induce changes in 1 However, several mechanisms to achieve the potential (1) with f > M pl consistent with a low energy description have been put forward in the literature [8][9][10][11]. It has also been pointed out that non-perturbative dynamics in the single field potential can make the predictions for subplanckian values of f consistent with CMB data [12].…”