What Planck does not tell us about inflation

Abstract

Planck data has not found the 'smoking gun' of non-Gaussianity that would have necessitated consideration of inflationary models beyond the simplest canonical single field scenarios. This raises the important question of what these results do imply for more general models, and in particular, multi-field inflation. In this paper we revisit four ways in which two-field scenarios can behave differently from single field models; two-field slow-roll dynamics, curvaton-type behaviour, inflation ending on an inhomogeneous hypersurface and modulated reheating. We study the constraints that Planck data puts on these classes of behaviour, focusing on the latter two which have been least studied in the recent literature. We show that these latter classes are almost equivalent, and extend their previous analyses by accounting for arbitrary evolution of the isocurvature mode which, in particular, places important limits on the Gaussian curvature of the reheating hypersurface. In general, however, we find that Planck bispectrum results only constrain certain regions of parameter space, leading us to conclude that inflation sourced by more than one scalar field remains an important possibility.

General analytic predictions of two-field inflation and perturbative reheating

“…[15,56] and arises due to the dynamical constraints imposed by the assumption of a sum-separable potential. The Inhomogeneous End of Inflation scenario allows |r A | 1 which can modify this result, even producing the dominant contribution to δN at linear order if the end of inflation hypersurface intercepts the inflationary bundle at a sufficiently large angle [13].…”

“…This result is not immediately derivable from our four-phase calculation since this requires phase B to be split into two subphases. As with the inflating curvaton, we emphasise that this calculation can easily be done by assembling the ingredients that we have provided in the requisite manner, and we only refrain from providing these details because this particular model has been recently studied elsewhere [13]. Instead, our calculation allows us to consider a new scenario where the reheating hypersurface for the φ field is modulated by its dependence on a fluid density ρ σ .…”

“…This is known as the Inhomogeneous End of Inflation scenario [3,5,[7][8][9][10][11][12] and has been recently summarised and constrained by Planck data in ref. [13]. Since the method of Vernizzi and Wands [1] tracks perturbations until the end of inflation, their work is equally applicable to any two-field separable potential where observable statistics attain constant conserved values before the end of inflation.…”

Non-Gaussianity in multiple three-form field inflation

“…These bounds are stringent, though it is too early to exclude noncanonical or multifield inflationary models by means of Gaussianity (see e.g. [17][18][19].) Despite the success of inflation driven by scalar fields, three-forms provide a viable alternative (and a viable model of dark energy) [20][21][22][23][24][25][26][27].…”

Arbitrary scalar-field and quintessence cosmological models

“…Hence Planck data 'severely limits the extensions of the simplest paradigm' [40]. On the other hand Planck data do not require the consideration of inflationary models beyond the simplest canonical single-field scenarios [42]. More specifically, a chaotic inflationary model, based on a quartic potential, is highly disfavored by the observations.…”