Power-counting and the validity of the classical approximation during inflation

Abstract

We use the power-counting formalism of effective field theory to study the size of loop corrections in theories of slow-roll inflation, with the aim of more precisely identifying the limits of validity of the usual classical inflationary treatments. We keep our analysis as general as possible in order to systematically identify the most important corrections to the classical inflaton dynamics. Although most slow-roll models lie within the semiclassical domain, we find the consistency of the Higgs-Inflaton scenario to be more delicate due to the proximity between the Hubble scale during inflation and the upper bound allowed by unitarity on the new-physics scale associated with the breakdown of the semiclassical approximation within the effective theory. Similar remarks apply to curvature-squared inflationary models.

Agravity

“…4 10 18 GeV is the reduced Planck mass. Special assumptions such as V (S) ∝ f (S) 2 make the Einstein-frame potential V E flat at S M Pl , with predictions compatible with present observations [7][8][9][10][11][12][13][14][15][16][17][18][19]. However this flattening is the result of a fine-tuning: in presence of generic Planck-suppressed operators V and f and thereby V E are generic functions of S/M Pl .…”

“…In the agravity context, such field must have a dimensionless logarithmic potential: this is why our predictions for r ≈ 8/N ≈ 0.13 differ from the tentative prediction r ≈ 12/N 2 ≈ 0.003 of a generic ξ-inflation model with mass parameters in the potential [7][8][9][10][11][12][13][14][15][16][17][18][19].…”

“…However, this is a quite unusual outcome of quantum field theory: it requires special models with flat potentials, and often field values above the Planck scale. Let us discuss this issue in the context of Starobinsky-like inflation models [7][8][9][10][11][12][13][14][15][16][17][18][19]: a class of inflation models favoured by Planck data [20]. Such models can be described in terms of one scalar S (possibly identified with the Higgs H) with a potential V (S) and a coupling to gravity − 1 2 f (S)R. Going to the Einstein frame (i.e.…”

“…In the limit where h or χ feel the vacuum expectation value of s as a constant mass term, one obtains Starobinsky inflation and Higgs ξ-inflation [7][8][9][10][11][12][13][14][15][16][17][18][19]: agravity dictates how they can hold above the Planck scale. Leaving a full analysis to a future work, we here want to explore the possibility that the inflaton is the field s that dynamically generates the Planck scale, as discussed in section 3.…”

Inflation and String Theory

“…Its bottom-up naturalness is discussed in [228,229]. The scalar spectral tilt and the tensor-to-scalar ratio are…”