Quantum corrections to inflaton and curvaton dynamics

Abstract

We compute the fully renormalized one-loop effective action for two interacting and self-interacting scalar fields in FRW space-time. We then derive and solve the quantum corrected equations of motion both for fields that dominate the energy density (such as an inflaton) and fields that do not (such as a subdominant curvaton). In particular, we introduce quantum corrected Friedmann equations that determine the evolution of the scale factor. We find that in general, gravitational corrections are negligible for the field dynamics. For the curvaton-type fields this leaves only the effect of the flat-space Coleman-Weinberg-type effective potential, and we find that these can be significant. For the inflaton case, both the corrections to the potential and the Friedmann equations can lead to behaviour very different from the classical evolution. Even to the point that inflation, although present at tree level, can be absent at one-loop order.

Quantum corrections to scalar field dynamics in a slow-roll space-time

“…Therefore, in the minimally coupled case ξ = 0 we recovered the classical relation (2.45) between the time-derivatives of the mean field and the Hubble rate. For comparison, in [20] it was found that expanding up to four gradients around Minkowski space, the corrections to the Friedmann equations involve kinetic terms, and the new contributions in energy density and pressure are no longer the same. Also in the present case, however, the quantum correction to the potential force in the field equation does not follow from simple variation from the potential-like quantum contribution in the Friedmann equation, which prevents from using a full analogy with the classical slow-roll formalism.…”

“…These are typically based on a gradient expansion around the Minkowski vacuum, either through adiabatic regularisation [12][13][14][15][16] or at the level of the action using the Schwinger-deWitt expansion [17][18][19][20] for the 1PI effective action. In contrast to the 1PI expansion, in the 2-particle-irreducible (2PI) expansion one uses the dressed propagator in the Feynman diagrams.…”

“…It is a function of the field ϕ through δ, and a function of the instantaneous ǫ and H. The same correction enters in the energy density and the pressure, and does not involve the kinetic or gradient terms for the scalar field. In [20,48], it was found that expanding up to four gradients around Minkowski space, the corrections to the Friedmann equations involve kinetic terms (derivatives of ϕ), and the new contributions in energy density and pressure are no longer the same. This for instance prevented manipulations similar to the classical slow-roll equations to go through.…”

“…In the latter case, we choose m ph = 0 and λ ph ∼ 10 −12 to find for the IR enhancement factor 20) while H 2 C /M 2 ph ≈ 2(N C + 1)/9. Hence we get for the size of the V Q -induced quantum corrections 3λ ph…”

Radiative corrections from heavy fast-roll fields during inflation

“…where we ignored all U V divergent terms, which are regularisation scheme dependent (related and more detailed computations can be found in [54][55][56][57][58][59]). Now we notice a potential subtlety: if we are interested in a single field case, the inflaton has to be very light compared to the Hubble mass in order to generate density perturbations during inflation.…”