Abstract
We consider the dynamics of a quantum scalar field in the background of a slow-roll inflating Universe. We compute the one-loop quantum corrections to the field and Friedmann equation of motion, in both a 1PI and a 2PI expansion, to leading order in slow-roll. Generalizing the works of [1-3], we then solve these equations to compute the effect on the primordial power spectrum, for the case of a self-interacting inflaton and a self-interacting spectator field. We find that for the inflaton the corrections are negligible due to the smallness of the coupling constant despite the large IR enhancement of the loop contributions. For a curvaton scenario, on the other hand, we find tension in using the 1PI loop corrections, which may indicate that the quantum corrections could be non-perturbatively large in this case, thus requiring resummation.
Highlights
Field, the curvaton, sources the fluctuations by dominating the energy density briefly during the right epoch
In this work we have considered the dynamics of a massive φ4 scalar field theory in slow-roll quasi-de Sitter Universe
We have renormalized the equations of motion with the slow-rolling vacuum state, ie. expanding around de Sitter rather than Minkowski vacuum
Summary
We will assume that the classical metric background is slow-rolling, in the sense that the deviation from pure exponential expansion (de Sitter space), can be written as an expansion in the small quantities ǫ and δH ,3 ǫ. The renormalized quantum corrected equations of motion can be derived to one-loop order in 1PI expansion without explicit reference to the effective action [48]. The advantage of this approach is that the finite parts of the counter terms will be suited for the particular space-time geometry of interest. Where we have set Λ → −Λ/(8πG) and α → 1/(16πG) in order to match with standard convention, and we further split the energy-momentum tensor into classical, quantum and counter-term contributions, respectively: Tμν ≡ TμCν + TμQν + δTμν ≡ TμCν + TμQν ,. Higher order gravitational tensors in δTμgν result from the variation of the gravitational counter term Sδg[gμν] and their expressions in a FRW space-time can be found in appendix A.
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