Infrared dynamics of massive scalars from the complementary series in de Sitter space

Abstract

We continue a previous study about the infrared loop effects in the D-dimensional de Sitter space for a real scalar φ 4 theory from the complementary series whose bare mass belongs to the interval √ 3 4 (D − 1) < m ≤ D−1 2 , in units of the Hubble scale. The lower bound comes from the appearance of discrete states in the mass spectrum of the theory when that bound is violated, causing large IR loop effects in the vertices. We derive an equation which allows to perform a selfconsistent resummation of the leading IR contributions from all loops to the two-point correlation functions in an expanding Poincaré patch of the de Sitter manifold. The resummation can be done for density perturbations of the Bunch-Davies state which violate the de Sitter isometry. There exist solutions having a singular (exploding) behavior and therefore the backreaction can change the de Sitter geometry.

Quantum heating as an alternative of reheating

“…Furthermore this fact has been observed in de Sitter space [56,57] in strong electric field backgrounds [60,61], in the case of loop corrections to the Hawking radiation [62] and in the case of moving mirrors [63,64]. In all, even fundamental quantum fields in nonstationary situations reveal a similar behavior to quantum fields in a medium, as in condensed matter theory.…”

“…Furthermore, it can be shown that for massive fields vertexes also do not receive growing corrections [57]. (Note that this is not true for very light fields [56].) Thus, we continue with the two-loop sunset diagrams for the Keldysh propagator.…”

“…This is due to the nonstationarity of the inflationary expansion and due to the presence of interactions in the quantum field theory [57] (see also [56]). In non-Gaussian (self-interacting) theories in nonstationary situations initial ground state of the quantum field theory is changing in time that may reveal itself in dramatic changes of correlation functions, which are not observed in the proper vacuum quantum field theory measurements and calculations.…”

“…The other secular effects are present in generic nonstationary situations and appear when the time separation between arguments of the two-point function is growing (see e.g. introduction of [56] for the review). The latter type of secular effects leads just to a mass renormalization or reveals a quasiparticle instability, if any.…”

“…However, even for very big mass and for vanishing initial density it may be comparatively relevant, if the expansion stage is long enough, as we show in the present paper. It goes without saying that for light fields there can be even more dramatic effects [56].…”