Light scalars on cosmological backgrounds

Abstract

Abstract:We study the behaviour of a light quartically self-interacting scalar field φ on curved backgrounds that may be described with the cosmological equation state parameter w. At leading order in the non-perturbative 2PI expansion we find a general formula for the variance φ 2 and show for several previously unexplored cases, including matter domination and kination, that the curvature of space can induce a significant excitation of the field. We discuss how the generation of a non-zero variance for w = −1 can be understood as a process of self-regulation of the infrared divergences very similarly to what is known to occur in de Sitter space. To conclude, the appearance of an effective mass due to self-interaction is generic for a light scalar in curved space and can have important implications for reheating, vacuum stability and dark matter generation.

Abelian Higgs model in power-law inflation: the propagators in the unitary gauge

“…Nevertheless, it should be a better background model than de Sitter for studying quantum loop effects in the primordial universe, as it does capture the effect of a non-vanishing principal slow-roll parameter, and notably, it is still tractable enough to allow for analytic computations. Thus far there have been several reports on loop computations in power-law inflation, and general slow-roll inflation, some utilizing perturbative methods [7,[12][13][14][15], and some employing resummation/non-perturbative techniques [16][17][18]. Noteworthy is also the recent construction [19] of the one-loop effective potential in general inflationary models in which the principal slow roll parameter ǫ(t) is a general function of time.…”

“…The scaling in (1.7) was further corroborated for the same model in ref. [18] by solving the gap equation resulting from the 2PI Dyson-Schwinger equation in power-law inflation. The scaling of scalar fluctuations in the scalar electrodynamics model ΦΦ † ∝ H 2 is qualitatively different from the de Sitter case, where this quantity is just a constant, and if correct might account for interesting effects imparted on the vector.…”

Quantum correlators in Friedmann spacetimes: The omnipresent de Sitter spacetime and the invariant vacuum noise

“…The solid curves correspond to curves of constant timelike co-ordinate τ and the dashed curves correspond to curves of constant spacelike co-ordinate l. The co-ordinates (τ, l) are related to the co-moving co-ordinates through conformal time η = −e −Ht /H and Eq. (13). The shaded regions are not covered by this co-ordinate system because: (i) the shaded region corresponding to Z > 1 are timelike separated from the origin O of the comoving co-ordinates and (ii) no points in the shaded region marked Z < −1 can be connected to O by a spacelike geodesic segment (see the discussion around Eq.…”

“…It can be easily verified that the acceptable solutions to this equation, given in terms of K 1 (ml) reproduces the correct two point functions of the flat spacetime Lorentz invariant field theory. 13 2.2 Quantum Correlators and power spectra…”

“…In addition to enriching our theoretical understanding of quantum field theory, such studies also seem to be relevant to identify the seeds of structure formation as the quantum fluctuations in the early universe [8][9][10][11]. This problem, as well as the backreaction of quantum fluctuations, have been the subject of numerous investigations (e.g., [12,13]). Moreover, such investigations, especially in the context of a de Sitter universe, have highlighted several theoretical issues which are rather special to this context [14][15][16][17][18][19][20][21][22][23].…”