The thermal history of the plasma and high-frequency gravitons

Abstract

Possible deviations from a radiation-dominated evolution, occurring prior to the synthesis of light nuclei, impacted on the spectral energy density of high-frequency gravitons. For a systematic scrutiny of this situation, the ΛCDM paradigm must be complemented by (at least two) physical parameters describing, respectively, a threshold frequency and a slope. The supplementary frequency scale sets the lower border of a high-frequency domain where the spectral energy grows with a slope which depends, predominantly, upon the total sound speed of the plasma right after inflation. While the infra-red region of the graviton energy spectrum is nearly scale-invariant, the expected signals for typical frequencies larger than 0.01 nHz are hereby analyzed in a modelindependent framework by requiring that the total sound speed of the post-inflationary plasma be smaller than the speed of light. Current (e.g. low-frequency) upper limits on the tensor power spectra (determined from the combined analysis of the three large-scale data sets) are shown to be compatible with a detectable signal in the frequency range of wide-band interferometers. In the present context, the scrutiny of the early evolution of the sound speed of the plasma can then be mapped onto a reliable strategy of parameter extraction including not only the well established cosmological observables but also the forthcoming data from wide band interferometers.1 e-mail address: massimo.giovannini@cern.ch 5 The overdot will denote throughout the paper a derivation with respect to the cosmic time coordinate t while the prime will denote a derivation with respect to the conformal time coordinate τ .6 Forthcoming projects like Clover [27], Brain [28], Quiet [29] and Spider [30] have polarization as specific target.

The refractive index of relic gravitons

“…The lack of detection of a stochastic background of relic gravitons either by ground based detectors or by space-borne interferometers may therefore provide a further (and potentially much more stringent) bound on the rate of variation of the refractive index. 17 The sensitivity is often expressed by means of S h or in terms of its square root [10]. The precise relation between S h and Ω gw is given by S h (ν, τ 0 ) = 7.981 × 10 −43 (100 Hz/ν) 3 h 2 0 Ω gw (ν, τ 0 ) Hz −1 .…”

“…The equation obeyed by h ij ( x, τ ) follows from the second order action: 8) which reduces to the conventional action [10,25] in the limit n(τ ) → 1. Note that in Eq.…”

“…At high frequencies the anisotropic stress induced by waterfall fields may lead to an enhancement of the spectral energy density (see third paper in Ref. [10]). Both effects will be neglected in what follows for two independent reasons.…”

“…(3.2) and (3.3) the expression of the mode function during the radiation epoch shall be written as: 10) where…”

The propagating speed of relic gravitational waves and their refractive index during inflation

“…The transition to the domination of the dark energy does not affect the slope and it has a mild effect on the amplitude of the spectrum [24][25][26][27]; this effect will be included in the actual estimates of Sect. 4 by following the approach already pursued in [26,27].…”