Secondary graviton spectra and waterfall-like fields

Abstract

The secondary spectra of the gravitons induced by a waterfall-like field are computed and the general bounds on the spectral energy density of the tensor modes of the geometry are translated into explicit constraints on the amplitude and slope of the waterfall spectrum. The obtained results are compared with the primary gravitational wave spectra of the concordance model and of its neighboring extensions as well as with the direct Ligo/Virgo bounds on stochastic backgrounds of relic gravitons. Space-borne interferometers (such as Lisa, Bbo, Decigo) seem to be less relevant but their potential implications are briefly outlined.Comment: 21 pages, 5 figure

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].…”

“…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]. A similar comment holds for other effects which are customarily associated with potential suppression of the amplitude of the power in the intermediate frequency branch such as the neutrino free streaming [30,31] or the effective evolution of number of relativistic species.…”

“…The independent variation of the tensor spectral index n T and of the tensor to scalar ratio r T (k p ) can be investigated from the absolute normalization of the spectral energy density [26,27]. When the relevant modes are today inside the Hubble radius 18 the relation between the spectral energy density and the power spectrum at the corresponding time is given by:…”

“…(3.40). In the first approach we can compute the transfer function for the amplitude as [20,26,27,[33][34][35]]…”

“…By using the transfer function for the tensor amplitude, the spectral energy density for frequencies ν ν eq can be simply given by: where d A is the (comoving) angular diameter distance to decoupling and R0 is the fraction of critical energy density attributed to massless particles (photons and neutrinos in the concordance paradigm). The second strategy is to use the direct integration of the mode functions and discuss the transfer function directly in terms of the spectral energy density [26,27,35]: where ν eq denotes the equality frequency:…”