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But, apart from the fact that such a behaviour seems rather implausible, or at least is not suggested by any cosmological mechanism, in the detection at broadband detectors like VIRGO, one must also take into account that, even if we gain in the height of the signal, this is partially compensated by the fact that we lose because of the reduction of the useful frequency band ∆f , see eq. (78). It is sometimes useful to think in terms of the dimensionless amplitude hc (f ) instead of h20 Ωgw . From eq.

4 (112) (113) One extra species of light neutrino, at the same temperature as the photons, would contribute one unit to Nν , but all species, weighted with their energy density, contribute to Nν , which of course in general is not an integer. For i = gravitons, we have gi = 2 and (Ti /T )4 = ρgw /ργ , where ργ = 2(π 2 /30)T 4 is the photon energy density. If gravitational waves give the only extra contribution to Nν , compared to the standard model with Nν = 3, then ρgw Ti 4 =2 , (114) gi T ργ i=extra bosons and therefore ρgw ργ NS 7 = (Nν − 3) , 8 (115) where the subscript NS reminds that this equality holds at time of nucleosynthesis.

The deviations for smaller redshift can be found in [243]. For zLSS = 1100, eq. (130) gives θLSS ∼ 2o . The temperature fluctuations over an angle θ are related to alm by δT T 2 θ ∼ l2 |alm |2 , for (131) 200o . (132) θ Therefore multipoles up to, say, l ∼ 30, are due to large angle fluctuations, and the corresponding anisotropies alm are dominated by the Sachs-Wolfe effect, due either to scalar perturbations or to GWs. l∼ 45 The waves that were outside the horizon at the last scattering, today have a frequency, √ f< zLSS H0 ≃ 10−16 Hz , (133) where in the last equality we have taken zLSS = O(103 ).