(ed.). Gravitational waves (IOP, 2001)(422s).

Observational bounds 207Table 12.10. Minimum values of h 2 0 gw for one year of observation, for(δ, α) = (0.95, 0.05), for optimally-filtered four-detector correlations.VIRGO ⋆ LIGO-WA ⋆ LIGO-LA ⋆ GEO-600VIRGO ⋆ LIGO-WA ⋆ LIGO-LA ⋆ TAMA-300VIRGO ⋆ LIGO-LA ⋆ GEO-600 ⋆ TAMA-300VIRGO ⋆ LIGO-WA ⋆ GEO-600 ⋆ TAMA-3003.7 × 10 −61.4 × 10 −52.2 × 10 −52.7 × 10 −5of the minimum detectable value on the total observation time: what changes fromone case to another is only the numerical factors multiplying T −1/2tot . Although theimprovement in sensitivity is limited the availability of the signals from variousdetectors would be important in ruling out spurious effects.12.5 Observational boundsWe close this section discussing what is actually known from the observationalside about the stochastic background. At present, there are strict limits on thisbackground in only a couple of frequency ranges, but other than that, only onevery general constraint. In the following we will only discuss the general one, thenucleosynthesis bound, because it is the only relevant one for the frequency region1Hz< f < 1 kHz covered by the ground based detectors. The other bounds areinferred from the timing irregularities in the arrival times of the pulses emitted bysome millisecond pulsars and the anisotropies on large angular scales of the CMB.They, respectively, constrain gw in the frequency regions f ∼ 10 −8 Hz and10 −18 Hz º f º 10 −16 Hz, which are far below any frequency band accessiblefor the present-day ground- or space-based experiments. A complete discussionof these bounds can be found in [4].Nucleosynthesis successfully predicts the primordial abundances ofdeuterium, 3 He, 4 He and 7 Li in terms of one cosmological parameter η, thebaryon to photon ratio. In the prediction parameters of the underlying particletheory also enter, which are therefore constrained in order not to spoil theagreement. In particular, the prediction is sensitive to the effective number ofspecies at the time of nucleosynthesis, g ∗ = g(T ≃ 1 MeV). With somesimplifications, the dependence on g ∗ can be understood as follows. A crucialparameter in the computations of nucleosynthesis is the ratio of the numberdensity of neutrons, n n , to the number density of protons, n p . As long as thermalequilibrium is maintained we have (for non-relativistic nucleons, as appropriateat T ∼ 1 MeV) n n /n p = exp(−Q/T ) where Q = m n − m p ≃ 1.3 MeV.Equilibrium is maintained by the process pe ↔ nν, with width Ɣ pe→nν , as longas this width is greater than H . When the rate drops below the Hubble constantH , the process cannot compete anymore with the expansion of the universe and,