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

Chapter 12Generalities on the stochastic GWbackground12.1 IntroductionThe stochastic gravitational-wave background (SGWB) is a random noise ofgravity waves with no evidence of any sharp specific characters in either the timeor frequency domain. The important fact to note is that with the exception of acomponent associated with the random superposition of many weak signals frombinary-star systems, the SGWB could be the result of processes that took placeduring the early stages of the evolution of the universe.This potential cosmological origin clearly emerges from the calculation ofthe time at which the graviton decouples from the evolution of the rest of theuniverse. For a given particle species the decoupling time t dec is defined as thetime when its interaction rate Ɣ equals the expansion rate of the universe, asmeasured by the Hubble parameter H . In fact, it can be shown [1] that, underassumptions usually met, the number of interactions that the particle species sufferfrom t dec onward is less than one. This implies that the spectrum of a particlespecies produced after the decoupling retains memory of the state of the universeat that time. The only change in the character of these particles is a redshift of themagnitude of their three-momentum due to the expansion of the universe.On purely dimensional grounds, at a given temperature T the interaction ratefor particles that interact only gravitationally is [1]:Ɣ ∼ G 2 N T 5 = T 5where G is the Newton constant and M Pl = 1/ √ G = 1.22 × 10 19 GeV is thePlanck mass (we always use units ¯h = c = k B = 1). Because in the radiationdominatedera (before the time t eq of equal matter and radiation energy density)H ∼ T 2 /M Pl , one has:T dec ∼ M Pl .M 4 Pl181