Cosmological background of gravitational waves

Abstract

Several different astrophysical sources of gravitational radiation have been discussed at this workshop. I would like to briefly review expected properties of the cosmological background of gravitational waves. Let me however begin with a general introduction. After formulating the general theory of relativity Albert Einstein showed that in the weak field approximation equations of general relativity possess wave like solutions. Let the background spacetime be the Minkowski spacetime parametrized by the Cartesian coordinates, then ηαβ = Diag||+ 1,−1,−1,−1||, (1) where α, β = 0, 1, · · · , 3. Slightly perturbed Minkowski spacetime will be described by the metric tensor gαβ(x ) = ηαβ + hαβ(x ), (2) where hαβ(x) ≪ 1 represent small perturbations. Using the standard definition of the Ricci tensor and keeping only terms linear in h we obtain