Radio Astronomy and Cosmology (eBook)

337 F(e) = (z) where the angle between the directions III and 112 is equal to 8. r is the angular diameter effective distance of the epoch for recombination. F (8) ~ve have F(e) : f (e) ~ (S"e; ) e. . ~ is a Bessel function. It is assumed here that the spectrum of gravitational waves takes the form 1/ hI'::: hoK for all relevant wavelengths, a is beam width of the radio antenna, d/= d~, and ~ is the duration of the process of recombinations in /-time. The results for different beam widths are shown in Fig. 1. 338 I. D. NOVIKOV 1-. . . -__ 0. 5 1 1. 5 2 e' 0. 5 o and for a l' (solid line) and Fig. 1. The function f(8) for n for a = 2' (dotted line). These formula should be used in analysing the implications of future observations. Comparison with the observational data now available enables us to establish an upper limit for the energy density of long gravitational waves. This method is most sensitive for gravitational waves with A ~ ct The fluctuations ~; due to these waves have scale ~ 0. 03 GW rec 4 radian. If, according to modern observations, we take ~; < 10- , then 8 26 ~GW/Ey < 10- for those gravitational waves which have A = 5. 10 cm GW today where Ey is the energy density of relict radiation. The fluctuations ~TT due to long gravitational waves with A = ct .