OPEN UNIVERSE GRISHCHUK-ZELDOVICH EFFECT

The Grishchuk-Zel'dovich effect is the contribution to the microwave b ackground anisotropy from an extremely large scale adiabatic density p erturbation, on the standard hypothesis that this perturbation is a ty pical realization of a homogeneous Gaussian random field. We analyze t his effect in open universes, corresponding to a density parameter Ome ga(0) < 1 with no cosmological constant, and concentrate on the recent ly discussed supercurvature modes. The effect is present in all of the low multipoles of the anisotropy, in contrast with the Omega(0) = 1 c ase where only the quadrupole receives a contribution. However, for no value of Omega(0) can a very large scale perturbation generate a spec trum capable of matching observations across a wide range of multipole s. We evaluate the magnitude of the effect coming from a given wave nu mber as a function of the magnitude of the density perturbation, conve niently specified by the mean-square curvature perturbation. From the absence of the effect at the observed level, we find that, for 0.25 le ss than or equal to Omega(0) less than or equal to 0.8, a curvature pe rturbation of order unity is permitted only for inverse wave numbers m ore than one thousand times the size of the observable universe, As Om ega(0) tends to one, the constraint weakens to the flat space result t hat the inverse wave number be more than a 100 times the size of the o bservable universe, whereas for Omega(0) < 0.25 it becomes stronger. W e explain the physical meaning of these results, by relating them to t he correlation length of the perturbation. Finally, in an Appendix we consider the dipole anisotropy and show that it always leads to weaker constraints.