Tensor perturbations in inflationary models as a probe of cosmology

In principle, the tensor metric (gravity-wave) perturbations that arise in inflationary models can, beyond probing the underlying inflationary model, provide information about the Universe: ionization history, presence of a cosmological constant, and epoch of matter-radiation equality. Because tensor perturbations give rise to the anisotropy of the cosmic background radiation (CBR) solely through the Sachs-Wolfe effect we are able to calculate analytically their contribution to the variance of the multipole moments of the CBR temperature anisotropy. In so doing, we carefully take account of the effect of tensor perturbations that entered the Hubble radius during both the matter-dominated and radiation-dominated epochs by means of a transfer function. (Previously, only those modes that entered during the matter era were properly taken into account.) The striking feature in the spectrum of multipole amplitudes is a dramatic falloff for l≳ √1+${\mathit{z}}_{\mathrm{LSS}}$ , where ${\mathit{z}}_{\mathrm{LSS}}$ is the redshift of the last-scattering surface, which depends upon the ionization history of the Universe. Finally, using our transfer function we provide a more precise formula for the energy density in stochastic gravitational waves from inflation, and, using the Cosmic Background Explorer Differential Microwave Radiometer (COBE DMR) quadrupole normalization, we express this energy density in terms of the ‘‘tilt’’ of the spectrum of tensor perturbations alone and show that it is unlikely that the stochastic background of gravity waves can be detected directly in the foreseeable future.