Polarization of the Microwave Background in Inflationary Cosmology

Abstract

We evaluate the large scale polarization of the cosmic microwave background induced, via Thomson scattering prior to decoupling, by nearly scale-invariant spectra of scalar and tensor metric perturbations, such as those predicted by most inflationary models of the early Universe. We solve the radiative transfer equation for the polarized photon distribution function analytically, for wavelengths of order or larger than the horizon size at decoupling, assuming no reionization. The induced polarization is proportional to the redshift induced by the perturbations at decoupling and to the duration of the decoupling transition. Normalizing the spectra to the quadrupole anisotropy measured by the COBE satellite, the expected degree of linear polarization is $P\lsim 10^{-7}$, more than two orders of magnitude smaller than current bounds. The dependence of $P$ with the tilt in the spectrum away from scale invariance is too weak to be of observational relevance or to provide a sensitive discrimination between scalar and tensor fluctuations. The variation of $P$ with the angular scale is significant.

11 pages, (1 figure, not included, available upon request), LaTex file

References in corpus (8)

• COBE, Gravitational Waves, Inflation and Extended Inflation
• Cosmic Microwave Background Probes Models of Inflation
• The Imprint of Gravitational Waves on the Cosmic Microwave Background
• Polarization of the Microwave Background due to Primordial Gravitational Waves
• Grand Unification, Gravitational Waves, and the Cosmic Microwave Background Anisotropy
• Observing the Inflaton Potential
• The gravitational wave contribution to CMB anisotropies and the amplitude of mass fluctuations from COBE results
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