Tensor-Induced CMB Temperature-Polarization Correlation in Reionized Universes

We reexamine the temperature-polarization correlation function of the cosmic microwave background induced by tensor mode with a scale-invariant spectrum in reionized standard cold dark matter models. It is found that the sign of the correlation function is positive on all angular scales even in a model with substantial reionization. PACS numbers: 98.70.Vc, 98.80.Es Typeset using REVTEX ∗[email protected] 1 The detection of the large-angle anisotropy of the cosmic microwave background (CMB) by the COBE DMR experiment [1] has incited a lot of studies in this area [2]. It is now well established that CMB anisotropies are genuine imprint of the early universe, which could potentially be used to determine to a high precision virtually all cosmological parameters of interest [3]. Future missions such as NASA MAP and ESA Planck Surveyor would measure the anisotropy spectrum in high-precision; the polarization spectrum, expected with an order of magnitude below the anisotropy, would also be measured to provide complementary information to anisotropy. It was first pointed out by Crittenden et al. that the correlation between the temperature and polarization anisotropies offers a test of physics on the last scattering surface, as well as a possibility of distinguishing the scalar and tensor perturbations [4,5]. They found that in a universe with standard recombination the sign of the tensor-induced temperaturepolarization (TQ) correlation function is opposite to that for scalar mode on large scales. With substantial early ionization, polarization is greatly enhanced on large scales and a geometrical effect causes the tensor correlation function to reverse sign for θ > 30 [5]. TQ correlation will be measured by MAP and Planck at small scales. In addition, polarization experiments such as ground-based POLAR [6] and SPOrt/ISSA [7] will observe large-scale polarization as to test the thermal history of the early universe. In particular, the latter with full-sky coverage will be sensitive to TQ correlation [8]. Although TQ correlation has been studied extensively [9,10], it is worthwhile to reexamine and work out explicitly the TQ correlation function in reionized universes. We will follow closely the method of Ref. [4,5]. We find a correction term to their tensor correlation function that renders it a positive function irrespective of the reionization history. Our result should be useful to the large-scale polarization experiments. Here we do not repeat detailed calculations. Only necessary steps for obtaining correlation functions are given. For tensor +-mode, the Stokes parameters induced by a Fourier mode with wavevector k in the direction of an unit vector p̂ are: