Weak Lensing of the Cosmic Microwave Background by Foreground Gravitational Waves

Weak lensing distortion of the background cosmic microwave background (CMB) temperature and polarization patterns by the foreground density fluctuations is well studied in the literature. We discuss the gravitational lensing modification to CMB anisotropies and polarization by a stochastic background of primordial gravitational waves between us and the last scattering surface. While density fluctuations perturb CMB photons via gradient-type deflections only, foreground gravitational waves distort CMB anisotropies via both gradient- and curl-type displacements. The latter is a rotation of background images, while the former is related to the lensing convergence. For a primordial background of inflationary gravitational waves, with an amplitude corresponding to a tensor-to-scalar ratio below the current upper limit of $\sim$ 0.3, the resulting modifications to the angular power spectra of CMB temperature anisotropy and polarization are below the cosmic variance limit. At tens of arcminute angular scales and below, these corrections, however, are above the level at which systematics must be controlled in all-sky anisotropy and polarization maps with no instrumental noise and other secondary and foreground signals.Comment: 11 pages, 4 figures; Revised version updates the numerical calculation for several corrections to the analytical formulation of lensing by foreground gravitational waves. Main conclusions unchanged. Version accepted for publication in Phys. Rev.

Gravitational Lensing as a Probe of Quintessence

A large number of cosmological studies now suggest that roughly two-thirds of the critical energy density of the Universe exists in a component with negative pressure. If the equation of state of such an energy component varies with time, it should in principle be possible to identify such a variation using cosmological probes over a wide range in redshift. Proper detection of any time variation, however, requires cosmological probes beyond the currently studied range in redshift of $\sim$ 0.1 to 1. We extend our analysis to gravitational lensing statistics at high redshift and suggest that a reliable sample of lensed sources, out to a redshift of $\sim$ 5, can be used to constrain the variation of the equation of state, provided that both the redshift distribution of lensed sources and the selection function involved with the lensed source discovery process are known. An exciting opportunity to catalog an adequate sample of lensed sources (quasars) to probe quintessence is now available with the ongoing Sloan Digital Sky Survey. Writing $w(z)\approx w_0 + z (dw/dz)_0$, we study the expected accuracy to which the equation of state today $w_0$ and its rate of change $(dw/dz)_0$ can simultaneously be constrained. Such a determination can rule out some missing-energy candidates, such as classes of quintessence models or a cosmological constant.Comment: Accepted for publication in ApJ Letters (4 pages, including 4 figures

Gravitational Lensing and the Hubble Deep Field

We calculate the expected number of multiply-imaged galaxies in the Hubble Deep Field (HDF), using photometric redshift information for galaxies with m_I < 27 that were detected in all four HDF passbands. A comparison of these expectations with the observed number of strongly lensed galaxies constrains the current value of Omega_m-Omega_Lambda, where Omega_m is the mean mass density of the universe and Omega_Lambda is the normalized cosmological constant. Based on current estimates of the HDF luminosity function and associated uncertainties in individual parameters, our 95% confidence lower limit on Omega_m-Omega_Lambda ranges between -0.44, if there are no strongly lensed galaxies in the HDF, and -0.73, if there are two strongly lensed galaxies in the HDF. If the only lensed galaxy in the HDF is the one presently viable candidate, then, in a flat universe (Omega_m+Omega_Lambda=1), Omega_Lambda < 0.79 (95% C.L.). These limits are compatible with estimates based on high-redshift supernovae and with previous limits based on gravitational lensing.Comment: 4 pages (aipproc.sty), 2 figures. To appear in "After the dark ages: when galaxies were young," proceedings of the 9th Annual October Astrophysics Conference, eds. S. S. Holt & E. P. Smit

Future weak lensing constraints in a dark coupled universe

Coupled cosmologies can predict values for the cosmological parameters at low redshifts which may differ substantially from the parameters values within non-interacting cosmologies. Therefore, low redshift probes, as the growth of structure and the dark matter distribution via galaxy and weak lensing surveys constitute a unique tool to constrain interacting dark sector models. We focus here on weak lensing forecasts from future Euclid and LSST-like surveys combined with the ongoing Planck cosmic microwave background experiment. We find that these future data could constrain the dimensionless coupling to be smaller than a few $\times 10^{-2}$. The coupling parameter $\xi$ is strongly degenerate with the cold dark matter energy density $\Omega_{c}h^2$ and the Hubble constant $H_0$.These degeneracies may cause important biases in the cosmological parameter values if in the universe there exists an interaction among the dark matter and dark energy sectors.Comment: 8 pages, 6 figure

Non-Gaussian Covariance of CMB B-modes of Polarization and Parameter Degradation

The B-mode polarization lensing signal is a useful probe of the neutrino mass and to a lesser extent the dark energy equation of state as the signal depends on the integrated mass power spectrum between us and the last scattering surface. This lensing B-mode signal, however, is non-Gaussian and the resulting non-Gaussian covariance to the power spectrum cannot be ignored as correlations between B-mode bins are at a level of 0.1. For temperature and E-mode polarization power spectra, the non-Gasussian covariance is not significant, where we find correlations at the 10^{-5} level even for adjacent bins. The resulting degradation on neutrino mass and dark energy equation of state is about a factor of 2 to 3 when compared to the case where statistics are simply considered to be Gaussian. We also discuss parameter uncertainties achievable in upcoming experiments and show that at a given angular resolution for polarization observations, increasing the sensitivity beyond a certain noise value does not lead to an improved measurement of the neutrino mass and dark energy equation of state with B-mode power spectrum. For Planck, the resulting constraints on the sum of the neutrino masses is ~ 0.2 eV and on the dark energy equation of state parameter we find, sigma_w ~ 0.5.Comment: 11 pages, 5 figures, minor changes, submitted to PR