We have constructed the first all-sky CMB temperature and polarization lensed maps based on a high-resolution cosmological N-body simulation, the Millennium Simulation (MS). We have exploited the lensing potential map obtained using a map-making procedure (Carbone et al. 2008) which integrates along the line-of-sight the MS dark matter distribution by stacking and randomizing the simulation boxes up to $z = 127$, and which semi-analytically supplies the large-scale power in the angular lensing potential that is not correctly sampled by the N-body simulation. The lensed sky has been obtained by properly modifying the latest version of the LensPix code (Lewis 2005) to account for the MS structures. We have also produced all-sky lensed maps of the so-called $ψ_E$ and $ψ_B$ potentials, which are directly related to the electric and magnetic types of polarization. The angular power spectra of the simulated lensed temperature and polarization maps agree well with semi-analytic estimates up to $l < 2500$, while on smaller scales we find a slight excess of power which we interpret as being due to non-linear clustering in the MS. We also observe how non-linear lensing power in the polarised CMB is transferred to large angular scales by suitably misaligned modes in the CMB and the lensing potential. This work is relevant in view of the future CMB probes, as a way to analyse the lensed sky and disentangle the contribution from primordial gravitational waves.
Weak lensing of the CMB changes the unlensed temperature anisotropy and polarization power spectra. Accounting for the lensing effect will be crucial to obtain accurate parameter constraints from sensitive CMB observations. Methods for computing the lensed power spectra using a low-order perturbative expansion are not good enough for percent-level accuracy. Non-perturbative flat-sky methods are more accurate, but curvature effects change the spectra at the 0.3-1% level. We describe a new, accurate and fast, full-sky correlation-function method for computing the lensing effect on CMB power spec…
Modelling of the weak lensing of the CMB will be crucial to obtain correct cosmological parameter constraints from forthcoming precision CMB anisotropy observations. The lensing affects the power spectrum as well as inducing non-Gaussianities. We discuss the simulation of full sky CMB maps in the weak lensing approximation and describe a fast numerical code. The series expansion in the deflection angle cannot be used to simulate accurate CMB maps, so a pixel remapping must be used. For parameter estimation accounting for the change in the power spectrum but assuming Gaussianity is sufficient t…
Supernova distance and primary CMB anisotropy measurements provide powerful probes of the dark energy evolution in a flat universe but degrade substantially once curvature is marginalized. We show that lensed CMB polarization power spectrum measurements, accessible to next generation ground based surveys such as SPTpol or QUIET, can remove the curvature degeneracy at a level sufficient for the SNAP and Planck surveys and allow a measurement of sigma(w_p)=0.03, sigma(w_a)=0.3 jointly with sigma(Omega_K)=0.0035. This expectation assumes that the sum of neutrino masses is independently known to b…
A method for ray-tracing through n-body simulations has been recently proposed. It is based on a periodic universe covered by simulation boxes. Photons move along appropriate directions to avoid periodicity effects. Here, an improved version of this method is applied to simulate lensed CMB maps and maps of lens deformations. Particle mesh n-body simulations with appropriate boxes and resolutions are used to evolve the nonlinear inhomogeneities until present time. The resulting maps are statistically analyzed to look for deviations from Gaussianity. These deviations are measured --for the first…
Hu [Phys. Rev. D62 (2000) 043007] has presented a harmonic-space method for calculating the effects of weak gravitational lensing on the cosmic microwave background (CMB) over the full sky. Computing the lensed power spectra to first order in the deflection power requires one to formulate the lensing displacement beyond the tangent-space approximation. We point out that for CMB polarization this displacement must undergo geometric corrections on the spherical sky to maintain statistical isotropy of the lensed fields. Although not discussed by Hu, these geometric effects are implicit in his ana…
Samples of high-redshift galaxies are easy to select in the millimetre/submillimetre (mm/submm) waveband using sensitive telescopes, because their flux density-redshift relations are expected to be flat, and so the selection function is almost redshift-independent at redshifts greater than 0.5. Source counts are expected to be very steep in the mm/submm waveband, and so the magnification bias due to gravitational lensing is expected to be very large, both for lensing by field galaxies and for lensing by clusters. Recent submm-wave observations of lensed images in clusters have constrained the …
Gravitational lensing distorts the cosmic microwave background (CMB) temperature and polarization fields and encodes valuable information on distances and growth rates at intermediate redshifts into the lensed power spectra. The non-Gaussian bandpower covariance induced by the lenses is negligible to l=2000 for all but the B polarization field where it increases the net variance by up to a factor of 10 and favors an observing strategy with 3 times more area than if it were Gaussian. To quantify the cosmological information, we introduce two lensing observables, characterizing nearly all of the…
The effect of weak gravitational lensing on the cosmic microwave background (CMB) temperature anisotropies and polarization will provide access to cosmological information that cannot be obtained from the primary anisotropies alone. We compare the information content of the lensed B-mode polarization power spectrum, properly accounting for the non-Gaussian correlations between the power on different scales, with that of the unlensed CMB fields and the lensing potential. The latter represent the products of an (idealised) optimal analysis that exploits the lens-induced non-Gaussianity to recons…
Inflationary cosmologies predict Gaussian primordial fluctuations, but subsequent gravitational lensing of the CMB disturbs its Gaussianity. Knowledge of the specific signature of lensing is necessary to distinguish a lensed Gaussian sky from an intrinsically non-Gaussian one. In this paper we investigate the pattern of non-Gaussian features in the CMB resulting from gravitational lensing, both analytically and numerically. We describe the lensed CMB temperature distribution using the formalism of generating functionals and obtain the complete picture of emerging non-Gaussian effects. To test …
Several recent papers have studied lensing of the CMB by large-scale structures, which probes the projected matter distribution from $z=10^3$ to $z\simeq 0$. This interest is motivated in part by upcoming high resolution, high sensitivity CMB experiments, such as APEX/SZ, ACT, SPT or Planck, which should be sensitive to lensing. In this paper we examine the reconstruction of the large-scale dark matter distribution from lensed CMB temperature anisotropies. We go beyond previous work in using numerical simulations to include higher order, non-Gaussian effects and study how well the quadratic es…
We consider the weak lensing effect induced by linear cosmological perturbations on the cosmic microwave background (CMB) polarization anisotropies. We find that the amplitude of the lensing peak in the BB mode power spectrum is a faithful tracer of the dark energy dynamics at the onset of cosmic acceleration. This is due to two reasons. First, the lensing power is non-zero only at intermediate redshifts between the observer and the source, keeping record of the linear perturbation growth rate at the corresponding epoch. Second, the BB lensing signal is expected to dominate over the other sour…
The measurement of angular diameter distance to galaxy clusters, through combined Sunyaev-Zel'dovich (SZ) effect data with X-ray emission observations, is now a well-known probe of cosmology. Using a combination of SZ data and a map of the lensed CMB anisotropies by the galaxy cluster potential, we propose an alternative geometric technique to measure distance information primarily through cluster related multi-frequency CMB measurements. We discuss necessary requirements to implement this measurement, potential errors including systematic biases, and the extent to which cosmological parameter…
We use the large cosmological Millennium Simulation (MS) to construct the first all-sky maps of the lensing potential and the deflection angle, aiming at gravitational lensing of the CMB, with the goal of properly including small-scale non-linearities and non-Gaussianity. Exploiting the Born approximation, we implement a map-making procedure based on direct ray-tracing through the gravitational potential of the MS. We stack the simulation box in redshift shells up to $z\sim 11$, producing continuous all-sky maps with arcminute angular resolution. A randomization scheme avoids repetition of str…
Large scale structure deflects cosmic microwave background (CMB) photons. Since large angular scales in the large scale structure contribute significantly to the gravitational lensing effect, a realistic simulation of CMB lensing requires a sufficiently large sky area. We describe simulations that include these effects, and present both effective and multiple plane ray-tracing versions of the algorithm, which employs spherical harmonic space and does not use the flat sky approximation. We simulate lensed CMB maps with an angular resolution of ~0.9 arcmin. The angular power spectrum of the simu…
A new generation of CMB experiments will soon make sensitive high resolution maps of the microwave sky. At angular scales less than $\sim$10 arcminutes, most CMB anisotropies are generated at z $< 1000$, rather than at the surface of last scattering. Therefore, these maps potentially contain an enormous amount of information about the evolution of structure. Whereas spectral information can distinguish the thermal Sunyaev-Zeldovich (tSZ) effect from other anisotropies, the spectral form of anisotropies generated by the gravitational lensing and the kinetic Sunyaev-Zeldovich (kSZ) effects are i…
We give a brief review of the known effects of a dynamical vacuum cosmological component, the dark energy, on the anisotropies of the cosmic microwave background (CMB). We distinguish between a "classic" class of observables, used so far to constrain the average of the dark energy abundance in the redshift interval in which it is relevant for acceleration, and a "modern" class, aiming at the measurement of its differential redshift behavior. We show that the gravitationally lensed CMB belongs to the second class, as it can give a measure of the dark energy abundance at the time of equality wit…
Weak gravitational lensing has several important effects on the cosmic microwave background (CMB): it changes the CMB power spectra, induces non-Gaussianities, and generates a B-mode polarization signal that is an important source of confusion for the signal from primordial gravitational waves. The lensing signal can also be used to help constrain cosmological parameters and lensing mass distributions. We review the origin and calculation of these effects. Topics include: lensing in General Relativity, the lensing potential, lensed temperature and polarization power spectra, implications for c…
We discuss the four-point correlation function, or the trispectrum in Fourier space, of CMB temperature and polarization anisotropies due to the weak gravitational lensing effect by intervening large scale structure. We discuss the squared temperature power spectrum as a probe of this trispectrum and, more importantly, as an observational approach to extracting the power spectrum of the deflection angle associated with the weak gravitational lensing effect on the CMB. We extend previous discussions on the trispectrum and associated weak lensing reconstruction from CMB data by calculating non-G…
Gravitational lensing of the cosmic microwave background (CMB) polarization field has been recognized as a potentially valuable probe of the cosmological density field. We apply likelihood-based techniques to the problem of lensing of CMB polarization and show that if the B-mode polarization is mapped, then likelihood-based techniques allow significantly better lensing reconstruction than is possible using the previous quadratic estimator approach. With this method the ultimate limit to lensing reconstruction is not set by the lensed CMB power spectrum. Second-order corrections are known to pr…
Some aspects of gravitational lensing by large scale structure (LSS) are investigated. We show that lensing causes the damping tail of the cosmic microwave background (CMB) power spectrum to fall less rapidly with decreasing angular scale than previously expected. This is due to a transfer of power from larger to smaller angular scales which produces a fractional change in power spectrum that increases rapidly beyond $\ell \sim 2000$. We also find that lensing produces a nonzero mean magnification of structures on surfaces of constant redshift if weighted by area on the sky. This is a result o…
We discuss the kinetic Sunyaev-Zel'dovich (SZ) contribution to cosmic microwave background (CMB) temperature fluctuations due to coherent rotational velocity component of electrons within halos. This effect produces a distinct dipole-like temperature distribution across the the cluster, and provides a promising way to measure the angular momentum distribution of gas inside clusters. Information obtained from such a measurement may provide new insights to the origin and evolution of angular momentum in hierarchical structure formation theory. For typical, well relaxed, clusters of mass a few ti…
The curl (B) modes of cosmic microwave background (CMB) polarization anisotropies are a unique probe of the primordial background of inflationary gravitational waves (IGWs). Unfortunately, the B-mode polarization anisotropies generated by gravitational waves at recombination are confused with those generated by the mixing of gradient-mode (E-mode) and B-mode polarization anisotropies as CMB photons propagate through the Universe and are gravitationally lensed. We describe here a method for delensing CMB polarization anisotropies using observations of anisotropies in the cosmic 21-cm radiation …