1,037 research outputs found
Analyzing weak lensing of the cosmic microwave background using the likelihood function
Future experiments will produce high-resolution temperature maps of the cosmic microwave background (CMB) and are expected to reveal the signature of gravitational lensing by intervening large-scale structures. We construct all-sky maximum-likelihood estimators that use the lensing effect to estimate the projected density (convergence) of these structures, its power spectrum, and cross-correlation with other observables. This contrasts with earlier quadratic-estimator approaches that Taylor expanded the observed CMB temperature to linear order in the lensing deflection angle; these approaches gave estimators for the temperature-convergence correlation in terms of the CMB three-point correlation function and for the convergence power spectrum in terms of the CMB four-point correlation function, which can be biased and nonoptimal due to terms beyond the linear order. We show that for sufficiently weak lensing, the maximum-likelihood estimator reduces to the computationally less demanding quadratic estimator. The maximum likelihood and quadratic approaches are compared by evaluating the root-mean-square (rms) error and bias in the reconstructed convergence map in a numerical simulation; it is found that both the rms errors and bias are of order 1 percent for the case of Planck and of order 10–20 percent for a 1 arcminute beam experiment. We conclude that for recovering lensing information from temperature data acquired by these experiments, the quadratic estimator is close to optimal, but further work will be required to determine whether this is also the case for lensing of the CMB polarization field
Intrinsic alignment-lensing interference as a contaminant of cosmic shear
Cosmic shear surveys have great promise as tools for precision cosmology, but can be subject to systematic errors including intrinsic ellipticity correlations of the source galaxies. The intrinsic alignments are believed to be small for deep surveys, but this is based on intrinsic and lensing distortions being uncorrelated. Here we show that the gravitational lensing shear and intrinsic shear need not be independent: correlations between the tidal field and the intrinsic shear cause the intrinsic shear of nearby galaxies to be correlated with the gravitational shear acting on more distant galaxies. We estimate the magnitude of this effect for two simple intrinsic-alignment models: one in which the galaxy ellipticity is linearly related to the tidal field, and one in which it is quadratic in the tidal field as suggested by tidal torque theory. The first model predicts a gravitational-intrinsic (GI) correlation that can be much greater than the intrinsic-intrinsic (II) correlation for broad redshift distributions, and that remains when galaxies pairs at similar redshifts are rejected. The second model, in its simplest form, predicts no gravitational-intrinsic correlation. In the first model, and assuming a normalization consistent with recently claimed detections of intrinsic correlations, we find that the GI correlation term can exceed the usual II term by >1 order of magnitude and the intrinsic correlation induced B-mode by 2 orders of magnitude. These interference effects can suppress the lensing power spectrum for a single broad redshift bin by of order ∼10% at zs=1 and ∼30% at zs=0.5. We conclude that, depending on the intrinsic-alignment model, the GI correlation may be the dominant contaminant of the lensing signal and can even affect cross spectra between widely separated bins. We describe two ways to constrain this effect, one based on density-shear correlations and one based on scaling of the cross correlation tomography signal with redshift
Reconstruction of lensing from the cosmic microwave background polarization
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 produce a curl
component of the lensing deflection field that cannot be described by a
potential; we show that this does not significantly affect the reconstruction
at noise levels greater than 0.25 microK arcmin. The reduction of the mean
squared error in the lensing reconstruction relative to the quadratic method
can be as much as a factor of two at noise levels of 1.4 microK arcmin to a
factor of ten at 0.25 microK arcmin, depending on the angular scale of
interest.Comment: matches PRD accepted version. 28 pages, 8 fig
Lensing effect on polarization in microwave background: extracting convergence power spectrum
Matter inhomogeneities along the line of sight deflect the cosmic microwave
background (CMB) photons originating at the last scattering surface at redshift
. These distortions modify the pattern of CMB polarization. We
identify specific combinations of Stokes and parameters that correspond
to spin 0, variables and can be used to reconstruct the projected matter
density. We compute the expected signal to noise as a function of detector
sensitivity and angular resolution. With Planck satellite the detection would
be at a few level. Several times better detector sensitivity would be
needed to measure the projected dark matter power spectrum over a wider range
of scales, which could provide an independent confirmation of the projected
matter power spectrum as measured from other methods.Comment: 17 pages, 5 figures, accepted for publication in PR
Polarization of the Microwave Background in Defect Models
We compute the polarization power spectra for global strings, monopoles,
textures and nontopological textures, and compare them to inflationary models.
We find that topological defect models predict a significant (1 microK)
contribution to magnetic type polarization on degree angular scales, which is
produced by the large vector component of the defect source. We also
investigate the effect of decoherence on polarization. It leads to a smoothing
of acoustic oscillations both in temperature and polarization power spectra and
strongly suppresses the cross-correlation between temperature and polarization
relative to inflationary models. Presence or absence of magnetic polarization
or cross-correlation would be a strong discriminator between the two theories
of structure formation and will be testable with the next generation of CMB
satellites.Comment: 4 pages, 3 figures, RevTeX fil
Lensing Induced Cluster Signatures in Cosmic Microwave Background
We show that clusters of galaxies induce step-like wiggles on top of the
cosmic microwave background (CMB). The direction of the wiggle is parallel to
the large scale gradient of CMB allowing one to isolate the effect from other
small scale fluctuations. The effect is sensitive to the deflection angle
rather than its derivative (shear or magnification) and is thus tracing outer
parts of the cluster with higher sensitivity than some other methods. A typical
amplitude of the effect is where
is the velocity dispersion of the cluster and several
signals extend out to a fraction of a degree. We derive the expressions for the
temperature profile for several simple parameterized cluster models and
identify some degeneracies between parameters. Finally, we discuss how to
separate this signal from other imprints on CMB using custom designed filters.
Detection of this effect is within reach of the next generation of small scale
CMB telescopes and could provide information about the cluster density profile
beyond the virial radius.Comment: 10 pages, 3 figures, submitted to Ap
Lensing of the CMB: Non Gaussian aspects
We study the generation of CMB anisotropies by gravitational lensing on small
angular scales. We show these fluctuations are not Gaussian. We prove that the
power spectrum of the tail of the CMB anisotropies on small angular scales
directly gives the power spectrum of the deflection angle. We show that the
generated power on small scales is correlated with the large scale gradient.
The cross correlation between large scale gradient and small scale power can be
used to test the hypothesis that the extra power is indeed generated by
lensing. We compute the three and four point function of the temperature in the
small angle limit. We relate the non-Gaussian aspects presented in this paper
as well as those in our previous studies of the lensing effects on large scales
to the three and four point functions. We interpret the statistics proposed in
terms of different configurations of the four point function and show how they
relate to the statistic that maximizes the S/N.Comment: Changes to match accepted version in PRD, 20 pages 10 figures. Better
resolution images of the figures can be found at
http://www.sns.ias.edu/~matiasz/RESEARCH/cmblensing.htm
Gravitational lensing as a contaminant of the gravity wave signal in CMB
Gravity waves (GW) in the early universe generate B-type polarization in the
cosmic microwave background (CMB), which can be used as a direct way to measure
the energy scale of inflation. Gravitational lensing contaminates the GW signal
by converting the dominant E polarization into B polarization. By
reconstructing the lensing potential from CMB itself one can decontaminate the
B mode induced by lensing. We present results of numerical simulations of B
mode delensing using quadratic and iterative maximum-likelihood lensing
reconstruction methods as a function of detector noise and beam. In our
simulations we find the quadratic method can reduce the lensing B noise power
by up to a factor of 7, close to the no noise limit. In contrast, the iterative
method shows significant improvements even at the lowest noise levels we
tested. We demonstrate explicitly that with this method at least a factor of 40
noise power reduction in lensing induced B power is possible, suggesting that
T/S=10^-6 may be achievable in the absence of sky cuts, foregrounds, and
instrumental systematics. While we do not find any fundamental lower limit due
to lensing, we find that for high-sensitivity detectors residual lensing noise
dominates over the detector noise.Comment: 6 pages, 2 figures, submitted to PR
Early reionization by decaying particles and cosmic microwave background radiation
We study the reionization scenario in which ionizing UV photons emitted from
decaying particle, in addition to usual contributions from stars and quasars,
ionize the universe. It is found that the scenario is consistent with both the
first year data of the Wilkinson Microwave Anisotropy Probe and the fact that
the universe is not fully ionized until z \sim 6 as observed by Sloan Digital
Sky Survey. Likelihood analysis revealed that rather broad parameter space can
be chosen. This scenario will be discriminated by future observations,
especially by the EE polarization power spectrum of cosmic microwave background
radiation.Comment: 5 pages, 5 figures, fig 2, table 1, and some typos are correcte
Detection of large scale intrinsic ellipticity-density correlation from the Sloan Digital Sky Survey and implications for weak lensing surveys
The power spectrum of weak lensing shear caused by large-scale structure is
an emerging tool for precision cosmology, in particular for measuring the
effects of dark energy on the growth of structure at low redshift. One
potential source of systematic error is intrinsic alignments of ellipticities
of neighbouring galaxies (II correlation) that could mimic the correlations due
to lensing. A related possibility pointed out by Hirata and Seljak (2004) is
correlation between the intrinsic ellipticities of galaxies and the density
field responsible for gravitational lensing shear (GI correlation). We present
constraints on both the II and GI correlations using 265 908 spectroscopic
galaxies from the SDSS, and using galaxies as tracers of the mass in the case
of the GI analysis. The availability of redshifts in the SDSS allows us to
select galaxies at small radial separations, which both reduces noise in the
intrinsic alignment measurement and suppresses galaxy- galaxy lensing (which
otherwise swamps the GI correlation). While we find no detection of the II
correlation, our results are nonetheless statistically consistent with recent
detections found using the SuperCOSMOS survey. In contrast, we have a clear
detection of GI correlation in galaxies brighter than L* that persists to the
largest scales probed (60 Mpc/h) and with a sign predicted by theoretical
models. This correlation could cause the existing lensing surveys at z~1 to
underestimate the linear amplitude of fluctuations by as much as 20% depending
on the source sample used, while for surveys at z~0.5 the underestimation may
reach 30%. (Abridged.)Comment: 16 pages, matches version published in MNRAS (only minor changes in
presentation from original version
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