362 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
Lyman-alpha transfer in primordial hydrogen recombination
Cosmological constraints from the cosmic microwave background (CMB)
anisotropies rely on accurate theoretical calculations of the cosmic
recombination history. Recent work has emphasized the importance of radiative
transfer calculations due to the high optical depth in the HI Lyman lines.
Transfer in the Lyman-alpha line is dominated by true emission and absorption,
Hubble expansion, and resonant scattering. Resonant scattering causes photons
to diffuse in frequency due to random kicks from the thermal velocities of
hydrogen atoms, and also to drift toward lower frequencies due to energy loss
via atomic recoil. Past analyses of Lyman-alpha transfer during the
recombination era have either considered a subset of these processes, ignored
time dependence, or incorrectly assumed identical emission and absorption
profiles. We present here a fully time-dependent radiative transfer calculation
of the Lyman-alpha line including all of these processes, and compare it to
previous results that ignored the resonant scattering. We find a faster
recombination due to recoil enhancement of the Lyman-alpha escape rate, leading
to a reduction in the free electron density of 0.45% at z=900. This results in
an increase in the small-scale CMB power spectrum that is negligible for the
current data but will be a 0.9 sigma correction for Planck. We discuss the
reasons why we find a smaller correction than some other recent computations.Comment: 16 pages, 7 figures, matches PRD accepted version. Fixed bug in
numerical transport code, resulting in slightly reduced effect on
recombination histor
Spectroscopic source redshifts and parameter constraints from weak lensing and the cosmic microwave background
Weak lensing is a potentially robust and model-independent cosmological probe, but its accuracy is dependent on knowledge of the redshift distribution of the source galaxies used. The most robust way to determine the redshift distribution is via spectroscopy of a subsample of the source galaxies. We forecast constraints from combining cosmic microwave background (CMB) anisotropies with cosmic shear using a spectroscopically determined redshift distribution, varying the number of spectra Nspec obtained from 64 to [infinity]. The source redshift distribution is expanded in a Fourier series, and the amplitudes of each mode are considered as parameters to be constrained via both the spectroscopic and weak lensing data. We assume independent source redshifts, and consider in what circumstances this is a good approximation (the sources are clustered and for narrow spectroscopic surveys with many objects this results in the redshifts being correlated). It is found that for the surveys considered and for a prior of 0.04 on the calibration parameters, the addition of redshift information makes significant improvements on the constraints on the cosmological parameters; however, beyond Nspec ~ few × 10^3 the addition of further spectra will make only a very small improvement to the cosmological parameters. We find that a better calibration makes large Nspec more useful. Using an eigenvector analysis, we find that the improvement continues with even higher Nspec, but not in directions that dominate the uncertainties on the standard cosmological parameters
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
Detecting primordial gravitational waves with circular polarization of the redshifted 21 cm line: II. Forecasts
In the first paper of this series, we showed that the CMB quadrupole at high
redshifts results in a small circular polarization of the emitted 21 cm
radiation. In this paper we forecast the sensitivity of future radio
experiments to measure the CMB quadrupole during the era of first cosmic light
(). The tomographic measurement of 21 cm circular polarization allows
us to construct a 3D remote quadrupole field. Measuring the -mode component
of this remote quadrupole field can be used to put bounds on the
tensor-to-scalar ratio . We make Fisher forecasts for a future Fast Fourier
Transform Telescope (FFTT), consisting of an array of dipole antennas in a
compact grid configuration, as a function of array size and observation time.
We find that a FFTT with a side length of 100 km can achieve after ten years of observation and with a sky coverage
. The forecasts are dependent on the evolution of the
Lyman- flux in the pre-reionization era, that remains observationally
unconstrained. Finally, we calculate the typical order of magnitudes for
circular polarization foregrounds and comment on their mitigation strategies.
We conclude that detection of primordial gravitational waves with 21 cm
observations is in principle possible, so long as the primordial magnetic field
amplitude is small, but would require a very futuristic experiment with
corresponding advances in calibration and foreground suppression techniques.Comment: 19 pages, matches PRD accepted versio
Cosmological hydrogen recombination: The effect of extremely high-n states
Calculations of cosmological hydrogen recombination are vital for the
extraction of cosmological parameters from cosmic microwave background (CMB)
observations, and for imposing constraints to inflation and re-ionization. The
Planck} mission and future experiments will make high precision measurements of
CMB anisotropies at angular scales as small as l~2500, necessitating a
calculation of recombination with fractional accuracy of ~10^{-3}. Recent work
on recombination includes two-photon transitions from high excitation states
and many radiative transfer effects. Modern recombination calculations
separately follow angular momentum sublevels of the hydrogen atom to accurately
treat non-equilibrium effects at late times (z<900). The inclusion of extremely
high-n (n>100) states of hydrogen is then computationally challenging,
preventing until now a determination of the maximum n needed to predict CMB
anisotropy spectra with sufficient accuracy for Planck. Here, results from a
new multi-level-atom code (RecSparse) are presented. For the first time,
`forbidden' quadrupole transitions of hydrogen are included, but shown to be
negligible. RecSparse is designed to quickly calculate recombination histories
including extremely high-n states in hydrogen. Histories for a sequence of
values as high as n_max=250 are computed, keeping track of all angular momentum
sublevels and energy shells of the hydrogen atom separately. Use of an
insufficiently high n_max value (e.g., n_max=64) leads to errors (e.g., 1.8
sigma for Planck) in the predicted CMB power spectrum. Extrapolating errors,
the resulting CMB anisotropy spectra are converged to 0.5 sigma at
Fisher-matrix level for n_max=128, in the purely radiative case.Comment: 19 pages, 12 figures, replaced with version published in Physical
Review D (added discussion of collisions)
Ultrafast effective multi-level atom method for primordial hydrogen recombination
Cosmological hydrogen recombination has recently been the subject of renewed
attention because of its importance for predicting the power spectrum of cosmic
microwave background anisotropies. It has become clear that it is necessary to
account for a large number n >~ 100 of energy shells of the hydrogen atom,
separately following the angular momentum substates in order to obtain
sufficiently accurate recombination histories. However, the multi-level atom
codes that follow the populations of all these levels are computationally
expensive, limiting recent analyses to only a few points in parameter space. In
this paper, we present a new method for solving the multi-level atom
recombination problem, which splits the problem into a computationally
expensive atomic physics component that is independent of the cosmology, and an
ultrafast cosmological evolution component. The atomic physics component
follows the network of bound-bound and bound-free transitions among excited
states and computes the resulting effective transition rates for the small set
of "interface" states radiatively connected to the ground state. The
cosmological evolution component only follows the populations of the interface
states. By pre-tabulating the effective rates, we can reduce the recurring cost
of multi-level atom calculations by more than 5 orders of magnitude. The
resulting code is fast enough for inclusion in Markov Chain Monte Carlo
parameter estimation algorithms. It does not yet include the radiative transfer
or high-n two-photon processes considered in some recent papers. Further work
on analytic treatments for these effects will be required in order to produce a
recombination code usable for Planck data analysis.Comment: Version accepted by Phys. Rev. D. Proof of equivalence of effective
and standard MLA methods moved to the main text. Some rewording
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