73,601 research outputs found
Improving small-scale CMB lensing reconstruction
Over the past decade, the gravitational lensing of the Cosmic Microwave
Background (CMB) has become a powerful tool for probing the matter distribution
in the Universe. The standard technique used to reconstruct the CMB lensing
signal employs the quadratic estimator (QE) method, which has recently been
shown to be suboptimal for lensing measurements on very small scales in
temperature and polarization data. We implement a simple, more optimal method
for the small-scale regime, which involves taking the direct inverse of the
background gradient. We derive new techniques to make continuous maps of
lensing using this "Gradient-Inversion" (GI) method and validate our method
with simulated data, finding good agreement with predictions. For idealized
simulations of lensing cross- and autospectra that neglect foregrounds, we
demonstrate that our method performs significantly better than previous
quadratic estimator methods in temperature; at , it reduces errors
on the lensing auto-power spectrum by a factor of for both idealized
CMB-S4 and Simons Observatory-like experiments and by a factor of
for cross-correlations of CMB-S4-like lensing reconstruction and the true
lensing field. We caution that the level of the neglected small-scale
foreground power, while low in polarization, is very high in temperature;
though we briefly outline foreground mitigation methods, further work on this
topic is required. Nevertheless, our results show the future potential for
improved small-scale CMB lensing measurements, which could provide stronger
constraints on cosmological parameters and astrophysics at high redshifts
CMB Lensing Reconstruction in Real Space
We explore the reconstruction of the gravitational lensing field of the
cosmic microwave background in real space showing that very little statistical
information is lost when estimators of short range on the celestial sphere are
used in place of the customary estimators in harmonic space, which are nonlocal
and in principle require a simultaneous analysis of the entire sky without any
cuts or excisions. Because virtually all the information relevant to lensing
reconstruction lies on angular scales close to the resolution scale of the sky
map, the gravitational lensing dilatation and shear fields (which unlike the
deflection field or lensing potential are directly related to the observations
in a local manner) may be reconstructed by means of quadratic combinations
involving only very closely separated pixels. Even though harmonic space
provides a more natural context for understanding lensing reconstruction
theoretically, the real space methods developed here have the virtue of being
faster to implement and are likely to prove useful for analyzing realistic maps
containing a galactic cut and possibly numerous small excisions to exclude
point sources that cannot be reliably subtracted.Comment: 21 pages, 8 figure
Reconstruction of signals with unknown spectra in information field theory with parameter uncertainty
The optimal reconstruction of cosmic metric perturbations and other signals
requires knowledge of their power spectra and other parameters. If these are
not known a priori, they have to be measured simultaneously from the same data
used for the signal reconstruction. We formulate the general problem of signal
inference in the presence of unknown parameters within the framework of
information field theory. We develop a generic parameter uncertainty
renormalized estimation (PURE) technique and address the problem of
reconstructing Gaussian signals with unknown power-spectrum with five different
approaches: (i) separate maximum-a-posteriori power spectrum measurement and
subsequent reconstruction, (ii) maximum-a-posteriori power reconstruction with
marginalized power-spectrum, (iii) maximizing the joint posterior of signal and
spectrum, (iv) guessing the spectrum from the variance in the Wiener filter
map, and (v) renormalization flow analysis of the field theoretical problem
providing the PURE filter. In all cases, the reconstruction can be described or
approximated as Wiener filter operations with assumed signal spectra derived
from the data according to the same recipe, but with differing coefficients.
All of these filters, except the renormalized one, exhibit a perception
threshold in case of a Jeffreys prior for the unknown spectrum. Data modes,
with variance below this threshold do not affect the signal reconstruction at
all. Filter (iv) seems to be similar to the so called Karhune-Loeve and
Feldman-Kaiser-Peacock estimators for galaxy power spectra used in cosmology,
which therefore should also exhibit a marginal perception threshold if
correctly implemented. We present statistical performance tests and show that
the PURE filter is superior to the others.Comment: 21 pages, 5 figures, accepted by PR
CMB lensing reconstruction using cut sky polarization maps and pure B modes
Detailed measurements of the CMB lensing signal are an important scientific goal of ongoing groundbased CMB polarization experiments, which are mapping the CMB at high resolution over small patches of the sky. In this work we simulate CMB polarization lensing reconstruction for the EE and EB quadratic estimators with current-generation noise levels and resolution, and show that without boundary effects the known and expected zeroth and first order Nð0Þ and Nð1Þ biases provide an adequate model for nonsignal contributions to the lensing power spectrum estimators. Small sky areas present a number of additional challenges for polarization lensing reconstruction, including leakage of E modes into B modes. We show how simple windowed estimators using filtered pure B modes can greatly reduce the mask-induced meanfield lensing signal and reduce variance in the estimators. This provides a simple method (used with recent observations) that gives an alternative to more optimal but expensive inverse-variance filtering
Reconstruction of signals with unknown spectra in information field theory with parameter uncertainty
The optimal reconstruction of cosmic metric perturbations and other signals
requires knowledge of their power spectra and other parameters. If these are
not known a priori, they have to be measured simultaneously from the same data
used for the signal reconstruction. We formulate the general problem of signal
inference in the presence of unknown parameters within the framework of
information field theory. We develop a generic parameter uncertainty
renormalized estimation (PURE) technique and address the problem of
reconstructing Gaussian signals with unknown power-spectrum with five different
approaches: (i) separate maximum-a-posteriori power spectrum measurement and
subsequent reconstruction, (ii) maximum-a-posteriori power reconstruction with
marginalized power-spectrum, (iii) maximizing the joint posterior of signal and
spectrum, (iv) guessing the spectrum from the variance in the Wiener filter
map, and (v) renormalization flow analysis of the field theoretical problem
providing the PURE filter. In all cases, the reconstruction can be described or
approximated as Wiener filter operations with assumed signal spectra derived
from the data according to the same recipe, but with differing coefficients.
All of these filters, except the renormalized one, exhibit a perception
threshold in case of a Jeffreys prior for the unknown spectrum. Data modes,
with variance below this threshold do not affect the signal reconstruction at
all. Filter (iv) seems to be similar to the so called Karhune-Loeve and
Feldman-Kaiser-Peacock estimators for galaxy power spectra used in cosmology,
which therefore should also exhibit a marginal perception threshold if
correctly implemented. We present statistical performance tests and show that
the PURE filter is superior to the others.Comment: 21 pages, 5 figures, accepted by PR
Reconstructing Projected Matter Density from Cosmic Microwave Background
Gravitational lensing distorts the cosmic microwave background (CMB)
anisotropies and imprints a characteristic pattern onto it. The distortions
depend on the projected matter density between today and redshift . In this paper we develop a method for a direct reconstruction of the
projected matter density from the CMB anisotropies. This reconstruction is
obtained by averaging over quadratic combinations of the derivatives of CMB
field. We test the method using simulations and show that it can successfully
recover projected density profile of a cluster of galaxies if there are
measurable anisotropies on scales smaller than the characteristic cluster size.
In the absence of sufficient small scale power the reconstructed maps have low
signal to noise on individual structures, but can give a positive detection of
the power spectrum or when cross correlated with other maps of large scale
structure. We develop an analytic method to reconstruct the power spectrum
including the effects of noise and beam smoothing. Tests with Monte Carlo
simulations show that we can recover the input power spectrum both on large and
small scales, provided that we use maps with sufficiently low noise and high
angular resolution.Comment: 21 pages, 9 figures, submitted to PR
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