106 research outputs found

### Primordial Non-Gaussianity in the Cosmic Microwave Background

In the last few decades, advances in observational cosmology have given us a
standard model of cosmology. We know the content of the universe to within a
few percent. With more ambitious experiments on the way, we hope to move beyond
the knowledge of what the universe is made of, to why the universe is the way
it is. In this review paper we focus on primordial non-Gaussianity as a probe
of the physics of the dynamics of the universe at the very earliest moments. We
discuss 1) theoretical predictions from inflationary models and their
observational consequences in the cosmic microwave background (CMB)
anisotropies; 2) CMB--based estimators for constraining primordial
non-Gaussianity with an emphasis on bispectrum templates; 3) current
constraints on non-Gaussianity and what we can hope to achieve in the near
future; and 4) non-primordial sources of non-Gaussianities in the CMB such as
bispectrum due to second order effects, three way cross-correlation between
primary-lensing-secondary CMB, and possible instrumental effects.Comment: 27 pages, 8 figures; Invited Review for the Journal "Advances in
Astronomy"; references adde

### Constraining a spatially dependent rotation of the Cosmic Microwave Background Polarization

Following Kamionkowski (2008), a quadratic estimator of the rotation of the
plane of polarization of the CMB is constructed. This statistic can estimate a
spatially varying rotation angle. We use this estimator to quantify the
prospects of detecting such a rotation field with forthcoming experiments. For
PLANCK and CMBPol we find that the estimator containing the product of the E
and B components of the polarization field is the most sensitive. The variance
of this EB estimator, N(L) is roughly independent of the multipole L, and is
only weakly dependent on the instrumental beam. For FWHM of the beam size ~
5'-50', and instrument noise $\Delta_p ~ 5-50 uK-arcmin, the scaling of
variance N(L) can be fitted by a power law N(L)=3.3 x 10^{-7} \Delta^2_p
(FWHM)^{1.3} sq-deg. For small instrumental noise \Delta_p \leq 5 uK-arcmin,
the lensing B-modes become important, saturating the variance to ~10^{-6}
sq-deg even for an ideal experiment. Upcoming experiments like PLANCK will be
able to detect a power spectrum of the rotation angle, C^{\alpha \alpha}(L), as
small as 0.01 sq-deg, while futuristic experiment like CMBPol will be able to
detect rotation angle power spectrum as small as 2.5 x 10^{-5} sq-deg. We
discuss the implications of such constraints, both for the various physical
effects that can rotate the polarization as photons travel from the last
scattering surface as well as for constraints on instrumental systematics that
can also lead to a spurious rotation signal. Rotation of the CMB polarization
generates B-modes which will act as contamination for the primordial B-modes
detection. We discuss an application of our estimator to de-rotate the CMB to
increase the sensitivity for the primordial B-modes.Comment: 11 pages, 5 figure

### Detection of primordial non-Gaussianity (fNL) in the WMAP 3-year data at above 99.5% confidence

We present evidence for the detection of primordial non-Gaussianity of the
local type (fNL), using the temperature information of the Cosmic Microwave
Background (CMB) from the WMAP 3-year data. We employ the bispectrum estimator
of non-Gaussianity described in (Yadav et al. 2007) which allows us to analyze
the entirety of the WMAP data without an arbitrary cut-off in angular scale.
Using the combined information from WMAP's two main science channels up to
lmax=750 and the conservative Kp0 foreground mask we find 27 < fNL < 147 at 95%
C.L., with a central value of fNL=87. This corresponds to a rejection of fNL=0
at more than 99.5% significance. We find that this detection is robust to
variations in lmax, frequency and masks, and that no known foreground,
instrument systematic, or secondary anisotropy explains our signal while
passing our suite of tests. We explore the impact of several analysis choices
on the stated significance and find 2.5 sigma for the most conservative view.
We conclude that the WMAP 3-year data disfavors canonical single field
slow-roll inflation.Comment: 4 pages, 2 figures, 1 tables, submitted to PRL, references added. New
version has several additional tests and systematic error estimates. Results
largely unchange

### Higher-Order Gravitational Lensing Reconstruction using Feynman Diagrams

We develop a method for calculating the correlation structure of the Cosmic
Microwave Background (CMB) using Feynman diagrams, when the CMB has been
modified by gravitational lensing, Faraday rotation, patchy reionization, or
other distorting effects. This method is used to calculate the bias of the
Hu-Okamoto quadratic estimator in reconstructing the lensing power spectrum up
to O(\phi^4) in the lensing potential $\phi$. We consider both the diagonal
noise TTTT, EBEB, etc. and, for the first time, the off-diagonal noise TTTE,
TBEB, etc. The previously noted large O(\phi^4) term in the second order noise
is identified to come from a particular class of diagrams. It can be
significantly reduced by a reorganization of the $\phi$ expansion. These
improved estimators have almost no bias for the off-diagonal case involving
only one $B$ component of the CMB, such as EEEB.Comment: 17 pages, 17 figure

### Gravitational Lensing of the CMB: a Feynman Diagram Approach

We develop a Feynman diagram approach to calculating correlations of the
Cosmic Microwave Background (CMB) in the presence of distortions. As one
application, we focus on CMB distortions due to gravitational lensing by Large
Scale Structure (LSS). We study the Hu-Okamoto quadratic estimator for
extracting lensing from the CMB and derive the noise of the estimator up to
${\mathcal O}(\phi^4)$ in the lensing potential $\phi$. The previously noted
large ${\mathcal O}(\phi^4)$ term can be significantly reduced by a
reorganization of the $\phi$ expansion. Our approach makes it simple to obtain
expressions for quadratic estimators based on any CMB channel. We briefly
discuss other applications to cosmology of this diagrammatic approach, such as
distortions of the CMB due to patchy reionization, or due to Faraday rotation
from primordial axion fields.Comment: 5 pages, 8 figures, v2: journal versio

### Fast Estimator of Primordial Non-Gaussianity from Temperature and Polarization Anisotropies in the Cosmic Microwave Background

Measurements of primordial non-Gaussianity ($f_{NL}$) open a new window onto
the physics of inflation. We describe a fast cubic (bispectrum) estimator of
$f_{NL}$, using a combined analysis of temperature and polarization
observations. The speed of our estimator allows us to use a sufficient number
of Monte Carlo simulations to characterize its statistical properties in the
presence of real world issues such as instrumental effects, partial sky
coverage, and foreground contamination. We find that our estimator is optimal,
where optimality is defined by saturation of the Cramer Rao bound, if noise is
homogeneous. Our estimator is also computationally efficient, scaling as
$O(N^{3/2})$ compared to the $O(N^{5/2})$ scaling of the brute force bispectrum
calculation for sky maps with $N$ pixels. For Planck this translates into a
speed-up by factors of millions, reducing the required computing time from
thousands of years to just hours and thus making $f_{NL}$ estimation feasible
for future surveys. Our estimator in its current form is optimal if noise is
homogeneous. In future work our fast polarized bispectrum estimator should be
extended to deal with inhomogeneous noise in an analogous way to how the
existing fast temperature estimator was generalized.Comment: Submitted to Ap

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