Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userMeasuring the primordial power spectrum: Principal component analysis of the cosmic microwave background
86
0
0.0
(
0
)
Authors
Samuel Leach
Ask ChatGPT about the research
No Arabic abstract
We implement and investigate a method for measuring departures from scale-invariance, both scale-dependent as well as scale-free, in the primordial power spectrum of density perturbations using cosmic microwave background (CMB) C_l data and a principal component analysis technique. The primordial power spectrum is decomposed into a dominant scale-invariant Gaussian adiabatic component plus a series of orthonormal modes whose detailed form only depends the noise model for a particular CMB experiment. However, in general these modes are localised across wavenumbers with 0.01 < k < 0.2 Mpc^-1, displaying rapid oscillations on scales corresponding the acoustic peaks where the sensitivity to primordial power spectrum is greatest. The performance of this method is assessed using simulated data for the Planck satellite, and the full cosmological plus power spectrum parameter space is integrated out using Markov Chain Monte Carlo. As a proof of concept we apply this data compression technique to the current CMB data from WMAP, ACBAR, CBI and VSA. We find no evidence for the breaking of scale-invariance from measurements of four PCA mode amplitudes, which is translated to a constraint on the scalar spectral index n_S(k_0=0.04 Mpc^-1)=0.94+-0.04 in accordance with WMAP studies.
rate research
Read More
We derive a fast way for measuring primordial non-Gaussianity in a nearly full-sky map of the cosmic microwave background. We find a cubic combination of sky maps combining bispectrum configurations to capture a quadratic term in primordial fluctuations. Our method takes only N^1.5 operations rather than N^2.5 of the bispectrum analysis (1000 times faster for l=512), retaining the same sensitivity. A key component is a map of underlying primordial fluctuations, which can be more sensitive to the primordial non-Gaussianity than a temperature map. We also derive a fast and accurate statistic for measuring non-Gaussian signals from foreground point sources. The statistic is 10^6 times faster than the full bispectrum analysis, and can be used to estimate contamination from the sources. Our algorithm has been successfully applied to the Wilkinson Microwave Anisotropy Probe sky maps by Komatsu et al. (2003).
We develop two methods for estimating the power spectrum, C_l, of the cosmic microwave background (CMB) from data and apply them to the COBE/DMR and Saskatoon datasets. One method involves a direct evaluation of the likelihood function, and the other is an estimator that is a minimum-variance weighted quadratic function of the data. Applied iteratively, the quadratic estimator is not distinct from likelihood analysis, but is rather a rapid means of finding the power spectrum that maximizes the likelihood function. Our results bear this out: direct evaluation and quadratic estimation converge to the same C_ls. The quadratic estimator can also be used to directly determine cosmological parameters and their uncertainties. While the two methods both require O(N^3) operations, the quadratic is much faster, and both are applicable to datasets with arbitrary chopping patterns and noise correlations. We also discuss approximations that may reduce it to O(N^2) thus making it practical for forthcoming megapixel datasets.
We consider the distribution of the non-Gaussian signal induced by weak lensing on the primary total intensity cosmic microwave background (CMB) anisotropies. Our study focuses on the three point statistics exploiting an harmonic analysis based on the CMB bispectrum. By considering the three multipoles as independent variables, we reveal a complex structure of peaks and valleys determined by the re-projection of the primordial acoustic oscillations through the lensing mechanism. We study the dependence of this system on the expansion rate at the epoch in which the weak lensing power injection is relevant, probing the dark energy equation of state at redshift corresponding to the equivalence with matter or higher ($w_infty$). We evaluate the impact of the bispectrum observable on the CMB capability of constraining the dark energy dynamics. We perform a maximum likelihood analysis by varying the dark energy abundance, the present equation of state $w_0$ and $w_infty$. We show that the projection degeneracy affecting a pure power spectrum analysis in total intensity is broken if the bispectrum is taken into account. For a Planck-like experiment, assuming nominal performance, no foregrounds or systematics, and fixing all the parameters except $w_0$, $w_infty$ and the dark energy abundance, a percent and ten percent precision measure of $w_0$ and $w_infty$ is achievable from CMB data only. These results indicate that the detection of the weak lensing signal by the forthcoming CMB probes may be relevant to gain insight into the dark energy dynamics at the onset of cosmic acceleration.
We present the XFaster analysis package. XFaster is a fast, iterative angular power spectrum estimator based on a diagonal approximation to the quadratic Fisher matrix estimator. XFaster uses Monte Carlo simulations to compute noise biases and filter transfer functions and is thus a hybrid of both Monte Carlo and quadratic estimator methods. In contrast to conventional pseudo-$C_ell$ based methods, the algorithm described here requires a minimal number of simulations, and does not require them to be precisely representative of the data to estimate accurate covariance matrices for the bandpowers. The formalism works with polarization-sensitive observations and also data sets with identical, partially overlapping, or independent survey regions. The method was first implemented for the analysis of BOOMERanG data, and also used as part of the Planck analysis. Here, we describe the full, publicly available analysis package, written in Python, as developed for the analysis of data from the 2015 flight of the SPIDER instrument. The package includes extensions for self-consistently estimating null spectra and for estimating fits for Galactic foreground contributions. We show results from the extensive validation of XFaster using simulations, and its application to the SPIDER data set.
We present a determination by the Archeops experiment of the angular power spectrum of the cosmic microwave background anisotropy in 16 bins over the multipole range l=15-350. Archeops was conceived as a precursor of the Planck HFI instrument by using the same optical design and the same technology for the detectors and their cooling. Archeops is a balloon-borne instrument consisting of a 1.5 m aperture diameter telescope and an array of 21 photometers maintained at ~100 mK that are operating in 4 frequency bands centered at 143, 217, 353 and 545 GHz. The data were taken during the Arctic night of February 7, 2002 after the instrument was launched by CNES from Esrange base (Sweden). The entire data cover ~ 30% of the sky.This first analysis was obtained with a small subset of the dataset using the most sensitive photometer in each CMB band (143 and 217 GHz) and 12.6% of the sky at galactic latitudes above 30 degrees where the foreground contamination is measured to be negligible. The large sky coverage and medium resolution (better than 15 arcminutes) provide for the first time a high signal-to-noise ratio determination of the power spectrum over angular scales that include both the first acoustic peak and scales probed by COBE/DMR. With a binning of Delta(l)=7 to 25 the error bars are dominated by sample variance for l below 200. A companion paper details the cosmological implications.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
