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Register a new userDeconvolution of window effect in galaxy power spectrum analysis
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We develop a new method for deconvolving the smearing effect of the survey window in the analysis of the galaxy multipole power spectra from a redshift survey. This method is based on the deconvolution theorem, and is compatible with the use of the fast Fourier transform. It is possible to measure the multipole power spectra deconvolved from the window effect efficiently. Applying this method to the luminous red galaxy sample of the Sloan Digital Sky Survey data release 7 as well as mock catalogues, we demonstrate how the method works properly. Using this deconvolution technique, the amplitude of the multipole power spectrum is corrected. Besides, the covariance matrices of the deconvolved power spectra get quite close to the diagonal form. This is also advantageous in the study of the BAO signature.
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We present the galaxy power spectrum in general relativity. Using a novel approach, we derive the galaxy power spectrum taking into account all the relativistic effects in observations. In particular, we show independently of survey geometry that relativistic effects yield no divergent terms (proportional to $k^{-4}P_m(k)$ or $k^{-2}P_m(k)$ on all scales) that would mimic the signal of primordial non-Gaussianity. This cancellation of such divergent terms is indeed expected from the equivalence principle, meaning that any perturbation acting as a uniform gravity on the scale of the experiment cannot be measured. We find that the unphysical infrared divergence obtained in previous calculations occurred only due to not considering all general relativistic contributions consistently. Despite the absence of divergent terms, general relativistic effects represented by non-divergent terms alter the galaxy power spectrum at large scales (smaller than the horizon scale). In our numerical computation of the full galaxy power spectrum, we show the deviations from the standard redshift-space power spectrum due to these non-divergent corrections. We conclude that, as relativistic effects significantly alter the galaxy power spectrum at $klesssim k_{eq}$, they need to be taken into account in the analysis of large-scale data.
We present two novel methods for the estimation of the angular power spectrum of cosmic microwave background (CMB) anisotropies. We assume an absolute CMB experiment with arbitrary asymmetric beams and arbitrary sky coverage. The methods differ from earlier ones in that the power spectrum is estimated directly from time-ordered data, without first compressing the data into a sky map, and they take into account the effect of asymmetric beams. In particular, they correct the beam-induced leakage from temperature to polarization. The methods are applicable to a case where part of the sky has been masked out to remove foreground contamination, leaving a pure CMB signal, but incomplete sky coverage. The first method (DQML) is derived as the optimal quadratic estimator, which simultaneously yields an unbiased spectrum estimate and minimizes its variance. We successfully apply it to multipoles up to $ell$=200. The second method is derived as a weak-signal approximation from the first one. It yields an unbiased estimate for the full multipole range, but relaxes the requirement of minimal variance. We validate the methods with simulations for the 70 GHz channel of {tt Planck} surveyor, and demonstrate that we are able to correct the beam effects in the $TT$, $EE$, $BB$, and $TE$ spectra up to multipole $ell$=1500. Together the two methods cover the complete multipole range with no gap in between.
We present a joint likelihood analysis of the real-space power spectrum and bispectrum measured from a variety of halo and galaxy mock catalogs. A novel aspect of this work is the inclusion of nonlinear triangle configurations for the bispectrum, made possible by a complete next-to-leading order (one-loop) description of galaxy bias, as is already common practice for the power spectrum. Based on the goodness-of-fit and the unbiasedness of the parameter posteriors, we accomplish a stringent validation of this model compared to the leading order (tree-level) bispectrum. Using measurement uncertainties that correspond to an effective survey volume of $6,(mathrm{Gpc}/h)^3$, we determine that the one-loop corrections roughly double the applicable range of scales, from $sim 0.17,h/mathrm{Mpc}$ (tree-level) to $sim 0.3,h/mathrm{Mpc}$. This converts into a $1.5 - 2$x improvement on constraints of the linear bias parameter at fixed cosmology, and a $1.5 - 2.4$x shrinkage of uncertainties on the amplitude of fluctuations $A_s$, which clearly demonstrates the benefit of extracting information from nonlinear scales despite having to marginalize over a larger number of bias parameters. Besides, our precise measurements of galaxy bias parameters up to fourth order allow for thorough comparisons to coevolution relations, showing excellent agreement for all contributions generated by the nonlocal action of gravity. Using these relations in the likelihood analysis does not compromise the model validity and is crucial for obtaining the quoted improvements on $A_s$. We also analyzed the impact of higher-derivative and scale-dependent stochastic terms, finding that for a subset of our tracers the former can boost the performance of the tree-level model with constraints on $A_s$ that are only slightly degraded compared to the one-loop model.
Cross-power spectrum is a quadratic estimator between two maps that can provide unbiased estimate of the underlying power spectrum of the correlated signals, which is therefore used for extracting the power spectrum in the WMAP data. In this paper we discuss the limit of cross-power spectrum and derive the residual from uncorrelated signal, which is the source of error in power spectrum extraction. We employ the estimator to extract window functions by crossing pairs of extragalactic point sources. We desmonstrate its usefulness in WMAP Difference Assembly maps where the window functions are measured via Jupiter and then extract the window functions of the 5 WMAP frequency band maps.
We investigate the potential of the galaxy power spectrum to constrain compensated isocurvature perturbations (CIPs), primordial fluctuations in the baryon density that are compensated by fluctuations in CDM density to ensure an unperturbed total matter density. We show that CIPs contribute to the galaxy overdensity at linear order, and if they are close to scale-invariant, their effects are nearly perfectly degenerate with the local PNG parameter $f_{rm nl}$ if they correlate with the adiabatic perturbations. This degeneracy can however be broken by analyzing multiple galaxy samples with different bias parameters, or by taking CMB priors on $f_{rm nl}$ into account. Parametrizing the amplitude of the CIP power spectrum as $P_{sigmasigma} = A^2P_{mathcal{R}mathcal{R}}$ (where $P_{mathcal{R}mathcal{R}}$ is the adiabatic power spectrum) we find, for a number of fiducial galaxy samples in a simplified forecast setup, that constraints on $A$, relative to those on $f_{rm nl}$, of order $sigma_{A}/sigma_{f_{rm nl}} approx 1-2$ are achievable for CIPs correlated with adiabatic perturbations, and $sigma_{A}/sigma_{f_{rm nl}} approx 5$ for the uncorrelated case. These values are independent of survey volume, and suggest that current galaxy data are already able to improve significantly on the tightest existing constraints on CIPs from the CMB. Future galaxy surveys that aim to achieve $sigma_{f_{rm nl}} sim 1$ have the potential to place even stronger bounds on CIPs.
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