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Register a new userImplementing spectra response function approaches for fast calculation of power spectra and bispectra
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Perturbation theory of large-scale structures of the Universe at next-to-leading order and next-to-next-to-leading order provides us with predictions of cosmological statistics at sub-percent level in the mildly non-linear regime. Its use to infer cosmological parameters from spectroscopic surveys, however, is hampered by the computational cost of making predictions for a large number of parameters. In order to reduce the running time of the codes, we present a fast scheme in the context of the regularized perturbation theory approach and applied it to power spectra at 2-loop level and bispectra at 1-loop level, including the impact of binning. This method utilizes a Taylor expansion of the power spectrum as a functional of the linear power spectrum around fiducial points at which costly direct evaluation of perturbative diagrams is performed and tabulated. The computation of the predicted spectra for arbitrary cosmological parameters then requires only one-dimensional integrals that can be done within a few minutes. It makes this method suitable for Markov chain Monte-Carlo analyses for cosmological parameter inference.
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With the advent of a new generation of cosmological experiments that will provide high-precision measurements of the cosmic microwave background (CMB) and galaxies in the large-scale structure, it is pertinent to examine the potential of performing a joint analysis of multiple cosmological probes. In this paper, we study the cosmological information content contained in the one-loop power spectra and tree bispectra of galaxies cross-correlated with CMB lensing. We use the FFTLog method to compute angular correlations in spherical harmonic space, applicable for wide angles that can be accessed by forthcoming galaxy surveys. We find that adding the bispectra and cross-correlations with CMB lensing offers a significant improvement in parameter constraints, including those on the total neutrino mass, $M_ u$, and local non-Gaussianity amplitude, $f_{rm NL}$. In particular, our results suggest that the combination of the Vera C. Rubin Observatorys Legacy Survey of Space and Time (LSST) and CMB-S4 will be able to achieve $sigma(M_ u)=42$ meV from galaxy and CMB lensing correlations, and $sigma(M_ u)=12$ meV when further combined with the CMB temperature and polarization data, without any prior on the optical depth.
We investigate the statistical power of higher-order statistics and cross-correlation statistics to constrain the primordial non-Gaussianity from the imaging surveys. In particular, we consider the local-type primordial non- Gaussianity and discuss how well one can tightly constrain the higher-order non-Gaussian parameters ($g_{rm NL}$ and $tau_{rm NL}$) as well as the leading order parameter $f_{rm NL}$ from the halo/galaxy clustering and weak gravitational lensing measurements. Making use of a strong scale-dependent behavior in the galaxy/halo clustering, Fisher matrix analysis reveals that the bispectra can break the degeneracy between non-Gaussian parameters ($f_{rm NL}$, $g_{rm NL}$ and $tau_{rm NL}$) and this will give simultaneous constraints on those three parameters. The combination of cross-correlation statistics further improves the constraints by factor of 2. As a result, upcoming imaging surveys like the Large Synoptic Survey Telescope have the potential to improve the constraints on the primordial non-Gaussianity much tighter than those obtained from the CMB measurement by Planck, giving us an opportunity to test the single-sourced consistency relation, $tau_{rm NL} ge (36/25) f_{rm NL}^2$.
The statistical distribution of galaxies is a powerful probe to constrain cosmological models and gravity. In particular the matter power spectrum $P(k)$ brings information about the cosmological distance evolution and the galaxy clustering together. However the building of $P(k)$ from galaxy catalogues needs a cosmological model to convert angles on the sky and redshifts into distances, which leads to difficulties when comparing data with predicted $P(k)$ from other cosmological models, and for photometric surveys like LSST. The angular power spectrum $C_ell(z_1,z_2)$ between two bins located at redshift $z_1$ and $z_2$ contains the same information than the matter power spectrum, is free from any cosmological assumption, but the prediction of $C_ell(z_1,z_2)$ from $P(k)$ is a costly computation when performed exactly. The Angpow software aims at computing quickly and accurately the auto ($z_1=z_2$) and cross ($z_1 eq z_2$) angular power spectra between redshift bins. We describe the developed algorithm, based on developments on the Chebyshev polynomial basis and on the Clenshaw-Curtis quadrature method. We validate the results with other codes, and benchmark the performance. Angpow is flexible and can handle any user defined power spectra, transfer functions, and redshift selection windows. The code is fast enough to be embedded inside programs exploring large cosmological parameter spaces through the $C_ell(z_1,z_2)$ comparison with data. We emphasize that the Limbers approximation, often used to fasten the computation, gives wrong $C_ell$ values for cross-correlations.
The Chern-Simons term, through which the cosmic Axion-like field couples to the electromagnetic field, has the effect to rotate CMB polarization directions and to break the CPT symmetry. This rotation will change the CMB power spectra, no matter isotropic or anisotropic the rotation angle is. In this paper we revisit this issue by further considering the correlations between the (anisotropic) rotation angle $alpha$ and the CMB temperature and (unrotated) $E$ polarization fields. These correlations could be generated in the Axion-like models with nonzero potential under the adiabatic initial condition. We first investigate how these correlations contribute further modifications to the CMB power spectra, then calculate the CMB bispectra for the temperature and rotated polarization fields. These bispectra would vanish if the $Talpha$ and $Ealpha$ correlations are absent. So, they are useful in searching for CPT violation and the $Talpha$ and $Ealpha$ correlations arisen in the Axion-like models.
We present ECLIPSE (Efficient Cmb poLarization and Intensity Power Spectra Estimator), an optimized implementation of the Quadratic Maximum Likelihood (QML) method for the estimation of the power spectra of the Cosmic Microwave Background (CMB). This approach allows one to reduce significantly the computational costs associated to this technique, allowing to estimate the power spectra up to higher multipoles than previous implementations. In particular, for a resolution of $N_mathrm{side}=64$, $ell_{mathrm{max}}=192$ and a typical Galactic mask, the number of operations can be reduced by approximately a factor of 1000 in a full analysis including intensity and polarization with respect to an efficient direct implementation of the method. In addition, if one is interested in studying only polarization, it is possible to obtain the power spectra of the E and B modes with a further reduction of computational resources without degrading the results. We also show that for experiments observing a small fraction of the sky, the Fisher matrix becomes singular and, in this case, the standard QML can not be applied. To solve this problem, we have developed a binned version of the method that is unbiased and of minimum variance. We also test the robustness of the QML estimator when the assumed fiducial model differs from that of the sky and show the performance of an iterative approach. Finally, we present a comparison of the results obtained by QML and a pseudo-$C_{ell}$ estimator (NaMaster) for a next-generation satellite, showing that, as expected, QML produces significantly smaller errors at low multipoles. The ECLIPSE fast QML code developed in this work will be made publicly available.
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