Combining Full-Shape and BAO Analyses of Galaxy Power Spectra: A 1.6% CMB-independent constraint on H0

We present cosmological constraints from a joint analysis of the pre- and post-reconstruction galaxy power spectrum multipoles from the final data release of the Baryon Oscillation Spectroscopic Survey (BOSS). Geometric constraints are obtained from the positions of BAO peaks in reconstructed spectra, analyzed in combination with the unreconstructed spectra in a full-shape (FS) likelihood using a joint covariance matrix, giving stronger parameter constraints than FS-only or BAO-only analyses. We introduce a new method for obtaining constraints from reconstructed spectra based on a correlated theoretical error, which is shown to be simple, robust, and applicable to any flavor of density-field reconstruction. Assuming $\Lambda$CDM with massive neutrinos, we analyze data from two redshift bins $z_\mathrm{eff}=0.38,0.61$ and obtain $1.6\%$ constraints on the Hubble constant $H_0$, using only a single prior on the current baryon density $\omega_b$ from Big Bang Nucleosynthesis (BBN) and no knowledge of the power spectrum slope $n_s$. This gives $H_0 = 68.6\pm1.1\,\mathrm{km\,s}^{-1}\mathrm{Mpc}^{-1}$, with the inclusion of BAO data sharpening the measurement by $40\%$, representing one of the strongest current constraints on $H_0$ independent of cosmic microwave background data. Restricting to the best-fit slope $n_s$ from Planck (but without additional priors on the spectral shape), we obtain a $1\%$ $H_0$ measurement of $67.8\pm 0.7\,\mathrm{km\,s}^{-1}\mathrm{Mpc}^{-1}$. We find strong constraints on the cosmological parameters from a joint analysis of the FS, BAO, and Planck data. This sets new bounds on the sum of neutrino masses $\sum m_\nu < 0.14\,\mathrm{eV}$ (at $95\%$ confidence) and the effective number of relativistic degrees of freedom $N_\mathrm{eff} = 2.90^{+0.15}_{-0.16}$, though contours are not appreciably narrowed by the inclusion of BAO data.Comment: 42 pages, 12 figures, accepted by JCAP, likelihoods available at https://github.com/Michalychforever/lss_montepython (minor typo corrected

Exploring degeneracies in modified gravity with weak lensing

By considering linear-order departures from general relativity, we compute a novel expression for the weak lensing convergence power spectrum under alternative theories of gravity. This comprises an integral over a 'kernel' of general relativistic quantities multiplied by a theory-dependent 'source' term. The clear separation between theory-independent and -dependent terms allows for an explicit understanding of each physical effect introduced by altering the theory of gravity. We take advantage of this to explore the degeneracies between gravitational parameters in weak lensing observations.Comment: 17 pages, 7 figures. v2: Minor changes to match version accepted by PR

Regularization-free estimation in trace regression with symmetric positive semidefinite matrices

Over the past few years, trace regression models have received considerable attention in the context of matrix completion, quantum state tomography, and compressed sensing. Estimation of the underlying matrix from regularization-based approaches promoting low-rankedness, notably nuclear norm regularization, have enjoyed great popularity. In the present paper, we argue that such regularization may no longer be necessary if the underlying matrix is symmetric positive semidefinite (\textsf{spd}) and the design satisfies certain conditions. In this situation, simple least squares estimation subject to an \textsf{spd} constraint may perform as well as regularization-based approaches with a proper choice of the regularization parameter, which entails knowledge of the noise level and/or tuning. By contrast, constrained least squares estimation comes without any tuning parameter and may hence be preferred due to its simplicity

Robust Inversion Methods for Aerosol Spectroscopy

The Fast Aerosol Spectrometer (FASP) is a device for spectral aerosol measurements. Its purpose is to safely monitor the atmosphere inside a reactor containment. First we describe the FASP and explain its basic physical laws. Then we introduce our reconstruction methods for aerosol particle size distributions designed for the FASP. We extend known existence results for constrained Tikhonov regularization by uniqueness criteria and use those to generate reasonable models for the size distributions. We apply a Bayesian model-selection framework on these pre-generated models. We compare our algorithm with classical inversion methods using simulated measurements. We then extend our reconstruction algorithm for two-component aerosols, so that we can simultaneously retrieve their particle-size distributions and unknown volume fractions of their two components. Finally we present the results of a numerical study for the extended algorithm.Comment: 37 pages, 3 figure