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We evaluate the effectiveness of early dark energy (EDE) in addressing the Hubble tension using the luminous red galaxy (LRG), quasar (QSO), and emission line galaxy (ELG) samples from the completed eBOSS survey. We perform cosmological parameter measurements based on full shape analysis of the power spectrum employing the effective field theory of large-scale structure (EFTofLSS). EDE is known to strongly suffer from volume projection effects, complicating cosmological constraints' interpretation. To quantify the volume projection effects within an EDE full shape analysis, we explore the impact of different prior choices on the nuisance parameters of EFTofLSS through an extensive mock study. We compare classical Gaussian priors to the non-informative Jeffreys prior, known to mitigate volume projection effects in ΛCDM. Our full shape analysis combines eBOSS and BOSS data with Planck , external Baryon Acoustic Oscillation (BAO), PantheonPlus, and SH0ES supernova data. EDE reduces the tension from 5.2σ to 3σ compared to ΛCDM, yielding |$H_0=71.73_{-0.86}^{+0.82}$| km s−1 Mpc−1 with |$f_\mathrm{EDE} = 0.1179_{-0.022}^{+0.025}$| (Gaussian priors) and |$H_0=72.03_{-0.87}^{+0.82}$| km s−1 Mpc−1 with |$f_\mathrm{EDE} = 0.1399_{-0.022}^{+0.023}$| (Jeffreys prior). Although the Hubble tension is mitigated compared to ΛCDM, the inclusion of eBOSS data amplifies the tension within EDE from 2σ to 3σ, in contrast to the full shape analysis of BOSS data with Planck , external BAO, PantheonPlus, and SH0ES. This highlights the significance of incorporating additional large-scale structure data in discussions concerning models aiming to resolve the Hubble tension. [ABSTRACT FROM AUTHOR]

Empirical estimates of the band power covariance matrix are commonly used in cosmic microwave background (CMB) power spectrum analyses. While this approach easily captures correlations in the data, noise in the resulting covariance estimate can systematically bias the parameter fitting. Conditioning the estimated covariance matrix, by applying prior information on the shape of the eigenvectors, can reduce these biases and ensure the recovery of robust parameter constraints. In this work, we use simulations to benchmark the performance of four different conditioning schemes, motivated by contemporary CMB analyses. The simulated surveys measure the TT ,  TE , and EE power spectra over the angular multipole range 300 ≤ ℓ ≤ 3500 in Δℓ = 50 wide bins, for temperature map-noise levels of 10, 6.4, and |$2\, \mu$| K arcmin. We divide the survey data into N real = 30, 50, or 100 uniform subsets. We show the results of different conditioning schemes on the errors in the covariance estimate, and how these uncertainties on the covariance matrix propagate to the best-fitting parameters and parameter uncertainties. The most significant effect we find is an additional scatter in the best-fitting point, beyond what is expected from the data likelihood. For a minimal conditioning strategy, N real = 30, and a temperature map-noise level of 10 |$\, \mu$| K arcmin, we find the uncertainty on the recovered best-fitting parameter to be ×1.3 larger than the apparent posterior width from the likelihood (×1.2 larger than the uncertainty when the true covariance is used). Stronger priors on the covariance matrix reduce the misestimation of parameter uncertainties to |$\lt 1{{\ \rm per\ cent}}$|⁠. As expected, empirical estimates perform better with higher N real, ameliorating the adverse effects on parameter constraints. [ABSTRACT FROM AUTHOR]

The advent of new time domain surveys and the imminent increase in astronomical data expose the shortcomings of traditional time series analysis (such as power spectra analysis) in characterizing the abundantly varied, complex, and stochastic light curves of Active Galactic Nuclei (AGNs). Recent applications of novel methods from non-linear dynamics have shown promise in characterizing higher modes of variability and time-scales in AGN. Recurrence analysis in particular can provide complementary information about characteristic time-scales revealed by other methods, as well as probe the nature of the underlying physics in these objects. Recurrence analysis was developed to study dynamical trajectories in phase space, which can be constructed from 1D time series such as light curves. We apply the methods of recurrence analysis to two optical light curves of Kepler -monitored AGN. We confirm the detection and period of an optical quasi-periodic oscillation in one AGN, and confirm multiple other time-scales recovered from other methods ranging from 5 to 60 d in both objects. We detect regions in the light curves that deviate from regularity, provide evidence of determinism and non-linearity in the mechanisms underlying one light curve (KIC 9650712), and determine realizations of a linear stochastic process describe the dominant variability in the other light curve (Zwicky 229–015). We discuss possible underlying processes driving the dynamics of the light curves and their diverse classes of variability. [ABSTRACT FROM AUTHOR]

We describe an exact, flexible and computationally efficient algorithm for a joint inference of the large-scale structure and its power spectrum, building on a Gibbs sampling framework and present its implementationares (Algorithm for REconstruction and Sampling).ares is designed to reconstruct the 3D power spectrum together with the underlying dark matter density field in a Bayesian framework, under the reasonable assumption that the long-wavelength Fourier components are Gaussian distributed. As a resultares does not only provide a single estimate but samples from the joint posterior of the power spectrum and density field conditional on a set of observations. This enables us to calculate any desired statistical summary, in particular we are able to provide joint uncertainty information. We apply our method to mock catalogues, with highly structured observational masks and selection functions, in order to demonstrate its ability to infer the power spectrum from real data sets, while fully accounting for any mask induced mode coupling. [ABSTRACT FROM AUTHOR]

We present a semi-analytical method to investigate the systematic effects and statistical uncertainties of the calculated angular power spectrum when incomplete spherical maps are used. The computed power spectrum suffers in particular a loss of angular frequency resolution, which can be written as , where is the effective maximum extent of the partial spherical maps. We propose a correction algorithm to reduce systematic effects on the estimated , as obtained from the partial map projection on the spherical harmonic basis. We have derived near-optimal bands and weighting functions in -space for the power spectrum calculation using small maps, and a correction algorithm for partially masked spherical maps that contain information on the angular correlations on all scales. [ABSTRACT FROM AUTHOR]

The form of the primordial power spectrum has the potential to differentiate strongly between competing models of perturbation generation in the early universe and so is of considerable importance. The recent release of five years of Wilkinson Microwave Anisotropy Probe observations have confirmed the general picture of the primordial power spectrum as deviating slightly from scale invariance with a spectral tilt parameter of . None the less, many attempts have been made to isolate further features such as breaks and cut-offs using a variety of methods, some employing more than ∼10 varying parameters. In this paper, we apply the robust technique of the Bayesian model selection to reconstruct the optimal degree of structure in the spectrum. We model the spectrum simply and generically as piecewise linear in between ‘nodes’ in k space whose amplitudes are allowed to vary. The number of nodes and their k-space positions are chosen by the Bayesian evidence so that we can identify both the complexity and location of any detected features. Our optimal reconstruction contains, perhaps, surprisingly few features, the data preferring just three nodes. This reconstruction allows for a degree of scale dependence of the tilt with the ‘turn-over’ scale occurring around . More structure is penalized by the evidence as overfitting the data, so there is currently little point in attempting reconstructions that are more complex. [ABSTRACT FROM AUTHOR]

We develop the pseudo- Cℓ method for reconstructing the cosmic microwave background (CMB) temperature and polarization auto- and cross-power spectra, and estimate the pseudo- Cℓ covariance matrix for a realistic experiment on the cut sky. We calculate the full coupling equations for all six possible CMB power spectra, relating the observed pseudo- Cℓ values to the underlying all-sky Cℓ values, and test the reconstruction on both full-sky and cut-sky simulated CMB data sets. In particular we consider the reconstruction of the Cℓ from upcoming ground-based polarization experiments covering areas of a few hundred deg2 and find that the method is fast, unbiased and performs well over a wide range of multipoles from to . We then calculate the full covariance matrix between the modes of the pseudo-temperature and polarization power spectra, assuming that the underlying CMB fields are Gaussian randomly distributed. The complexity of the covariance matrix prohibits its rapid calculation, required for parameter estimation. Hence we present an approximation for the covariance matrix in terms of convolutions of the underlying power spectra. The coupling matrices in these expressions can be estimated by fitting to numerical simulations, circumventing direct and slow calculation, and further, inaccurate analytic approximations. We show that these coupling matrices are mostly independent of cosmology, and that the full covariance matrix for all six pseudo- Cℓ power spectra can be quickly and accurately calculated for any given cosmological model using this method. We compare these semi-analytic covariance matrices against simulations and find good agreement, the accuracy of which depends mainly on survey area and the range of cosmological parameters considered. [ABSTRACT FROM AUTHOR]

We presentXspect, a method to obtain estimates of the angular power spectrum of the cosmic microwave background (CMB) temperature anisotropies including analytical error bars developed for theArcheopsexperiment. Cross-power spectra are computed from a set of maps and each of them is in itself an unbiased estimate of the power spectrum as long as the detector noises are uncorrelated. Then, the cross-power spectra are combined into a final temperature power spectrum with error bars analytically derived from the cross-correlation matrix.This method presents three main useful properties: (1) no estimation of the noise power spectrum is needed; (2) complex weighting schemes including sky covering and map noise properties can be easily taken into account, and corrected for, for each input map; and (3) error bars are quickly computed analytically from the data themselves with no Monte Carlo simulations involved.Xspectalso permits the study of common fluctuations between maps from different sky surveys such as CMB, Sunyaev–Zel'dovich effect or mass fluctuations from weak lensing observations. [ABSTRACT FROM AUTHOR]