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Modified Growth with CAMB (MGCAMB) is a patch for the Einstein-Boltzmann solver CAMB for cosmological tests of gravity. Until now, MGCAMB was limited to scales well-described by linear perturbation theory. In this work, we extend the framework with a phenomenological model that can capture nonlinear corrections in a broad range of modified gravity theories. The extension employs the publicly available halo model reaction code ReACT, developed for modeling the nonlinear corrections to cosmological observables in extensions of the $\Lambda$CDM model. The nonlinear extension makes it possible to use a wider range of data from large scale structure surveys, without applying a linear scale cut. We demonstrate that, with the 3$\times$2pt Dark Energy Survey data, we achieve a stronger constraint on the linear phenomenological functions $\mu$ and $\Sigma$, after marginalizing over the additional nonlinear parameter $p_1$, compared to the case without the nonlinear extension and using a linear cut. The new version of MGCAMB is now forked with CAMB on GitHub allowing for compatibility with future upgrades., Comment: 8 pages, 5 figures; MGCAMB available at https://github.com/sfu-cosmo/MGCAMB/tree/NL_ext, and MGCobaya available at https://github.com/sfu-cosmo/MGCobaya/tree/NL_ext

The value of the Hubble constant determined from CMB and BAO measurements is directly dependent on the sound horizon at the photon-baryon decoupling. There has been significant interest in the possibility of new physics at the epoch around recombination that could reduce the sound horizon and increase the inferred value of $H_0$, thus helping to relieve the Hubble tension. One way to determine if new physics is required would be to measure $H_0$ from BAO and CMB without assuming any model for computing the sound horizon. In this study, we use the recently released DESI Year 1 BAO data combined with the CMB acoustic scale and the Planck $\Lambda$CDM prior on $\Omega_{\rm m} h^2$ to determine $H_0$ while treating the sound horizon at baryon decoupling $r_{\rm d}$ as a free parameter. We find $H_0=69.48 \pm 0.94$ km/s/Mpc, which is $\sim2\sigma$ larger than $H_0 = 67.44 \pm 0.47$ km/s/Mpc in the Planck-best-fit $\Lambda$CDM where $r_{\rm d}$ is derived using the standard recombination model. For comparison, we perform the same analysis using the pre-DESI BAO data with the CMB acoustic scale and the same prior on $\Omega_{\rm m} h^2$, finding $H_0= 68.05 \pm 0.94$ km/s/Mpc. This difference derives from the notably larger value of the product $r_{\rm d}h$ measured by DESI. We compare results obtained with and without including the Pantheon Plus sample of uncalibrated supernovae magnitudes in our analysis. Future BAO data from DESI will help determine if the cosmological model at the epoch of recombination model requires a modification., Comment: 6 pages, 2 figures, 1 table; added analysis with including the Pantheon+ SN sample, other minor changes in version 2; matches the version accepted to ApJLett

Scattering resonances have important applications in many areas of science and engineering. They are the replacement of discrete spectral data for problems on non-compact domains. In this paper, we consider the computation of scattering resonances defined on the exterior to a compact sound hard obstacle. The resonances are the eigenvalues of a holomorphic Fredholm operator function. We truncate the unbounded domain and impose the Dirichlet-to-Neumann (DtN) mapping. The problem is then discretized using the linear Lagrange element. Convergence of the resonances is proved using the abstract approximation theory for holomorphic Fredholm operator functions. The discretization leads to nonlinear algebraic eigenvalue problems, which are solved by the recently developed parallel spectral indicator methods. Numerical examples are presented for validation.

We extract key information of dark energy from current observations of BAO, OHD and $H_0$, and find hints of dynamical behaviour of dark energy. In particular, a dynamical dark energy model whose equation of state crosses $-1$ is favoured by observations. We also find that the Universe has started accelerating at a lower redshift than expected., Comment: 10 pages, 4 figures; version accepted to RAA

We develop methods to extract key dark energy information from cosmic distance measurements including the BAO scales and supernovae luminosity distances. Demonstrated using simulated datasets of the complete DESI, LSST and Roman surveys designed for BAO and SNe distance measurements, we show that using our method, the dynamical behaviour of the energy, pressure, equation of state (with its time derivative) of dark energy and the cosmic deceleration function can all be accurately recovered from high-quality data, which allows for robust diagnostic tests for dark energy models., Comment: 15 pages, 7 figures; version accepted to RAA

The small-scale linear information in galaxy samples typically lost during non-linear growth can be restored to a certain level by the density field reconstruction, which has been demonstrated for improving the precision of the baryon acoustic oscillations (BAO) measurements. As proposed in the literature, a joint analysis of the power spectrum before and after the reconstruction enables an efficient extraction of information carried by high-order statistics. However, the statistics of the post-reconstruction density field are difficult to model. In this work, we circumvent this issue by developing an accurate emulator for the pre-reconstructed, post-reconstructed, and cross power spectra ($P_{\rm pre}$, $P_{\rm post}$, $P_{\rm cross}$) up to $k=0.5~h~{\rm Mpc^{-1}}$ based on the \textsc{Dark Quest} N-body simulations. The accuracy of the emulator is at percent level, namely, the error of the emulated monopole and quadrupole of the power spectra is less than $1\%$ and $10\%$ of the ground truth, respectively. A fit to an example power spectra using the emulator shows that the constraints on cosmological parameters get largely improved using $P_{\rm pre}$+$P_{\rm post}$+$P_{\rm cross}$ with $k_{\rm max}=0.25~h~{\rm Mpc^{-1}}$, compared to that derived from $P_{\rm pre}$ alone, namely, the constraints on ($\Omega_m$, $H_0$, $\sigma_8$) are tightened by $\sim41 \%-55\%$, and the uncertainties of the derived BAO and RSD parameters ($\alpha_{\perp}$, $\alpha_{||}$, $f\sigma_8$) shrink by $\sim 28\%-54\%$, respectively. This highlights the complementarity among $P_{\rm pre}$, $P_{\rm post}$ and $P_{\rm cross}$, which demonstrates the efficiency and practicability of a joint $P_{\rm pre}$, $P_{\rm post}$ and $P_{\rm cross}$ analysis for cosmological implications., Comment: 19 pages, 11 figures, 2 tables; accepted for publication in ApJ

We perform a multitracer full-shape analysis in Fourier space based on the effective field theory of large-scale structure (EFTofLSS) using the complete Sloan Digital Sky Survey IV (SDSS-IV) extended Baryon Oscillation Spectroscopic Survey (eBOSS) DR16 luminous red galaxy (LRG) and emission line galaxy (ELG) samples. We study in detail the impact of the volume projection effect and different prior choices when doing the full-shape analysis based on the EFTofLSS model. We show that adopting a combination of Jeffreys prior and Gaussian prior can mitigate the volume effect and avoid exploring unphysical regions in the parameter space at the same time, which is crucial when jointly analysing the eBOSS LRG and ELG samples. We validate our pipeline using 1000 eBOSS EZmocks. By performing a multitracer analysis on mocks with comparable footprints, we find that cosmological constraints can be improved by $\sim10-35$ per cent depending on whether we assume zero stochastic terms in the cross power spectrum, which breaks the degeneracy and boosts the constraints on the standard deviation of matter density fluctuation $\sigma_8$. Combining with the Big Bang Nucleosynthesis (BBN) prior and fixing the spectral tilt $n_s$ to Planck value, our multitracer full-shape analysis measures $H_0=70.0\pm2.3~{\mathrm{km}}~{\mathrm{s}}^{-1}{\mathrm{Mpc}}^{-1}$, $\Omega_m=0.317^{+0.017}_{-0.021}$, $\sigma_8=0.787_{-0.062}^{+0.055}$ and $S_8=0.809_{-0.078}^{+0.064}$, consistent with the Planck~2018 results. In particular, the constraint on $\sigma_8$ is improved beyond that obtained from the single tracer analysis by $18$ per cent, or by $27$ per cent when assuming zero stochastic terms in the cross power spectrum., Comment: Match the accepted version

The Baryon Acoustic Oscillations (BAO) feature in the clustering of galaxies or quasars provides a ``standard ruler" for distance measurements in cosmology. In this work, we report a $2\sim3\sigma$ signal of the BAO dip feature in the galaxy density-ellipticity (GI) cross-correlation functions using the spectroscopic sample of the Baryon Oscillation Spectroscopic Survey (BOSS) CMASS, combined with the deep DESI Legacy Imaging Surveys for precise galaxy shape measurements. We measure the GI correlation functions and model them using the linear alignment model. We constrain the distance $D_V/r_{\mathrm{d}}$ to redshift $0.57$ to a precision of $3\sim5\%$, depending on the details of modeling. The GI measurement reduces the uncertainty of distance measurement by $\sim10\%$ on top of that derived from the galaxy-galaxy (GG) correlation. More importantly, for future large and deep galaxy surveys, the independent GI measurements can help sort out the systematics in the BAO studies., Comment: Main text 3 figures + supplementary 5 figures. Published in Nature Astronomy

We present a new version of MGCAMB, a patch for the Einstein-Boltzmann solver CAMB for cosmological tests of gravity. New features include a new cubic-spline parameterization allowing for a simultaneous reconstruction of $\mu$, $\Sigma$ and the dark energy density fraction $\Omega_X$ as functions of redshift, the option to work with a direct implementation of $\mu$, $\Sigma$ (instead of converting to $\mu$, $\gamma$ first), along with the option to test models with a scalar field coupled only to dark matter, and the option to include dark energy perturbations when working with $w\ne -1$ backgrounds, to restore consistency with CAMB in the GR limit. This version of MGCAMB comes with a Python wrapper to run it directly from the Python interface, an implementation in the latest version of CosmoMC, and can be used with Cobaya., Comment: 8 pages + 2 appendices, 4 figures, matches the version accepted to JCAP; MGCAMB, MGCosmoMC and MGCobaya available at https://github.com/sfu-cosmo/MGCAMB, https://github.com/sfu-cosmo/MGCosmoMC, https://github.com/sfu-cosmo/MGCobaya

We study the clustering properties of 1,307,530 AGNs/quasars in the CatWISE2020 catalog prepared using the Wide-field Infrared Survey Explorer (WISE) and Near-Earth Object Wide-field Infrared Survey Explorer (NEOWISE) survey data. For angular moments $\ell \gtrapprox 10$ ($\lessapprox 18^\circ$) down to non-linear scales, the results are in agreement with the standard $\Lambda$CDM cosmology, with a galaxy bias roughly matching that of the NRAO VLA Sky Survey (NVSS) AGNs. We further explore the redshift dependence of the fraction of infrared bright AGNs on stellar mass, $f_{\rm IB} \sim M_*^{\alpha_0 + \alpha_1 z}$, and find $\alpha_1=1.27^{+0.25}_{-0.30}$, ruling out a non-evolution hypothesis at $\approx 4.6\sigma$ confidence level. The results are consistent with the measurements obtained with NVSS AGNs, though considerably more precise thanks to the significantly higher number density of objects in CatWISE2020. The excess dipole and high clustering signal above angular scale $\approx 18^\circ$ remain anomalous., Comment: 11 pages, 11 figures

Regular convergence, together with various other types of convergence, has been studied since the 1970s for the discrete approximations of linear operators. In this paper, we consider the eigenvalue approximation of compact operators whose spectral problem can be written as the eigenvalue problem of some holomophic Fredholm operator function. Focusing on the finite element methods (conforming, discontinuous Galerkin, etc.), we show that the regular convergence of discrete holomorphic operator functions follows from the approximation property of the finite element spaces and the compact convergence of the discrete operators in some suitable Sobolev space. The convergence for eigenvalues is then obtained using the discrete approximation theory for the eigenvalue problems of holomorphic Fredholm operator functions. The result can be used to show the convergence of various finite element methods for eigenvalue problems such as the Dirhcilet eigenvalue problem and the biharmonic eigenvalue problem.

We propose a new consistency test for the $\Lambda$CDM cosmology using baryonic acoustic oscillations (BAO) and redshift space distortion (RSD) measurements from galaxy redshift surveys. Specifically, we determine the peak position of $f\sigma_8(z)$ in redshift $z$ offered by a RSD measurement, and compare it to the one predicted by the BAO observables assuming a flat $\Lambda$CDM cosmology. We demonstrate this new test using the simulated data for the DESI galaxy survey, and argue that this test complements those using the background observables alone, and is less subject to systematics in the RSD analysis, compared to traditional methods using values of $f\sigma_8(z)$ directly., Comment: 9 pages, 6 figures; accepted to Research in Astronomy and Astrophysics (RAA)

In this paper we will list a few important goals that need to be addressed in the next decade, also taking into account the current discordances between the different cosmological probes, such as the disagreement in the value of the Hubble constant $H_0$, the $\sigma_8$--$S_8$ tension, and other less statistically significant anomalies. While these discordances can still be in part the result of systematic errors, their persistence after several years of accurate analysis strongly hints at cracks in the standard cosmological scenario and the necessity for new physics or generalisations beyond the standard model. In this paper, we focus on the $5.0\,\sigma$ tension between the {\it Planck} CMB estimate of the Hubble constant $H_0$ and the SH0ES collaboration measurements. After showing the $H_0$ evaluations made from different teams using different methods and geometric calibrations, we list a few interesting new physics models that could alleviate this tension and discuss how the next decade's experiments will be crucial. Moreover, we focus on the tension of the {\it Planck} CMB data with weak lensing measurements and redshift surveys, about the value of the matter energy density $\Omega_m$, and the amplitude or rate of the growth of structure ($\sigma_8,f\sigma_8$). We list a few interesting models proposed for alleviating this tension, and we discuss the importance of trying to fit a full array of data with a single model and not just one parameter at a time. Additionally, we present a wide range of other less discussed anomalies at a statistical significance level lower than the $H_0$--$S_8$ tensions which may also constitute hints towards new physics, and we discuss possible generic theoretical approaches that can collectively explain the non-standard nature of these signals.[Abridged], Comment: Contribution to Snowmass 2021. 224 pages, 27 figures. Accepted for publication in JHEAp

The reconstruction method was proposed more than a decade ago to boost the signal of baryonic acoustic oscillations measured in galaxy redshift surveys, which is one of key probes for dark energy. After moving the observed overdensities in galaxy surveys back to their initial position, the reconstructed density field is closer to a linear Gaussian field, with higher-order information moved back into the power spectrum. We find that by jointly analysing power spectra measured from the pre- and post-reconstructed galaxy samples, higher-order information beyond the $2$-point power spectrum can be efficiently extracted, which generally yields an information gain upon the analysis using the pre- or post-reconstructed galaxy sample alone. This opens a window to easily use higher-order information when constraining cosmological models., Comment: 38 pages including 4 figures and 1 table, with a Supplement Information document attached; Version accepted to Communications Physics

Standard full-shape clustering analyses in Fourier space rely on a fixed power spectrum template, defined at the fiducial cosmology used to convert redshifts into distances, and compress the cosmological information into the Alcock-Paczynski parameters and the linear growth rate of structure. In this paper, we propose an analysis method that operates directly in the cosmology parameter space and varies the power spectrum template accordingly at each tested point. Predictions for the power spectrum multipoles from the TNS model are computed at different cosmologies in the framework of $\Lambda \rm{CDM}$. Applied to the final eBOSS QSO and LRG samples together with the low-z DR12 BOSS galaxy sample, our analysis results in a set of constraints on the cosmological parameters $\Omega_{\rm cdm}$, $H_0$, $\sigma_8$, $\Omega_{\rm b}$ and $n_s$. To reduce the number of computed models, we construct an iterative process to sample the likelihood surface, where each iteration consists of a Gaussian process regression. This method is validated with mocks from N-body simulations. From the combined analysis of the (e)BOSS data, we obtain the following constraints: $\sigma_8=0.877\pm 0.049$ and $\Omega_{\rm m}=0.304^{+0.016}_{-0.010}$ without any external prior. The eBOSS quasar sample alone shows a $3.1\sigma$ discrepancy compared to the Planck prediction., Comment: 13 pages, 7 figures

We construct cosmic void catalogues with the DIVE void finder upon SDSS BOSS DR12 and eBOSS DR16 galaxy samples with BAO reconstruction applied, and perform a joint BAO analysis using different types of galaxies and the corresponding voids. The BAO peak is evident for the galaxy-galaxy, galaxy-void, and void-void correlation functions of all datasets, including the ones cross correlating luminous red galaxy and emission line galaxy samples. Two multi-tracer BAO fitting schemes are then tested, one combining the galaxy and void correlation functions with a weight applied to voids, and the other using a single BAO dilation parameter for all clustering measurements of different tracers. Both methods produce consistent results with mock catalogues, and on average ~10 per cent improvements of the BAO statistical uncertainties are observed for all samples, compared to the results from galaxies alone. By combining the clustering of galaxies and voids, the uncertainties of BAO measurements from the SDSS data are reduced by 5 to 15 per cent, yielding 0.9, 0.8, 1.1, 2.3, and 2.9 per cent constraints on the distance $D_{_{\rm V}}(z)$, at effective redshifts of 0.38, 0.51, 0.70, 0.77, and 0.85, respectively. When combined with BAO measurements from SDSS MGS, QSO, and Ly$\alpha$ samples, as well as the BBN results, we obtain $H_0 = 67.58 \pm 0.91\,{\rm km}\,{\rm s}^{-1}\,{\rm Mpc}^{-1}$, $\Omega_{\rm m} = 0.290 \pm 0.015$, and $\Omega_\Lambda h^2 = 0.3241 \pm 0.0079$ in the flat-$\Lambda$CDM framework, where the 1$\,\sigma$ uncertainties are around 6, 6, and 17 per cent smaller respectively, compared to constraints from the corresponding anisotropic BAO measurements without voids and LRG-ELG cross correlations., Comment: 33 pages, 30 figures, published on MNRAS

There has been a significant interest in modifications of the standard $\Lambda$ Cold Dark Matter ($\Lambda$CDM) cosmological model prompted by tensions between certain datasets, most notably the Hubble tension. The late-time modifications of the $\Lambda$CDM model can be parametrized by three time-dependent functions describing the expansion history of the Universe and gravitational effects on light and matter in the Large Scale Structure. We perform the first joint Bayesian reconstruction of these three functions from a combination of recent cosmological observations, utilizing a theory-informed prior built on the general Horndeski class of scalar-tensor theories. This reconstruction is interpreted in light of the well-known $H_0$, the $S_8$ and the $A_L$ tensions. We identify the phenomenological features that alternative theories would need to have in order to ease some of the tensions, and deduce important constraints on broad classes of modified gravity models. Among other things, our findings suggest that late-time dynamical dark energy and modifications of gravity are not likely to offer a solution to the Hubble tension, or simultaneously solve the $A_L$ and $S_8$ tensions., Comment: 17 pages, 11 figures

Recently, in [1], we presented the first combined non-parametric reconstruction of the three time-dependent functions that capture departures from the standard cosmological model, $\Lambda$CDM, in the expansion history and gravitational effects on matter and light from the currently available combination of the background and large scale structure data. The reconstruction was performed with and without a theory-informed prior, built on the general Horndeski class of scalar-tensor theories, that correlates the three functions. In this work, we perform a decomposition of the prior and posterior covariances of the three functions to determine the structure of the modes that are constrained by the data relative to the Horndeski prior. We find that the combination of all data can constrain 15 combined eigenmodes of the three functions with respect to the prior. We examine and interpret their features in view of the well-known tensions between datasets within the $\Lambda$CDM model. We also assess the bias introduced by the simplistic parameterizations commonly used in the literature for constraining deviations from GR on cosmological scales., Comment: 19 pages, 6 figures

We measure the small-scale clustering of the Data Release 16 extended Baryon Oscillation Spectroscopic Survey Luminous Red Galaxy sample, corrected for fibre-collisions using Pairwise Inverse Probability weights, which give unbiased clustering measurements on all scales. We fit to the monopole and quadrupole moments and to the projected correlation function over the separation range $7-60\,h^{-1}$Mpc with a model based on the Aemulus cosmological emulator to measure the growth rate of cosmic structure, parameterized by $f\sigma_8$. We obtain a measurement of $f\sigma_8(z=0.737)=0.408\pm0.038$, which is $1.4\sigma$ lower than the value expected from 2018 Planck data for a flat $\Lambda$CDM model, and is more consistent with recent weak-lensing measurements. The level of precision achieved is 1.7 times better than more standard measurements made using only the large-scale modes of the same sample. We also fit to the data using the full range of scales $0.1-60\,h^{-1}$Mpc modelled by the Aemulus cosmological emulator and find a $4.5\sigma$ tension in the amplitude of the halo velocity field with the Planck+$\Lambda$CDM model, driven by a mismatch on the non-linear scales. This may not be cosmological in origin, and could be due to a breakdown in the Halo Occupation Distribution model used in the emulator. Finally, we perform a robust analysis of possible sources of systematics, including the effects of redshift uncertainty and incompleteness due to target selection that were not included in previous analyses fitting to clustering measurements on small scales., Comment: 19 pages, 16 figures, published in MNRAS

We investigate the large-scale clustering of the final spectroscopic sample of quasars from the recently completed extended Baryon Oscillation Spectroscopic Survey (eBOSS). The sample contains $343708$ objects in the redshift range $0.8

The LOFAR Two-metre Sky Survey (LoTSS) is an ongoing survey aiming to observe the entire Northern sky, providing an excellent opportunity to study the distribution and evolution of the large-scale structure of the Universe. The source catalogue from the public LoTSS first data release (DR1) covers 1% of the sky, and shows correlated noise or fluctuations of the flux density calibration on few degree scales. We explore the LoTSS DR1 to understand the survey systematics and data quality of this first data release. We produce catalog mocks to estimate uncertainties, and measure the angular clustering statistics of LoTSS galaxies, which fit the $\Lambda$CDM cosmology reasonably well. We employ a Markov chain Monte Carlo (MCMC) based Bayesian analysis to recover the best galaxy biasing scheme and multi-component source fraction for LoTSS DR1 above $1$ mJy assuming different possible redshift templates. After masking some noisy and uneven patches and with suitable flux density cuts, the LOFAR survey appears qualified for large-scale cosmological studies. The upcoming data releases from LOFAR are expected to be deeper and wider, and will therefore provide improved cosmological measurements., Comment: 12 pages, 16 figures, 1 Table, accepted for publication in ApJ