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A flat Friedmann–Robertson–Walker universe dominated by a cosmological constant ( Λ ) and cold dark matter (CDM) has been the working model preferred by cosmologists since the discovery of cosmic acceleration 1 , 2 . However, tensions of various degrees of significance are known to be present among existing datasets within the Λ CDM framework 3 – 11 . In particular, the Lyman-α forest measurement of the baryon acoustic oscillations (BAO) by the Baryon Oscillation Spectroscopic Survey 3 prefers a smaller value of the matter density fraction Ω M than that preferred by cosmic microwave background (CMB). Also, the recently measured value of the Hubble constant, H 0  = 73.24 ± 1.74 km s −1  Mpc −1 (ref. 12 ), is 3.4 σ higher than the 66.93 ± 0.62 km s −1  Mpc −1 inferred from the Planck CMB data 7 . In this work, we investigate whether these tensions can be interpreted as evidence for a non-constant dynamical dark energy. Using the Kullback–Leibler divergence 13 to quantify the tension between datasets, we find that the tensions are relieved by an evolving dark energy, with the dynamical dark energy model preferred at a 3.5 σ significance level based on the improvement in the fit alone. While, at present, the Bayesian evidence for the dynamical dark energy is insufficient to favour it over Λ CDM, we show that, if the current best-fit dark energy happened to be the true model, it would be decisively detected by the upcoming Dark Energy Spectroscopic Instrument survey 14 . Recent observations reveal tension between various cosmological probes. Assuming dark energy to be non-constant, depending on redshift, may relieve this tension. The Dark Energy Spectroscopic Instrument survey will be able to confirm this result.

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.Baryon Acoustic Oscillations (BAO) are formed in the early universe and can be measured galaxy redshift survey to probe dark energy, but this feature is degraded with galaxy structure evolution. The authors propose a method that simultaneously use pre- and post-reconstruction power spectra to extract higher order information for surveys to constrain cosmological models.

Comparing measurements of redshift-space distortions (RSDs) with geometrical observations of the expansion of the Universe offers tremendous potential for testing general relativity on very large scales. The basic linear theory of RSDs in the distant-observer limit has been known for 25 years and the effect has been conclusively observed in numerous galaxy surveys. The next generation of galaxy survey will observe many millions of galaxies over volumes of many tens of Gpc 3 . They will provide RSD measurements of such exquisite precision that we will have to carefully analyse and correct for many systematic deviations from this simple picture in order to fully exploit the statistical precision obtained. We review RSD theory and show how ubiquitous RSDs actually are, and then consider a number of potential systematic effects, shamelessly highlighting recent work in which we have been involved. This review ends by looking ahead to the future surveys that will make the next generation of RSD measurements.

The large-scale structure in the distribution of galaxies is thought to arise from the gravitational instability of small fluctuations in the initial density field of the Universe. A key test of this hypothesis is that forming superclusters of galaxies should generate a systematic infall of other galaxies. This would be evident in the pattern of recessional velocities, causing an anisotropy in the inferred spatial clustering of galaxies. Here we report a precise measurement of this clustering, using the redshifts of more than 141,000 galaxies from the two-degree-field (2dF) galaxy redshift survey. We determine the parameter β = Ω 0.6 / b = 0.43 ± 0.07, where Ω is the total mass-density parameter of the Universe and b is a measure of the ‘bias’ of the luminous galaxies in the survey. (Bias is the difference between the clustering of visible galaxies and of the total mass, most of which is dark.) Combined with the anisotropy of the cosmic microwave background, our results favour a low-density Universe with Ω ≈ 0.3.

Canadian astronomers and facilities have had a significant impact in wide-field astronomy. With community planning exercises underway this looks set to continue, with new capabilities and international collaborations in the near future.

Recent local measurements of the Hubble constant made using supernovae have delivered a value that differs by \\(\\sim\\)5\\(\\sigma\\) (statistical error) from predictions using the Cosmic Microwave Background (CMB), or using Baryon Acoustic Oscillations (BAO) and Big-Bang Nucleosynthesis (BBN) constraints, which are themselves consistent. The effective volume covered by the supernovae is small compared to the other probes, and it is therefore interesting to consider whether sample variance (often also called cosmic variance) is a significant contributor to the offset. We consider four ways of calculating the sample variance: (i) perturbation theory applied to the luminosity distance, which is the most common method considered in the literature; (ii) perturbation of cosmological parameters, as is commonly used to alleviate super-sample covariance in sets of N-body simulations; (iii) a new method based on the variance between perturbed spherical top-hat regions; (iv) using numerical N-body simulations. All give consistent results showing that, for the Pantheon supernova sample, sample variance can only lead to fluctuations in \\(H_0\\) of order \\(\\pm1\\) km s\\(^{-1}\\)Mpc\\(^{-1}\\) or less. While this is not in itself a new result, the agreement between the methods used adds to its robustness. Furthermore, it is instructive to see how the different methods fit together. We also investigate the internal variance of the \\(H_{0}\\) measurement using SH0ES and Pantheon data. By searching for an offset between measurements in opposite hemispheres, we find that the direction coincident with the CMB dipole has a higher \\(H_{0}\\) measurement than the opposite hemisphere by roughly 4 km s\\(^{-1}\\)Mpc\\(^{-1}\\). We compare this with a large number of simulations and find that the size of this asymmetry is statistically likely, but the preference of direction may indicate that further calibration is needed.

We investigate theoretical systematics caused by the application of the halo occupation distribution (HOD) to the study of galaxy clustering at non-linear scales. To do this, we repeat recent cosmological analyses using extended HOD models based on both the Aemulus and Aemulus \\(\\nu\\) simulation suites, allowing for variations in the dark matter halo shape, incompleteness, baryonic effects and position bias of central galaxies. We fit to the galaxy correlation function including the projected correlation function, redshift space monopole and quadrupole, and consider how the changes in HOD affect the retrieval of cosmological information. These extensions can be understood as an evaluation of the impact of the secondary bias in the clustering analysis. In the application of BOSS galaxies, these changes do not have a significant impact on the measured linear growth rate. But, we do find weak to mild evidence for some of the effects modeled by the empirical parameterizations adopted. The modeling is able to make the HOD approach more complete in terms of cosmological constraints. We anticipate that the future and better data can provide tighter constraints on the new prescriptions of the HOD model.

We measure and analyze galaxy clustering and the dependence on luminosity, color, age, stellar mass and specific star formation rate using Baryon Oscillation Spectroscopic Survey (BOSS) galaxies at \\(0.48

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