Modern cosmology relies on the assumption of large-scale isotropy and homogeneity of the Universe. However, locally the Universe is inhomogeneous and anisotropic. So, how can local measurements (at the 100 Mpc scale) be used to determine global cosmological parameters (defined at the 10 Gpc scale)? We use Buchert's averaging formalism and determine a set of locally averaged cosmological parameters in the context of the flat Lambda cold dark matter model. We calculate their ensemble means (i.e. their global values) and variances (i.e. their cosmic variances). We apply our results to typical survey geometries and focus on the study of the effects of local fluctuations of the curvature parameter. By this means we show, that in the linear regime cosmological backreaction and averaging can be reformulated as the issue of cosmic variance. The cosmic variance is found largest for the curvature parameter and discuss some of its consequences. We further propose to use the observed variance of cosmological parameters to measure the growth factor. [abbreviated]
Effect of inhomogeneity of the Universe on a gravitationally bound local system: A no-go result for explaining the secular increase in the astronomical unit
We pursue a program to confront observations with inhomogeneous extensions of the FLRW metric. The main idea is to test the Copernican principle rather than assuming it a priori. We consider the $Λ$CDM model endowed with a spherical $Λ$LTB inhomogeneity around us, that is, we assume isotropy and test the hypothesis of homogeneity. We confront the $Λ$LTB model with the latest available data from CMB, BAO, type Ia supernovae, local $H_0$, cosmic chronometers, Compton y-distortion and kinetic Sunyaev-Zeldovich effect. We find that these data can constrain tightly this extra inhomogeneity, almost …
We find an exact solution of Scalar-Tensor-Vector Gravity field equations that represents a black hole embedded in an expanding universe. This is the first solution of the kind found in the theory. We analyze the properties of the apparent horizons as well as the essential singularities of the metric, and compare it with the McVittie spacetime of General Relativity. Depending on the cosmological model adopted and the value of the free parameter $α$ of the theory, the solution describes a cosmological black hole, an inhomogeneity in an expanding universe, or a naked singularity. We use the latt…
Cosmic variance or galaxy bias? Disentangling finite-volume and galaxy formation effects in cosmological analysis
Institute for Fundamental Physics of the Universe (IFPU)（宇宙基本物理研究所）；SISSA - International School for Advanced Studies（国际高等研究院）；INAF - Osservatorio Astronomico di Trieste（的里雅斯特天文台）；INFN – National Institute for Nuclear Physics（意大利国家核物理研究所）；Instituto de Astrofísica de Canarias（加那利天体物理研究所）；Universidad de La Laguna（拉古纳大学）
We test a method to reduce unwanted sample variance when predicting Lyman-$α$ (ly$α$) forest power spectra from cosmological hydrodynamical simulations. Sample variance arises due to sparse sampling of modes on large scales and propagates to small scales through non-linear gravitational evolution. To tackle this, we generate initial conditions in which the density perturbation amplitudes are {\it fixed} to the ensemble average power spectrum -- and are generated in {\it pairs} with exactly opposite phases. We run $50$ such simulations ($25$ pairs) and compare their performance against $50$ sta…
Making cosmological inferences from the observed galaxy clustering requires accurate predictions for the mean clustering statistics and their covariances. Those are affected by cosmic variance -- the statistical noise due to the finite number of harmonics. The cosmic variance can be suppressed by fixing the amplitudes of the harmonics instead of drawing them from a Gaussian distribution predicted by the inflation models. Initial realizations also can be generated in pairs with 180 degrees flipped phases to further reduce the variance. Here, we compare the consequences of using paired-and-fixed…
György Paál, the Hungarian cosmologist died in 1992. This article was published twenty-five years later in the Hungarian Astronomical Association (HAA, MCSE in Hungarian) 2017 yearbook for his memory. After short introduction of the history of cosmology we briefly introduce the XX. century cosmological discoveries. For his early years G. Paál studied the large-scale inhomogeneity in the Universe. He was one of the first astronomer who realized some periodicity in the quasar redshift distribution. In the early 90s he also studied the galaxy redshift distribution in the so-called pencil-beam sur…
There are several solutions of Einstein field equations that describe an inhomogeneity in an expanding universe. Among these solutions, the McVittie metric and its generalizations have been investigated through decades, though a full understanding of them is still lacking. In this note, we explore the trajectories of photons and massive particles in generalized McVittie spacetimes. In the case of massless particles, we show that no circular orbits are possible for those models that admit cosmological singularities. We also analyze the trajectory of particles for a specific generalized McVittie…
We analyze whether a black hole can exist and survive in a universe that goes through a cosmological bounce. To this end, we investigate a central inhomogeneity embedded in a bouncing cosmological background modeled by the comoving generalized McVittie metric. Contrary to other dynamical metrics available in the literature, this solution allows for the interaction of the central object with the cosmological fluid. We show that the horizons associated with this metric change with cosmic time because they are coupled to the cosmic evolution as the mass of the central object is always proportiona…
Counts-in-cells (CIC) measurements contain a wealth of cosmological information yet are seldom used to constrain theories. Although we can predict the shape of the distribution for a given cosmology, to fit a model to the observed CIC probabilities requires the covariance matrix -- both the variance of counts in one probability bin and the covariance between counts in different bins. To date, there have been no general expressions for these variances. Here we show that correlations of particular levels, or "slices," of the density field determine the variance and covariance of CIC probabilitie…
Cosmic variance limits the accuracy of cosmological N-body simulations, introducing bias in statistics such as the power spectrum, halo mass function, or the cosmic shear. We provide new methods to measure and reduce the effect of cosmic variance in existing and new simulations. We ran pairs of simulations using phase-shifted initial conditions with matching amplitudes. We set the initial amplitudes of the Fourier modes to ensure that the average power spectrum of the pair is equal to the cosmic mean power spectrum from linear theory. The average power spectrum of a pair of such simulations re…
The Cosmological Principle states that the Universe is statistically isotropic and homogeneous on large scales. In particular, this implies statistical isotropy in the galaxy distribution, after removal of a dipole anisotropy due to the observer's motion. We test this hypothesis with number count maps from the NVSS radio catalogue. We use a local variance estimator based on patches of different angular radii across the sky and compare the source count variance between and within these patches. In order to assess the statistical significance of our results, we simulate radio maps with the NVSS …
Pulsar timing-array correlation measurements offer an exciting opportunity to test the nature of gravity in the cosmologically novel nanohertz gravitational wave regime. The stochastic gravitational wave background is assumed Gaussian and random, while there are limited pulsar pairs in the sky. This brings theoretical uncertainties to the correlation measurements, namely the pulsar variance due to pulsar samplings and the cosmic variance due to Gaussian signals. We demonstrate a straightforward calculation of the mean and the variances on the Hellings-Downs correlation relying on a power spect…
The impact of the cosmic variance on $H_0$ on cosmological analyses
$H_0$的局部（arXiv：1804.10655）和全局（arXiv：1605.02985）测量之间的当前$3.8 σ$张力无法通过一致性$Λ$ CDM模型完全解释。它可能是由未知的系统学或超出标准模型的物理学产生的。另一方面，众所周知，线性微扰理论预测哈勃参数$H_0$的宇宙方差，这导致其局部测定的系统误差。在这里，我们研究如何包括在可能性的宇宙方差$H_0$影响统计推断。特别是，我们认为$γ$ CDM，$w$ CDM和$γw$ CDM参数扩展的标准模型，我们约束与最新的CMB，BAO，SNe Ia，RSD和$H_0$数据。我们学到了两个重要的教训。首先，来自宇宙方差的系统误差--与模型无关--在考虑红移范围$0.0233 \le z \le 0.15$时约为$σ_{\text{cv}}\approx 0.88$ km s $^{-1}$ Mpc $^{-1}$（1.2\% $H_0^{\text{loc}}$），这与（arXiv：1804.10655）的主要分析相关，而在考虑更宽的红移范围$0.01 \le z \le 0.15$时约为$σ_{\text{cv}}\approx 1.5$ km s $^{-1}$ Mpc $^{-1}$（2.1\% $H_0^{\text{loc}}$）。尽管$σ_{\text{cv}}$影响局部$H_0$上的总误差预算，但它并不能显著缓解$…
Accurate mock catalogues are essential for assessing systematics in the cosmological analysis of large galaxy surveys. Anisotropic two-point clustering measurements from the same simulation show some scatter for different lines of sight (LOS), but are on average equal, due to cosmic variance. This results in scatter in the measured cosmological parameters. We use the OuterRim N-body simulation halo catalogue to investigate this, considering the 3 simulation axes as LOS. The quadrupole of the 2-point statistics is particularly sensitive to changes in the LOS, with sub-percent level differences …
We develop a theoretical framework to describe the cosmological observables on the past light cone such as the luminosity distance, weak lensing, galaxy clustering, and the cosmic microwave background anisotropies. We consider that all the cosmological observables include not only the background quantity, but also the perturbation quantity, and they are subject to cosmic variance, which sets the fundamental limits on the cosmological information that can be derived from such observables, even in an idealized survey with an infinite number of observations. To quantify the maximum cosmological i…
