Selected Topics in Numerical Methods for Cosmology
Sandro Dias Pinto Vitenti, Mariana Penna-Lima
备注：
23 pages, 3 figures. Contribution to the 3rd José Plínio Baptista School on Cosmology held in 2016 in Pedra Azul, Espírito Santo, Brazil. Submitted to Universe
The large amount of cosmological data already available (and in the near future) makes necessary the development of efficient numerical codes. Many software products have been implemented to perform cosmological analyses considering one or few probes. The need of multi-task software is rapidly increasing, in order to combine numerous cosmological probes along with their specificity (e.g., astrophysical descriptions and systematic errors). In this work we mention some of these libraries, bringing out some challenges they will face in the few-percent error era (on the cosmological parameters). We review some concepts of the standard cosmological model, and examine some specific topics on their implementation, bringing, for example, the discussion on how some quantities are numerically defined in different codes. We also consider implementation differences between public codes, mentioning their advantages/disadvantages.
We present galaxy velocity dispersions and dynamical mass estimates for 44 galaxy clusters selected via the Sunyaev-Zel'dovich (SZ) effect by the Atacama Cosmology Telescope. Dynamical masses for 18 clusters are reported here for the first time. Using \Nbody\ simulations, we model the different observing strategies used to measure the velocity dispersions and account for systematic effects resulting from these strategies. We find that the galaxy velocity distributions may be treated as isotropic, and that an aperture correction of up to 7 per cent in the velocity dispersion is required if the …
Precision cosmology has recently triggered new attention on the topic of approximate methods for the clustering of matter on large scales, whose foundations date back to the period from late '60s to early '90s. Indeed, although the prospect of reaching sub-percent accuracy in the measurement of clustering poses a challenge even to full N-body simulations, an accurate estimation of the covariance matrix of clustering statistics, not to mention the sampling of parameter space, requires usage of a large number (hundreds in the most favourable cases) of simulated (mock) galaxy catalogs. Combinatio…
These notes aim at presenting an overview of Bayesian statistics, the underlying concepts and application methodology that will be useful to astronomers seeking to analyse and interpret a wide variety of data about the Universe. The level starts from elementary notions, without assuming any previous knowledge of statistical methods, and then progresses to more advanced, research-level topics. After an introduction to the importance of statistical inference for the physical sciences, elementary notions of probability theory and inference are introduced and explained. Bayesian methods are then p…
Scalar fields have played an important role in the development of the fundamental theories of physics as well as in other branches of physics such as gravitation and cosmology. For a long time these escaped detection until 2012 year when the Higgs boson was observed for the first time. Since then alternatives to the general theory of relativity like the Brans-Dicke theory, scalar-tensor theories of gravity and their higher derivative generalizations -- collectively known as Horndeski theories -- have acquired renewed interest. In the present review we discuss on several selected topics regardi…
We apply the Velocity Distribution Function (VDF) to a sample of Sunyaev-Zel'dovich (SZ)-selected clusters, and we report preliminary cosmological constraints in the $σ_8$-$Ω_m$ cosmological parameter space. The VDF is a forward-modeled test statistic that can be used to constrain cosmological models directly from galaxy cluster dynamical observations. The method was introduced in Ntampaka et al. (2017) and employs line-of-sight velocity measurements to directly constrain cosmological parameters; it is less sensitive to measurement error than a standard halo mass function approach. The method …
We examine the stacked thermal Sunyaev-Zel\text{'}dovich (SZ) signals for a sample of galaxy cluster candidates from the Spitzer-HETDEX Exploratory Large Area (SHELA) Survey, which are identified in combined optical and infrared SHELA data using the redMaPPer algorithm. We separate the clusters into three richness bins, with average photometric redshifts ranging from 0.70 to 0.80. The richest bin shows a clear temperature decrement at 148 GHz in the Atacama Cosmology Telescope data, which we attribute to the SZ effect. All richness bins show an increment at 220 GHz, which we attribute to dust …
We present a catalog of 182 galaxy clusters detected through the Sunyaev-Zel'dovich effect by the Atacama Cosmology Telescope in a contiguous 987.5 deg$^{2}$ field. The clusters were detected as SZ decrements by applying a matched filter to 148 GHz maps that combine the original ACT equatorial survey with data from the first two observing seasons using the ACTPol receiver. Optical/IR confirmation and redshift measurements come from a combination of large public surveys and our own follow-up observations. Where necessary, we measured photometric redshifts for clusters using a pipeline that achi…
We review recent developments and results in testing general relativity (GR) at cosmological scales. The subject has witnessed rapid growth during the last two decades with the aim of addressing the question of cosmic acceleration and the dark energy associated with it. However, with the advent of precision cosmology, it has also become a well-motivated endeavor by itself to test gravitational physics at cosmic scales. We overview cosmological probes of gravity, formalisms and parameterizations for testing deviations from GR at cosmological scales, selected modified gravity (MG) theories, grav…
The prospect of nonparametric reconstructions of cosmological parameters from observational data sets has been a popular topic in the literature for a number of years. This has mainly taken the form of a technique based on Gaussian processes but this approach is exposed to several foundational issues ranging from overfitting to kernel consistency problems. In this work, we explore the possibility of using artificial neural networks (ANN) to reconstruct late-time expansion and large scale structure cosmological parameters. We first show how mock data can be used to design an optimal ANN for bot…
