Related papers: Topological Echoes of Primordial Physics in the Un…
We use numerical relativity simulations to describe the spacetime evolution during nonlinear structure formation in $\Lambda$CDM cosmology. Fully nonlinear initial conditions are set at an initial redshift $z\approx 300$, based directly on…
The article is part of a review volume on the formation of the first black holes and summarises FLRW-cosmologies, the statistical description of cosmic structures as Gaussian random fields, as well as fluid mechanics in the linear and…
Topologically ordered phases of matter display a number of unique characteristics, including ground states that can be interpreted as patterns of closed strings. In this paper, we consider the problem of detecting and distinguishing closed…
We study constraints on primordial mode-coupling from the power spectrum, squeezed-limit bispectrum and collapsed trispectrum of matter and halos. We describe these statistics in terms of long-wavelength $2$-point functions involving the…
Persistent homology provides a robust methodology to infer topological structures from point cloud data. Here we explore the persistent homology of point clouds embedded into a probabilistic setting, exploiting the theory of point…
Topological data analysis is becoming increasingly relevant to support the analysis of unstructured data sets. A common assumption in data analysis is that the data set is a sample---not necessarily a uniform one---of some high-dimensional…
Topological Data Analysis has grown in popularity in recent years as a way to apply tools from algebraic topology to large data sets. One of the main tools in topological data analysis is persistent homology. This paper uses undergraduate…
We investigate the dependence of the mass function of dark-matter haloes on their environment within the cosmic web of large-scale structure. A dependence of the halo mass function on large-scale mean density is a standard element of…
It has recently been proposed that the large-scale bias of dark matter halos depends sensitively on primordial non-Gaussianity of the local form. In this paper we point out that the strong scale dependence of the non-Gaussian halo bias…
We present mathematical models based on persistent homology for analyzing force distributions in particulate systems. We define three distinct chain complexes: digital, position, and interaction, motivated by different capabilities of…
Cosmic Voids are a promising probe of cosmology for spectroscopic galaxy surveys due to their unique response to cosmological parameters. Their combination with other probes promises to break parameter degeneracies. Due to simplifying…
Analysis of three-dimensional cosmological surveys has the potential to answer outstanding questions on the initial conditions from which structure appeared, and therefore on the very high energy physics at play in the early Universe. We…
The connections among galaxies, the dark matter halos where they form and the properties of the large-scale Cosmic Web still need to be completely disentangled. We use the cosmological hydrodynamical simulation TNG100 of the IllustrisTNG…
Using $N$-body simulations of cosmological large-scale structure formation, for the first time, we show that the anisotropic primordial non-Gaussianity (PNG) causes a scale-dependent modification, given by $1/k^2$ at small $k$ limit, in the…
In the standard cosmological model the dark energy (DE) and nonrelativistic (NR) matter densities are observationally determined to be comparable at the present time, in spite of their greatly different evolution histories. This `cosmic…
Assume that a finite set of points is randomly sampled from a subspace of a metric space. Recent advances in computational topology have provided several approaches to recovering the geometric and topological properties of the underlying…
We describe cosmological simulation techniques and their application to studies of cosmic structure formation, with particular attention to recent hydrodynamic simulations of structure in the high redshift universe. Collisionless N-body…
The evolution of a flat, isotropic and homogeneous universe is studied. The background geometry in the early phases of the universe is conjectured to be filled with causal bulk viscous cosmological fluid and dark energy. The energy density…
Adaptive SPH and N-body simulations were carried out to study the effect of gasdynamics on the structure of dark matter halos that result from the gravitational instability and fragmentation of cosmological pancakes. Such halos resemble…
Persistent homology probes topological properties from point clouds and functions. By looking at multiple scales simultaneously, one can record the births and deaths of topological features as the scale varies. In this paper we use a…