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The large-scale structure of the Universe is distributed in a cosmic web. Studying the distribution and clustering of dark matter particles and haloes may open up a new horizon for studying the physics of the dark Universe. In this work, we investigate the nearest neighbour statistics and spherical contact function in cosmological models with massive neutrinos. For this task, we use the relativistic N -body code, gevolution, and study particle snapshots at three different redshifts. In each snapshot, we find the haloes and evaluate the letter functions for them. We show that a generic behaviour can be found in the nearest neighbour, G (r), and spherical contact functions, F (r), which makes these statistics promising tools to constrain the total neutrino mass. [ABSTRACT FROM AUTHOR]

We describe a general constitutive framework for a teleparallel extension of the general theory of relativity. This approach goes beyond the teleparallel equivalent of general relativity (TEGR) by broadening the analogy with the electrodynamics of media. In particular, the main purpose of this paper is to investigate in detail a local constitutive extension of TEGR that is the local limit of non-local gravity. Within this framework, we study the modified Friedmann–Lemaître–Robertson–Walker cosmological models. Of these, the most cogent turns out to be the modified Cartesian flat model which is shown to be inconsistent with the existence of a positive cosmological constant. Moreover, dynamic dark energy and other components of the modified Cartesian flat model evolve differently with the expansion of the universe as compared to the standard flat cosmological model. The observational consequences of the modified Cartesian flat model are briefly explored and it is shown that the model is capable of resolving the H 0 tension. [ABSTRACT FROM AUTHOR]

Structures in the Universe are arranged into the cosmic web. Distributions, statistics, and evolutions of the structures can be used as probes for cosmological models. We investigate the number density of voids and dark matter haloes-in-voids in the excursion set theory (EST). We study the Markov and non-Markov frameworks of EST in both spherical and ellipsoidal collapse models. Afterward, we compare the number density of voids and haloes-in-voids in the standard lambda cold dark matter and the reconstructed model. The reconstructed model is a model-independent reconstruction based on background observations. This work explores the effects of the collapse model barrier in the different EST frameworks on the statistics of voids and the statistics of haloes-in-voids. Finally, we find the hint that cosmological models can be distinguished by the number density of haloes-in-voids in the 1.0−2.5 redshift range. The maximum difference is observed in z ∼ 1.9. [ABSTRACT FROM AUTHOR]

Nonlocal gravity (NLG), a classical extension of Einstein's theory of gravitation, has been studied mainly in linearized form. In particular, nonlinearities have thus far prevented the treatment of cosmological models in NLG. In this essay, we discuss the local limit of NLG and apply this limit to the expanding homogenous and isotropic universe. The theory only allows spatially flat cosmological models; furthermore, de Sitter spacetime is forbidden. The components of the model will have different dynamics with respect to cosmic time as compared to the standard Λ CDM model; specifically, instead of the cosmological constant, the modified flat model of cosmology involves a dynamic dark energy component in order to account for the accelerated phase of the expansion of the universe. [ABSTRACT FROM AUTHOR]

Within the framework of the local limit of nonlocal gravity (NLG), we investigate a class of Bianchi type I spatially homogeneous but anisotropic cosmological models. The modified field equations are presented in this case, and some special solutions are discussed in detail. This modified gravity theory contains a susceptibility function S(x) such that general relativity (GR) is recovered for S = 0. In the modified anisotropic cosmological models, we explore the contribution of S(t) and its temporal derivative to the local anisotropic cosmic acceleration. The implications of our results for observational cosmology are briefly discussed. [ABSTRACT FROM AUTHOR]

In non-linear scales, the matter density distribution is not Gaussian. Consequently, the widely used two-point correlation function is not adequate anymore to capture the matter density field's entire behaviour. Among all statistics beyond correlation functions, the spherical contact (or equivalently void function), and nearest neighbour distribution function seem promising tools to probe matter distribution in non-linear regime. In this work, we use haloes from cosmological N -body simulations, galaxy groups from the volume-limited galaxy group and central galaxies from mock galaxy catalogues, to compare the spherical contact with the nearest neighbour distribution functions. We also calculate the J-function (or equivalently the first conditional correlation function), for different samples. Moreover, we consider the redshift evolution and mass-scale dependence of statistics in the simulations and dependence on the magnitude of volume-limited samples in group catalogues as well as the mock central galaxies. The shape of the spherical contact probability distribution function is nearly skew-normal, with skewness and kurtosis being approximately 0.5 and 3, respectively. On the other hand, the nearest neighbour probability distribution function is nearly lognormal, with logarithmic skewness and kurtosis being approximately 0.1 and 2.5, respectively. Accordingly, the spherical contact distribution function probes larger scales compared to the nearest neighbour distribution function, which is influenced by details of structures. We also find a linear relation between the mean and variance of the spherical contact probability distribution function in simulations and mock galaxies, which could be used as a distinguishing probe of cosmological models. [ABSTRACT FROM AUTHOR]

The Hubble tension may introduce a new course of action to revise the standard Lambda cold dark matter (ΛCDM) model to unravel dark energy and dark matter physics. The Hubble parameter can be reconstructed by late-time observations of the background evolution model independently. We relate the reconstructed Hubble parameter to the structure formation and large-scale structure observables in this work. We use excursion set theory to calculate the number density of dark matter haloes and the mass function of progenitors. We obtain results for both the Markov and non-Markov extensions of excursion set theory in the context of spherical and ellipsoidal collapse. We show that the number density of dark matter haloes in the reconstructed model has ∼2σ difference in comparison with the Planck 2018 ΛCDM in the mass range M ≳ 1012 M⊙. We also compare the dark matter halo progenitor mass function with the pair-galaxy statistics and their mass assembly history from observational data of the Hubble Space Telescope Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey. Due to complications in distinguishing the ratio of accretion and merger in mass assembly, our result on the pair fraction is for illustration only. However, the ∼5 times more accurate observations will be promising for distinguishing the reconstructed model and the Planck 2018 ΛCDM. [ABSTRACT FROM AUTHOR]

We study primordial black holes (PBHs) formation in the excursion set theory (EST) in a vast range of PBHs masses with and without confirmed constraints on their abundance. In this work, we introduce a new concept of the first touch in the context of EST for PBHs formation. This new framework takes into account the earlier horizon re-entry of smaller masses. Our study shows that in the EST, it is possible to produce PBHs in different mass range, with enhanced power spectrum, which could make up all dark matter. We also show that in a broad blue-tilted power spectrum, the production of PBHs is dominated by smaller masses. Our analysis puts an upper limit |$\sim \,$| 0.1 on the amplitude of the curvature power spectrum at length scales relevant for PBHs formation. [ABSTRACT FROM AUTHOR]

The galactic scale challenges of dark matter such as 'missing satellite' problem and 'too big to fail' problem are the main caveats of standard model of cosmology. These challenges could be solved either by implementing the complicated baryonic physics or it could be considered as an indication to a new physics beyond the standard model of cosmology. The modification of collisionless dark matter models or the standard initial conditions are two promising venues for study. In this work, we investigate the effects of the deviations from scale invariant initial curvature power spectrum on number density of dark matter haloes. We develop the non-Markov extension of the excursion set theory to calculate the number density of dark matter substructures and dark matter halo progenitor mass distribution. We show that the plausible solution to 'too big to fail' problem could be obtained by a Gaussian excess in initial power in the scales of k * ∼ 3  h  Mpc−1 that is related to the mass scale of M * ∼ 1011 M⊙. We show that this deviation leads to the decrement of dark matter subhaloes in galactic scale, which is consistent with the current status of the non-linear power spectrum. Our proposal also has a prediction that the number density of Milky Way-type galaxies must be higher than the standard case. [ABSTRACT FROM AUTHOR]

The universe in large scales is structured as a network known as cosmic web. Filaments are one of the structural components of this web, which can be introduced as a novel probe to study the formation and evolution of structures and as a probe to study the cosmological models and to address the missing baryon problem. The aim of this work is to introduce an analytical framework to study the statistics of filaments such as number density of them and also to obtain the length-mass relation. For this objective, we model filaments as collapsed objects which have an extension in one direction, accordingly we use the ellipsoidal collapse to study the evolution of an over-dense region via gravitational instability. We find that the non-linear density of filaments in the epoch of formation is almost mass independent and is in order of ∼30. By introducing filament's extended condition , we find a fitting function for length-mass relation. For the statistics of filaments, we propose a novel framework named excursion set of saddle points. In this approach, we count the saddle points of the density field Hessian matrix, and relate it to the count of filaments. In addition, we addressed the filament in filament problem with up-crossing approximation. [ABSTRACT FROM AUTHOR]

The observed hemispherical power asymmetry in cosmic microwave background radiation can be explained by long-wavelength mode (long-mode) modulation. In this paper, we study the possibility of detecting this effect in the angular power spectrum of the 21-cm brightness temperature. For this task, we study the effect of the neutral hydrogen distribution on the angular power spectrum. This is done by formulating the bias parameter of the ionized fraction to the underlying matter distribution. We also discuss the possibility that the long-mode modulation is accompanied by a primordial non-Gaussianity of local type. In this case, we obtain the angular power spectrum with two effects of primordial non-Gaussianity and long-mode modulation. Finally, we show that the primordial non-Gaussianity enhances the long-mode modulated power of the 21-cm signal via the non-Gaussian scale-dependent bias up to four orders of magnitude. Accordingly, observations of the 21-cm signal with upcoming surveys, such as the Square Kilometer Array (SKA), will probably be capable of detecting hemispherical power asymmetry in the context of long-mode modulation. [ABSTRACT FROM AUTHOR]

Aims: In this work, we address the issue of peculiar velocity measurement in a perturbed Friedmann universe using the deviations from measured luminosity distances of standard candles from background FRW universe. We want to show and quantify the statement that in intermediate redshifts (), deviations from the background FRW model are not uniquely governed by peculiar velocities. Luminosity distances are modified by gravitational lensing. We also want to indicate the importance of relativistic calculations for peculiar velocity measurement at all redshifts. Methods: For this task, we discuss the relativistic correction on luminosity distance and redshift measurement and show the contribution of each of the corrections as lensing term, peculiar velocity of the source and Sachs-Wolfe effect. Then, we use the SNe Ia sample of Union 2, to investigate the relativistic effects, we consider. Results: We show that, using the conventional peculiar velocity method, that ignores the lensing effect, will result in an overestimate of the measured peculiar velocities at intermediate redshifts. Here, we quantify this effect. We show that at low redshifts the lensing effect is negligible compare to the effect of peculiar velocity. From the observational point of view, we show that the uncertainties on luminosity of the present SNe Ia data prevent us from precise measuring the peculiar velocities even at low redshifts (). [ABSTRACT FROM AUTHOR]

We propose a new probe to test the nature of gravity at various redshifts through large-scale cosmological observations. We use our void catalog, extracted from the Sloan Digital Sky Survey (SDSS, DR10), to trace the distribution of matter along the lines of sight to SNe Ia that are selected from the Union II catalog. We study the relation between SNe Ia luminosities and convergence and also the peculiar velocities of the sources. We show that the effects, on SNe Ia luminosities, of convergence and of peculiar velocities predicted by the theory of general relativity and theories of modified gravities are different and hence provide a new probe of gravity at various redshifts. We show that the present sparse large-scale data does not allow us to determine any statistically-significant deviation from the theory of general relativity but future more comprehensive surveys should provide us with means for such an exploration. [ABSTRACT FROM AUTHOR]

We propose an analytical approach to study non-Markov random walks by employing an exact enumeration method. Using the method, we derive an exact expansion for the first-passage time (FPT) distribution of any continuous differentiable non-Markov random walk with Gaussian or non-Gaussian multivariate distribution. As an example, we study the FPT distribution of the fractional Brownian motion with a Hurst exponent H ∈ (1/2, 1) that describes numerous non-Markov stochastic phenomena in physics, biology, and geology and for which the limit H = 1/2 represents a Markov process. [ABSTRACT FROM AUTHOR]