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Long-ranged, or power-law, behavior of correlation functions in both space and time is discussed for classical systems and for quantum systems at finite temperature, and is compared with the corresponding behavior in quantum systems at zero…
In models of modified gravity, extra degrees of freedom usually appear. They must be removed from the spectrum because they may indicate the presence of instabilities and because otherwise the model might not agree with observation. In the…
A general structure theorem on higher order invariants is proven. For an arithmetic group, the structure of the corresponding Hecke module is determined. It is shown that the module does not contain any irreducible submodule. This explains…
This paper is an exploration of the nuanced realm of reference frames within the framework of General Relativity. Our analysis exposes a violation of Earman's SP1 principle in scenarios involving fields that are dynamically uncoupled, a…
Alignments of galaxy clusters (the Binggeli effect), as well as of galaxies themselves have long been studied both observationally and theoretically. Here we test the influence of large-scales structures and tidal fields on the shapes and…
Observational surveys of galaxies are not trivially related to single-epoch snapshots from computer simulations. Observationally, an increase in the distance along the line-of-sight corresponds to an earlier cosmic time at which the…
An important part of cosmological model fitting relies on correlating distance indicators of objects (for example type Ia supernovae) with their redshift, often illustrated on a Hubble diagram. Comparing the observed correlation with a…
Consider a proposed model of the universe with $\hbar$ much greater than its well-known value of $10^{-34} Js$. In this model universe, very large objects can show quantum behaviors. In a scenario with large extra dimensions, $\hbar$ can…
In this paper, we study the effects of high-order operators on the non-relativistic Lifshitz holography in the framework of the Ho\v{r}ava-Lifshitz (HL) theory of gravity, which naturally contains high-order operators in order for the…
Several recent studies have shown how to properly calculate the observed clustering of galaxies in a relativistic context, and uncovered corrections to the Newtonian calculation that become significant on scales near the horizon. Here, we…
Cosmic variance is the uncertainty in observational estimates of the volume density of extragalactic objects such as galaxies or quasars arising from the underlying large-scale density fluctuations. This is often a significant source of…
In this paper we give five gauge-invariant systems of governing equations for first and second order scalar perturbations of flat Friedmann-Lema\^{i}tre universes that are minimal in the sense that they contain no redundant equations or…
It is possible that there may be differences in the fundamental physical parameters from one side of the observed universe to the other. I show that the cosmological constant is likely to be the most sensitive of the physical parameters to…
Since Lorentz invariance plays an important role in modern physics, it is of interest to test the possible Lorentz invariance violation (LIV). The time-lag (the arrival time delay between light curves in different energy bands) of Gamma-ray…
Using the gradient expansion approach, we formulate a nonlinear cosmological perturbation theory on super-horizon scales valid to $O(\epsilon^2)$, where $\epsilon$ is the expansion parameter associated with a spatial derivative. For…
In the present paper we consider controllability and observability of second order linear time invariant systems in matrix form. Without reducing into first order systems we show how the classical conditions for first order linear systems…
The evolution of cosmological large-scale perturbations is described in terms of the concordant model based on the recent discovery of cosmic vacuum. It is demonstrated that the process is robustly controlled by a few epoch-independent…
A consistent implementation of quantum gravity is expected to change the familiar notions of space, time and the propagation of matter in drastic ways. This will have consequences on very small scales, but also gives rise to correction…
We study a system of hard rods of finite size in one space dimension, which move by Brownian noise while avoiding overlap. We consider a scaling in which the number of particles tends to infinity while the volume fraction of the rods…
Standard cosmological models rely on an approximate treatment of gravity, utilizing solutions of the linearized Einstein equations as well as physical approximations. In an era of precision cosmology, we should ask: are these approximate…