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General relativistic corrections to the expansion rate of the Universe arise when the Einstein equations are averaged over a spatial volume in a locally inhomogeneous cosmology. It has been suggested that they may contribute to the observed…
Recently ({\em Class. Quant. Grav.} {\bf 20} 625-664) the concept of {\em causal mapping} between spacetimes --essentially equivalent in this context to the {\em chronological map} one in abstract chronological spaces--, and the related…
Numerical simulations are a versatile tool providing insight into the complicated process of structure formation in cosmology. This process is mainly governed by gravity, which is the dominant force on large scales. To date, a century after…
We perform large-scale cosmological simulations that solve Einstein's equations directly via numerical relativity. Starting with initial conditions sampled from the cosmic microwave background, we track the emergence of a cosmic web without…
For a freely evolving granular fluid, the buildup of spatial correlations in density and flow field is described using fluctuating hydrodynamics. The theory for incompressible flows is extended to the general, compressible case, including…
Quantum gravity places important consistency conditions on low-energy effective field theory, such as the absence of global symmetries. These may have important consequences in the search for particle physics beyond the Standard Model. We…
The principles of General Relativity allow for a non-vanishing cosmological constant, which can possibly be interpreted at least partially in terms of quantum-fluctuations of matter fields. Depending on sign and magnitude it can cause…
Let $X$ be a (data) set. Let $K(x,y)>0$ be a measure of the affinity between the data points $x$ and $y$. We prove that $K$ has the structure of a Newtonian potential $K(x,y)=\varphi(d(x,y))$ with $\varphi$ decreasing and $d$ a quasi-metric…
We discuss the fundamemtal constants in the Standard Model of particle physics, in particular possible changes of these constants on the cosmological time scale. The Grand Unification of the observed strong, electromagnetic and weak…
Symmetry invariant local interaction of a many body system leads to global constraints. We obtain explicit forms of the global macroscopic condition assuring that at the microscopic level the evolution respects the overall symmetry.
In a mean-field approximation within Kinetic Field Theory, it is possible to derive an accurate analytic expression for the power spectrum of present-day non-linear cosmic density fluctuations. It depends on the theory of gravity and the…
Cosmology in extended theories of gravity is considered assuming the Palatini variational principle, for which the metric and connection are independent variables. The field equations are derived to linear order in perturbations about the…
We consider a two-dimensional Coulomb gas of positive and negative pointlike unit charges interacting via a logarithmic potential. The density (rather than the charge) correlation functions are studied. In the bulk, the form-factor theory…
The gravitationally-driven evolution of cold dark matter dominates the formation of structure in the Universe over a wide range of length scales. While the longest scales can be treated by perturbation theory, a fully quantitative…
We study the consequences of the $f(R/\Box)$ gravity models for the Solar system and the large scale structure of the universe. The spherically symmetric solutions can be used to obtain bounds on the constant and the linear parts of the…
The emergence of macroscopic coherence in a many-body quantum system is a ubiquitous phenomenon across different physical systems and scales. This Chapter reviews key concepts characterizing such systems (correlation functions,…
Our recent interest is focused on establishing the necessary and sufficient conditions that guarantee a long-term stable evolution of both natural and artificial systems. Two necessary conditions, called global and local boundedness, are…
A uniform in space, oscillatory in time plasma equilibrium sustained by a time-dependent current density is analytically and numerically studied resorting to particle-in-cell simulations. The dispersion relation is derived from the Vlasov…
Starting from astrophysical indications that the fine structure constant might undergo a small cosmological time shift, we discuss the implications of such an effect from the point of view of particle physics. Grand unification implies…
The evolution of inhomogeneities in a spherical collapse model is studied by expanding the Einstein equation in powers of inverse radial parameter. In the linear regime, the density contrast is obtained for flat, closed and open universes.…