Related papers: Spectral Representation and the Averaging Problem …
This article looks at how inhomogeneous spacetime models may be significant for cosmology. First it looks at how the averaging process may affect large scale dynamics, with backreaction effects leading to effective contributions to the…
Using numerical ray tracing, the paper studies how the average distance modulus in an inhomogeneous universe differs from its homogeneous counterpart. The averaging is over all directions from a fixed observer not over all possible…
Special relativity (SR) with a privileged frame is a framework, which, like the standard relativity theory, is based on the relativity principle and the universality of the (two-way) speed of light but includes a privileged frame as an…
One of the biggest mysteries in cosmology is Dark Energy, which is required to explain the accelerated expansion of the universe within the standard model. But maybe one can explain the observations without introducing new physics, by…
We consider the Universe deep inside the cell of uniformity. At these scales, the Universe is filled with inhomogeneously distributed discrete structures (galaxies, groups and clusters of galaxies), which perturb the background Friedmann…
The ability to map the cosmological expansion has developed enormously, spurred by the turning point one decade ago of the discovery of cosmic acceleration. The standard model of cosmology has shifted from a matter dominated, standard…
Cosmography has been referred to as a solution to the inverse scattering problem, which is reasonable since it allows us to calculate cosmological bounds from data samplers by performing an expansion of the cosmological observables around…
Cosmological fine-tuning has traditionally been associated with the narrowness of the intervals in which the parameters of the physical models must be located to make life possible. A more thorough approach focuses on the probability of the…
WWe define the notion of a random metric space and prove that with probability one such a space is isometricto the Urysohn universal metric space. The main technique is the study of universal and random distance matrices; we relate the…
We review the most recent progress in our understanding of quantum mechanical observables in cosmology in the perturbative regime. It relies on an approach that considers them directly as functions of the data at the space-like boundary at…
In quantum cosmology, one applies quantum physics to the whole universe. While no unique version and no completely well-defined theory is available yet, the framework gives rise to interesting conceptual, mathematical and physical…
In the debate about galaxy correlation there are different questions which can be addressed separately: Which are the statistical methods able to properly detect scale invariance and describe, in general, the properties of irregular and…
Observational data in cosmology indicate a small, positive, and nonvanishing cosmological constant that dominates the energy budget of the present universe. The origin of the cosmological constant from a quantum perspective remains…
The statistical uncertainty in measuring the primordial density perturbations on a given comoving scale is dictated by the number of independent regions of that scale that are accessible to an observer. This number varies with cosmic time…
Parameterizing radiative transfer in means navigating trade-offs between physical accuracy and conceptual clarity. However, currently available schemes sit at the extremes of this spectrum: correlated-k schemes are fast and accurate but…
Scale symmetry is a fundamental symmetry of physics that seems however not to be fully realized in the universe. Here, we focus on the astronomical scales ruled by gravity, where scale symmetry holds and gives rise to a truly scale…
Current constraints on spatial curvature show that it is dynamically negligible: $|\Omega_{\rm K}| \lesssim 5 \times 10^{-3}$ (95% CL). Neglecting it as a cosmological parameter would be premature however, as more stringent constraints on…
Cosmography is a widely applied method to infer kinematics of the Universe at small cosmological scales while remaining agnostic about the theory of gravity at play. Usually cosmologists invoke the Friedmann-Lemaitre-Robertson-Walker (FLRW)…
Studies of the distribution and evolution of galaxies are of fundamental importance to modern cosmology; these studies, however, are hampered by the complexity of the competing effects of spectral and density evolution. Constructing a…
Laplacian spectral kernels and distances (e.g., biharmonic, heat diffusion, wave kernel distances) are easily defined through a filtering of the Laplacian eigenpairs. They play a central role in several applications, such as dimensionality…