Related papers: Cosmologies, singularities and quantum extremal su…
We consider the problem of describing the asymptotic behaviour of \textsc{FRW} universes near their spacetime singularities in general relativity. We find that the Bel-Robinson energy of these universes in conjunction with the Hubble…
We investigate future singularities originating from the anisotropy in the Universe. We formulate a new class of singularities in the homogeneous and anisotropic universe, comparing them with the known singularities in the homogeneous and…
This work investigates alternative theories of gravity, the solutions to their field equations and the constraints that can be imposed upon them from observation and experiment. Specifically, we consider the cosmologies and spherically…
Isotropic models in loop quantum cosmology allow explicit calculations, thanks largely to a completely known volume spectrum, which is exploited in order to write down the evolution equation in a discrete internal time. Because of genuinely…
We present results on quantum quenches in systems with a fixed number of particles in a large region. We show that the typical differences between local and global quenches present in systems with regular thermodynamic limit are lacking in…
We study the dynamics of the homogeneous and isotropic cosmological background in the recently proposed ``quantum phenomenological gravitational dynamics'', characterised by logarithmic corrections to the Bekenstein entropy. We show that…
In this work we analyze the possibility of sudden cosmological singularities, also known as type-II singularities, in the background of a Friedmann-Lema\^itre-Robertson-Walker (FLRW) geometry in an extension of General Relativity (GR) known…
K\"ahler's paper "\"Uber die Verzweigung einer algebraischen Funktion zweier Ver\"anderlichen in der Umgebung einer singul\"aren Stelle" offered a more perceptual view of the link of a complex plane curve singularity than that provided…
We survey some recent progress in the study of algebraic varieties X with log terminal singularities, especially, the uni-ruledness of the smooth locus X^0 of X, the fundamental group of X^0 and the automorphisms group on (smooth or…
We give an introduction into quantum cosmology with emphasis on its conceptual parts. After a general motivation we review the formalism of canonical quantum gravity on which discussions of quantum cosmology are usually based. We then…
The holographic bound states that the entropy in a region cannot exceed one quarter of the area (in Planck units) of the bounding surface. A version of the holographic principle that can be applied to cosmological spacetimes has recently…
We start by presenting a brief summary of fractional quantum mechanics, as means to convey a motivation towards fractional quantum cosmology. Subsequently, such application is made concrete with the assistance of a case study. Specifically,…
Alternative scenarios to the Big Bang singularity have been subject of intense research for several decades by now. Most popular in this sense have been frameworks were such singularity is replaced by a bounce around some minimal…
Mechanical fields over thin elastic surfaces can develop singularities at isolated points and curves in response to constrained deformations (e.g., crumpling and folding of paper), singular body forces and couples, distributions of isolated…
Scaling relations of galaxy clusters are a powerful probe of cosmic isotropy in the late Universe. Owing to their strong cosmological dependence, galaxy cluster scaling relations can obtain tight constraints on the spatial variation of…
If M is a manifold with compressible boundary, we analyze essential disks in M, as well as incompressible, but not necessarily boundary incompressible, surfaces in M. We are most interested in the case where M is a handlebody or compression…
The holographic entropy bound is discussed in cosmology. Inspired by the work of Fischler and Susskind [hep-th/9806039], we aim to define a special class of spherical systems in cosmology, within which the entropy of matter remains…
We study the geometry of surfaces in $\mathbb{R}^{4}$ with corank $1$ singularities. For such surfaces the singularities are isolated and at each point we define the curvature parabola in the normal space. This curve codifies all the second…
Besides expanding anisotropically, the universe can also be anisotropic at the level of its (spatial) curvature. In particular, models with anisotropic curvature and isotropic expansion leads both to a $\Lambda$CDM-like phenomenology and to…
The cosmological dynamics of multiple scalar/pseudoscalar fields are difficult to solve, especially when the field-space metric is curved. This presents a challenge in determining whether a given model can support cosmic acceleration,…