Related papers: Some integrals ocurring in a topology change probl…
Based on an extended time-space symmetry, a cylindrical model of gravitational geometrical dynamics with two time-like extra-dimensions leads to a microscopic geodesic description of the curved space-time. Due to interaction of a Higgs-like…
We provide integral curvature bounds for compact Riemannian manifolds that allow isometric immersions into a Euclidean space with low codimension in terms of the Betti numbers.
It has been recently proposed that gravity might be an entropic force. Although a well defined fundamental description for such a mechanism is still lacking, it is still possible to address the viability of phenomenological models of…
This note is about invariants of moduli spaces of curves. It includes their intersection theory and cohomology. Our main focus in on the distinguished piece containing the so called tautological classes. These are the most natural classes…
Recollapsing homogeneous and isotropic models present one of the key ingredients for cyclic scenarios. This is considered here within a quantum cosmological framework in presence of a free scalar field with, in turn, a negative cosmological…
Quantum cosmology is traditionally formulated in a minisuperspace setting, implicitly averaging fields over space to obtain homogeneous models. For universal reasons related to the uncertainty principle, quantum corrections then depend on…
A new approach for arbitrary dimension to the Friedmann cosmological models is presented. Taking suitable changes of the parameters of the spacetime the harmonic motion equations appear, where the curvature determines the angular frequency.…
The stationary points of the total scalar curvature functional on the space of unit volume metrics on a given closed manifold are known to be precisely the Einstein metrics. One may consider the modified problem of finding stationary points…
A spherically symmetric comoving fluid solution of Einstein's equations is adapted for cosmological application by extending the geometry of standard FRW cosmology using a generalised curvature term. The resulting model retains many of the…
The tenfold classification provides a powerful framework for organizing topological phases of matter based on symmetry and spatial dimension. However, it does not offer a systematic method for transitioning between classes or engineering…
The concordance model of cosmology favours a universe with a tiny positive cosmological constant. A tiniest positive constant curvature, profoundly alters the asymptotic structure, forcing a re-look at a theory of gravitational radiation.…
We present a systematic study of the cosmological dynamics resulting from an effective Hamiltonian, recently derived in loop quantum gravity using Thiemann's regularization and earlier obtained in loop quantum cosmology (LQC) by keeping the…
Different versions of consistent canonical realizations of hypersurface deformations of spherically symmetric space-times have been derived in models of loop quantum gravity, modifying the classical dynamics and sometimes also the structure…
A test space is the set of outcome-sets associated with a collection of experiments. This notion provides a simple mathematical framework for the study of probabilistic theories -- notably, quantum mechanics -- in which one is faced with…
We investigate the topology and geometry of compact submanifolds in space forms of nonnegative curvature that satisfy a lower bound on the sectional curvature, depending only on the length of the mean curvature vector of the immersion. We…
Is the universe finite or infinite, and what shape does it have? These fundamental questions, of which relatively little is known, are typically studied within the context of the standard model of cosmology where the universe is assumed to…
Quantum gravity is expected to impose constraints on the moduli spaces of massless fields that can arise in effective quantum field theories. A recent proposal asserts that the asymptotic volume growth of these spaces is severely…
We construct a positive constant curvature space by identifying some points along a Killing vector in a de Sitter Space. This space is the counterpart of the three-dimensional Schwarzschild-de Sitter solution in higher dimensions. This…
Quantum substitutions of Pisot type (and their quantum topological entropy) are introduced. Their utility as algorithms for optimal spacing is analyzed.
We provide a quantization of the Schwarzschild spacetime in the presence of a cosmological constant, based on midisuperspace methods developed in the spherically symmetric sector of loop quantum gravity, using in particular the 'improved…