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Modern astrophysical and cosmological models are plagued with two severe theoretical difficulties, namely, the dark energy and the dark matter problems. Relative to the former, high-precision observational data have confirmed with startling…
The accelerating expansion of the Universe points to a small positive vacuum energy density and negative vacuum pressure. A strong candidate is the cosmological constant in Einstein's equations of General Relativity. The vacuum dark energy…
Particles of the cosmic radiation, electrons and nuclei, transport a dominant positive electric charge. A tiny fraction of these particles of extremely high energies in favorable conditions overflow from galaxies. The overflowing of…
We find a cosmological solution corresponding to compactification of 10d supergravity on a warped conifold that easily circumvents `no-go' theorem given for a warped/flux compactification, providing new perspectives for the study of…
On a Riemannian manifold, lower Ricci curvature bounds are known to be characterized by geodesic convexity properties of various entropies with respect to the Kantorovich-Rubinstein-Wasserstein square distance from optimal transportation.…
The concept of a physical space, which actualizes Euclidean geometry, is not confined to the statics of solids but extensible to the phenomena where Newtonian mechanics is valid, defining its concept of time. The laws of propagation of…
Assuming virial equilibrium and Newtonian dynamics, low-mass early-type galaxies have larger velocity dispersions than expected from the amount of baryons they contain. The conventional interpretation of this finding is that their dynamics…
We model accelerated trips at high-velocity aboard light sails (beam-powered propulsion in general) and radiation rockets (thrust by anisotropic emission of radiation) in terms of Kinnersley's solution of general relativity and its…
Einstein-Cartan theory is an extension of the standard formulation of General Relativity where torsion (the antisymmetric part of the affine connection) is non-vanishing. Just as the space-time metric is sourced by the stress-energy tensor…
We study the generalizations of the original Alcubierre warp drive metric to the case of curved spacetime background. We find that the presence of a horizon is essential when one moves from spherical coordinates to Cartesian coordinates in…
This contribution intends to give a pedagogical introduction to the topic of dark energy (the mysterious agent supposed to drive the observed late time acceleration of the Universe) and to various observational tests which require only…
The more precise definition and the more fundamental understanding of the concepts of time, energy, entropy and information are building upon the new, relativistic foundation of gravity. This lecture is an attempt to explain the basic…
The Euclidean interpretation of special relativity which has been suggested by the author is a formulation of special relativity in ordinary 4D Euclidean space-time geometry. The natural and geometrically intuitive generalization of this…
Simple models are constructed for "acceleressence" dark energy: the latent heat of a phase transition occurring in a hidden sector governed by the seesaw mass scale v^2/M_Pl, where v is the electroweak scale and M_Pl the gravitational mass…
On a warped five-dimensional Friedmann-Lema\^{\i}tre-Robertson-Walker(FLRW) spacetime, dark energy can be induced by a U(1) scalar-gauge field on the brane. We consider a zero effective cosmological constant, i.e., the Randall-Sundrum(RS)…
We give a novel definition of gravitational energy for an arbitrary theory of gravity including quadratic-curvature corrections to Einstein equations. We focus on the theory in four dimensions, in presence of negative cosmological constant,…
Based on the cosmic holographic conjecture of Fischler and Susskind, we point out that the average energy density of the universe is bound from above by its entropy limit. Since Friedmann's equation saturates this relation, the measured…
A nonlocal generalization of Einstein's theory of gravitation is constructed within the framework of the translational gauge theory of gravity. In the linear approximation, the nonlocal theory can be interpreted as linearized general…
We investigate the influence of boundary terms in gravitational field theories, by considering that in the Einstein-Hilbert action the boundary can be described by a non-metric Weyl-type geometry. The gravitational action and the the field…
We show that the neutrino mass, the dark matter and the dark energy can be explained in a unified framework, postulating a new invisible Born-Infeld field, which we name "non-linear dark photon", undergoing a meV-scale dynamical…