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The notion of ``fundamental constant'' is heavily theory-laden. A natural, fairly precise formulation is possible in the context of the standard model (here defined to include gravity). Some fundamental constants have profound geometric…
We construct cubic gravity and its $f(P)$ extension and we investigate their early- and late-time cosmological applications. Cubic gravity is based on a particular invariant $P$, constructed from cubic contractions of the Riemann tensor,…
The time dependent conformally-flat spherical Rindler spacetime is investigated. The geometry has an apparent horizon that coincides with the causal horizon. The scalar acceleration of a static observer is constant and equals to the…
We analyze cosmography as a tool to constrain modified gravity theories. We take four distinct models and obtain their parameters in terms of the cosmographic parameters favored by observational data of strong gravitational lensing. We…
Accelerating universe or the existence of a small and positive cosmological constant is probably the most pressing obstacle as well as opportunity to significantly improving the models of four-dimensional cosmology from fundamental theories…
In the framework of a model of minimal of dilatonic gravity (MDG) with cosmological potential we consider: the relations of MDG with nonlinear gravity and string theory; natural cosmological units, defined by cosmological constant; the…
We discuss the cosmological constant problem in the context of higher codimension brane world scenarios with infinite-volume extra dimensions. In particular, by adding higher curvature terms in the bulk action we are able to find smooth…
In this paper, we study the cosmological viability conditions, the phase-space dynamics, and the cosmological evolution of f(R) gravity. In contrast to most previous works in the literature, which analyzed the background dynamics of f(R)…
It is shown that topological changes in space-time are necessary to make General Relativity compatible with the Newtonian limit and to solve the hierarchy of the fundamental interactions. We detail how topology and topological changes…
We consider fuzzy spacetime, quanta of area and related concepts in the context of latest approaches to Quantum Gravity and show its interface with usual non-Abelian gauge theory. We also discuss in this context a cosmology which correctly…
We simplify the gravitational equations which apply in accelerating spacetimes and are consistent with the cosmological principle. Solutions to these equations should be tantamount to all order re-summations of the perturbative leading…
We deduce the appearance of a polymeric phase in 4-dimensional simplicial quantum gravity by varying the values of the coupling constants and discuss the geometric structure of the phase in terms of ergodic moves. A similar result is true…
The accelerating expansion of the Universe points to a small positive value for the cosmological constant or vacuum energy density. We discuss recent ideas that the cosmological constant plus LHC results might hint at critical phenomena…
We consider cosmological model in 4+1 dimensions with variable scale factor in extra dimension and static external space. The time scale factor is changing. Variations of light velocity, gravity constant, mass and pressure are determined…
We present a space-velocity theory of gravitation in a 4-dimensional curved space. The solutions of the field equations yield 3 possibilities for the universe expansion but only the accelerating one is possible. Although the theory has no…
We introduce an asymptotic notion of positivity in algebraic geometry that turns out to be related to some high-dimensional convex sets. The dimension of the convex sets grows with the number of birational operations. In the case of complex…
This review is an up-to-date account of the use of numerical relativity to study dynamical, strong-gravity environments in a cosmological context. First, we provide a gentle introduction into the use of numerical relativity in solving…
The cosmological constant if considered as a fundamental constant, provides an information treatment for gravitation problems, both cosmological and of black holes. The efficiency of that approach is shown via gedanken experiments for the…
The trace anomaly induced dynamics of the conformal factor is investigated in four-dimensional quantum gravity with torsion. The constraints for the coupling constants of torsion matter interaction are obtained in the infrared stable fixed…
The estimation of the cosmological constant in inflationary Brane New World models is done. It is shown that basically it is quite large, of the same order as in anomaly-driven inflation. However, for some fine-tuning of bulk gravitational…