Related papers: Recent topics on the O'Hara energies
Two new one-parameter tracking behavior dark energy representations $\omega=\omega_0/(1+z)$ and $\omega=\omega_0 e^{z/(1+z)}/(1+z)$ are used to probe the geometry of the Universe and the property of dark energy. The combined type Ia…
The original singularity theorems of Penrose and Hawking were proved for matter obeying the Null Energy Condition or Strong Energy Condition respectively. Various authors have proved versions of these results under weakened hypotheses, by…
Future singularities arising in a family of models for the expanding Universe, characterized by sharing a convenient parametrization of the energy budget in terms of the deceleration parameter, are classified. Finite-time future…
We study M-theory compactified on twisted 7-tori with $G_2$-holonomy. The effective 4d supergravity has 7 chiral multiplets, each with a unit logarithmic K\"ahler potential. We propose octonion, Fano plane based superpotentials, codifying…
We use the newly released 182 Type Ia supernova data combined with the third-year Wilkinson Microwave Anisotropic Probe data (WMAP3) and large scale structure (LSS) information including SDSS and 2dFGRS to constrain the dark energy equation…
Given a positive definite kernel in a locally compact space, we study a minimal energy problem in the presence of an external field over the class of all nonnegative Radon measures that are supported by a given closed noncompact set,…
The variation of the energy for a gravitational system is directly defined from the Hamiltonian field equations of General Relativity. When the variation of the energy is written in a covariant form it splits into two (covariant)…
We consider a Kobayashi-Warren-Carter (KWC) type total variation energy with a fidelity term. Since the energy is non-convex, the profiles of minimizers are quite different from those of the original Rudin-Osher-Fatemi energy. In…
In this work we propose a novel composite method for accurate calculation of the energies of many-electron atoms. The dominant contribution to the energy (pair energies) are calculated by using explicitly correlated factorisable coupled…
Let $N=(\Omega,\sigma)$ and $M=(\Omega^*,\rho)$ be doubly connected Riemann surfaces and assume that $\rho$ is a smooth metric with bounded Gauss curvature $\mathcal{K}$ and finite area. The paper establishes the existence of homeomorphisms…
We consider the oscillating dark energy with periodic equation of state in two equivalent formulations: ideal fluid or scalar-tensor theory. It is shown that such dark energy suggests the natural way for the unification of early-time…
We study a problem in the theory of cubature formulas on the sphere: given $\theta \in (0, 1)$, determine the infimum of $\|\nu\|_\theta = \sum_{i = 1}^n \nu_i^\theta$ over cubature formulas $\nu$ of strength $t$, where $\nu_i$ are the…
We investigate observational constraints on the curvature of the universe not restricting ourselves to a cosmological constant as dark energy, in particular allowing a dark energy equation of state to evolve with time in several ways. We…
Despite its high significance in nonlinear elasticity, the neo-Hookean energy is still not known to admit minimisers in some appropriate admissible class. Using ideas from relaxation theory, we propose a larger minimisation space and a…
The adiabatic invariant nature of black hole horizon area in classical gravity suggests that in quantum theory the corresponding operator has a discrete spectrum. I here develop further an algebraic approach to black hole quantization which…
Einstein field equations under spherically symmetric space-times are considered here in connection to dark energy investigation. A set of solutions are obtained for a kinematical $\Lambda$ model, viz., $\Lambda \sim (\dot a/a)^2$ without…
We provide a space-time covariant Hamiltonian treatment for a finite-range gravitational theory. The Kuchar approach is used to demonstrate the bimetric picture of space-time in its most transparent form. This Hamiltonian formalism is…
The ancient Gamow liquid drop model of nuclear energies has had a renewed life as an interesting problem in the calculus of variations: Find a set $\Omega \subset \mathbb R^3$ with given volume A that minimizes the sum of its surface area…
Dark energy can be characterized by a canonical scalar field, known as quintessence. Quintessence allows for a dynamical equation of state $-1 \le \omega \le -\frac{1}{3}$. A previous study by Oikonomou and Chatzarakis have shown that a…
This review summarizes the current status of the energy conditions in general relativity and quantum field theory. We provide a historical review and a summary of technical results and applications, complemented with a few new derivations…