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An one-parameter regularization freedom of the Hamiltonian constraint for loop quantum gravity is analyzed. The corresponding spatially flat, homogenous and isotropic model includes the two well-known models of loop quantum cosmology as…
We propose possible properties of quantum gravity in de Sitter space, and find that they relate the value of the cosmological constant to parameters of the Standard Model. In de Sitter space we suggest (i) that the most sharply defined…
In the action formalism variations of metric tensors usually are limited by the Hubble horizon. Contrary, variations of quantum fields should be extended up to the event horizon, which is the real boundary of the spacetime. As the result…
The classical value of the Hamiltonian for a system with timelike boundary has been interpreted as a quasilocal energy. This quasilocal energy is not positive definite. However, we derive a `quasilocal dominant energy condition' which is…
When the cosmological constant, $\Lambda$, is interpreted as a thermodynamic variable in the study of black hole thermodynamics a very rich structure emerges. It is natural to interpret $\Lambda$ as a pressure and define the…
The first and second laws of thermodynamics should lead to a consistent scenario for discussing the cosmological constant problem. In the present study, to establish such a thermodynamic scenario, cosmological equations in a flat…
We derive the basic equations of the cosmological first-order post-Newtonian approximation from the recently formulated fully nonlinear and exact cosmological perturbation theory in Einstein's gravity. Apparently the latter, being exact,…
In the standard concordance cosmology the spatial curvature is assumed to be constant and zero (or at least very small). In particular, in numerical computations of the structure of the universe using N-body simulations, exact periodic…
It was shown that in the canonical ensemble the simple exactly soluble statistical model of nuclei decay into nucleons, which is a limiting case of the statistical multifragmentation model, predicts the nuclear first order phase transition…
We explore nonequilibrium features of certain operator algebras which appear in quantum gravity. The algebra of observables in a black hole background is a Type $\mathrm{II}_\infty$ von Neumann algebra. We discuss how this algebra can be…
We suggest an interpretation of Einstein Equations of General Relativity at large scales in which the Cosmological constant is exactly zero in the limit of zero spacetime variations of fundamental constants. We argue that in a…
In this paper we present two results in $(2+1)$ gravity coupled to nonlinear electrodynamics. First it is determined the general form of the electromagnetic field tensor in $(2+1)$ gravity coupled to nonlinear electrodynamics in stationary…
In the No-Boundary Universe a primordial black hole is created from a constrained gravitational instanton. The black hole created is immersed in the de Sitter background with a positive cosmological constant. The constrained instanton is…
For both extremal and non-extremal spherically symmetric black holes in theories with massless scalars and vectors coupled to gravity, we derive a general form of first-order gradient flow equations, equivalent to the equations of motion.…
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)…
A bouncing scenario of a flat homogeneous and isotropic universe is explored by using the reconstruction technique for the power-law parametrization of the Hubble parameter in a modified gravity theory with higher-order curvature and trace…
We report on some properties of a quantum black hole obtained recently. The correction to the Newtonian gravitational potential is proportional to a coupling $\alpha$, which is the only free parameter of the theory. We constrain the…
In this paper we will show that using the cosmological constant as a new thermodynamical state variable, the differential and integral mass formulas of the first law of thermodynamics for asymptotic flat spacetimes can be extended to (2+1)…
To empower the mathematical hitchhiker wishing to use operator methods in geometry and topology, we present this user's guide to first-order elliptic boundary value problems. Existence, regularity, and Fredholmness are discussed for general…
Time-symmetric cosmological theories, in which the initial and final states are arranged to have similar features or are independently fixed, have been quite extensively discussed in the literature. However, a more general and perhaps more…