Related papers: Cosmological Levinson theorem
Within the third quantisation formalism, we find solutions of the Wheeler-DeWitt in terms of two sets of modes that can be identified with the Hartle-Hawking's no boundary condition and with the Vilenkin's tunneling boundary condition,…
We consider semilinear wave equations with small initial data in two space dimensions. For a class of wave equations with cubic nonlinearity, we show the global existence of small amplitude solutions, and give an asymptotic description of…
The present paper shows how one might model Everettian quantum mechanics using hyperfinitely many worlds. A hyperfinite model allows one to consider idealized measurements of observables with continuous-valued spectra where different…
In many Hamiltonian systems, propagation of steadily travelling solitons or kinks is prohibited because of resonances with linear excitations. We show that Hamiltonian systems with resonances may admit an infinite number of travelling…
We quantize a Bianchi IX universe in Ho\v{r}ava-Lifshitz theory. For analytical tractability, we consider the small anisotropy limit of the Bianchi IX, that is, a perturbative anisotropic deformation of a closed, homogeneous and isotropic…
We consider the classical minisuperspace model describing a closed, homogeneous and isotropic Universe, with a positive cosmological constant. Upon canonical quantization, the infinite number of possible operator orderings in the quantum…
A scalar field generalization of Xanthopoulos's cylindrically symmetric solutions of the vacuum Einstein equation is obtained. The obtained solution preserves the properties of the Xanthopoulos solution, which are regular on the axis,…
The d'Alembertian $\Box\phi=0$ has solution $\phi=f(v)/r$, where $f$ is a function of a null coordinate $v$, and this allows creation of a divergent singularity out of nothing. In scalar-Einstein theory a similar situation arises both for…
A quantum cosmological model with radiation and a dilaton scalar field is analysed. The Wheeler-deWitt equation in the mini-superspace induces a Schr\"odinger equation, which can be solved. An explicit wavepacket is constructed for a…
Wheeler-Dewitt equation for the wave function of the universe appeared long ago in an approach to quantization of gravity. Presently, the universe considered as the microuniverse, very tiny universe compared to the outer universe to which…
We consider the energy of the Universe, from the pseudo-tensor point of view(Berman,1981). We find zero values, when the calculations are well-done.The doubts concerning this subject are clarified, with the novel idea that the justification…
Using the factorization approach of quantum mechanics, we obtain a family of iso-spectral scalar potentials for noncommutative quantum cosmology. The family we build is based on a scattering Wheeler-DeWitt solution for the potential…
We show that the solutions of the Wheeler-DeWitt equation in a homogeneous and isotropic universe are given by triconfluent Heun functions for the spatially closed, flat, and open geometries of the Friedmann-Robertson-Walker universe filled…
In this work, a flat Friedmann-Robertson-Walker (FRW) universe with dust and a cosmological constant is quantized. By means of a canonical transformation, the classical Hamiltonian is reduced to that of either a harmonic oscillator or…
We revisit the notion of quantum Lie algebra of symmetries of a noncommutative spacetime, its elements are shown to be the generators of infinitesimal transformations and are naturally identified with physical observables. Wave equations on…
A solution of the sourceless Einstein's equation with an infinite value for the cosmological constant \Lambda is discussed by using Inonu-Wigner contractions of the de Sitter groups and spaces. When \Lambda --> infinity, spacetime becomes a…
It is shown that the classical gravitational waves of super-horizon wavelengths are able to form the de Sitter accelerated expansion of the empty (with no matter fields) Universe. The contemporary Universe is about 70% empty and…
We generalize the well-known Bonnor-Melvin solution of the Einstein-Maxwell equations to the case of a non-vanishing cosmological constant. The spacetime is again cylindrically symmetric and static but, unlike the original solution, it…
Spherical gravitational wave is strictly forbidden in vacuum space in frame of general relativity by the Birkhoff theorem. We prove that spherical gravitational waves do exist in non-linear massive gravity, and find the exact solution.…
The Wheeler-DeWitt equation for the induced gravity theory is constructed in the minisuperspace approximation, and then solved using the WKB method under three types of boundary condition proposed respectively by Hartle & Hawking (``no…