Related papers: The no boundary density matrix
Recent works have suggested that the no-boundary proposal should be defined as a sum over regular, not necessarily compact, metrics. We show that such a prescription can be implemented in the presence of a scalar field. For concreteness, we…
We revisit the Hartle-Hawking no-boundary proposal. To extract probabilities, one must use the gravitational path integral (GPI) to compute not only the no-boundary amplitude, but also the norms by which its square is divided. We find that…
We propose a novel approach to the problem of cosmological perturbations in a braneworld model with induced gravity, which leads to a closed system of equations on the brane. We focus on a spatially closed brane that bounds the interior…
At the minisuperspace level of homogeneous models, the bare probability for a classical universe has a huge peak at small universes for the Hartle-Hawking `no-boundary' wavefunction, in contrast to the suppression at small universes for the…
Theoretical considerations motivate us to consider vacuum energy to be able to decay and to assume that the spatial geometry of the universe is closed. Combining both aspects leads to the possibility that the universe, or certain regions…
We generalize the spherical collapse model for the formation of bound objects to apply in a Universe with arbitrary positive cosmological constant. We calculate the critical condition for collapse of an overdense region and give exact…
One of the leading ideas for the beginning of the Universe is the Hartle-Hawking `No-Boundary Proposal.' Since the Cobordism Conjecture claims that any spacetime allows for a dynamical boundary, we suggest that one may equally well consider…
String compactifications typically require fluxes, for example in order to stabilise moduli. Such fluxes, when they thread internal dimensions, are topological in nature and take on quantised values. This poses the puzzle as to how they…
We present a barrier potential with bound states that is exactly solvable and determine the eigenfunctions and eigenvalues of the Hamiltonian. The equilibrium density matrix of a particle moving at temperature T in this nonlinear barrier…
Hawking's proposal that the Universe has no temporal boundary and hence no beginning depends on the notion of imaginary time and is usually referred to as the "no-boundary proposal." This paper discusses a simple alternative approach by…
We determine the inner product on the Hilbert space of wavefunctions of the universe by imposing the Hermiticity of the quantum Hamiltonian in the context of the minisuperspace model. The corresponding quantum probability density reproduces…
We investigate the appearance of the classical anisotropic universe from the no-boundary quantum state according to the prescription proposed by Hartle, Hawking and Hertog. Our model is homogeneous, anisotropic, closed universes with a…
Wheeler-DeWitt equation is applied to $k > 0$ Friedmann Robertson Walker metric with various types of matter. It is shown that if the Universe ends in the matter dominated era (e.g., radiation or pressureless gas) with zero cosmological…
We consider self-similar approximations of nonlinear hyperbolic systems in one space dimension with Riemann initial data and general diffusion matrix. We assume that the matrix of the system is strictly hyperbolic and the diffusion matrix…
Consider the Boltzmann equation in a general non-convex domain with the diffuse boundary condition. We establish optimal BV estimates for such solutions. Our method consists of a new $W^{1,1}-$trace estimate for the diffuse boundary…
Real physical systems are only understood, experimentally or theoretically, to a finite resolution so in their analysis there is generally an ignorance of possible short-range phenomena. It is also well-known that the boundary conditions of…
For $\Omega\subset \mathbb{R}^2$ a smooth and bounded domain, we derive a sharp universal energy estimate for non-negative solutions of free boundary problems on $\Omega$ arising in plasma physics. As a consequence, we are able to deduce…
Many cosmological models assume or imply that the total size of the universe is very large, perhaps even infinite. Here we argue instead that the universe might be comparatively small, in fact not much larger than the currently observed…
We find a novel phenomenon in the solution to the Wheeler-DeWitt equation by solving numerically the equation assuming $O(4)$-symmetry and imposing the Hartle-Hawking wave function as a boundary condition. In the slow-roll limit, as…
We study the statistical mechanics of the early radiation dominated universe in the context of a generalized uncertainty principle which supports the existence of a minimal length scale. Utilizing the resultant modified thermodynamical…