Journal ArticleDOI
Wave Function of the Universe
TLDR
In this article, the ground state amplitude for a three-manifold is given by a path integral over all compact positive-definite four-geometries which have the three-geometry as a boundary.Abstract:
The quantum state of a spatially closed universe can be described by a wave function which is a functional on the geometries of compact three-manifolds and on the values of the matter fields on these manifolds. The wave function obeys the Wheeler-DeWitt second-order functional differential equation. We put forward a proposal for the wave function of the "ground state" or state of minimum excitation: the ground-state amplitude for a three-geometry is given by a path integral over all compact positive-definite four-geometries which have the three-geometry as a boundary. The requirement that the Hamiltonian be Hermitian then defines the boundary conditions for the Wheeler-DeWitt equation and the spectrum of possible excited states. To illustrate the above, we calculate the ground and excited states in a simple minisuperspace model in which the scale factor is the only gravitational degree of freedom, a conformally invariant scalar field is the only matter degree of freedom and $\ensuremath{\Lambda}g0$. The ground state corresponds to de Sitter space in the classical limit. There are excited states which represent universes which expand from zero volume, reach a maximum size, and then recollapse but which have a finite (though very small) probability of tunneling through a potential barrier to a de Sitter-type state of continual expansion. The path-integral approach allows us to handle situations in which the topology of the three-manifold changes. We estimate the probability that the ground state in our minisuperspace model contains more than one connected component of the spacelike surface.read more
Citations
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Journal ArticleDOI
Non-Gaussian features of primordial fluctuations in single field inflationary models
TL;DR: In this article, the three point correlation functions for primordial scalar and tensor fluctuations in single field inflationary models were computed in the slow roll limit, where the answer is given terms of the two usual slow roll parameters.
Journal ArticleDOI
Quantization of four-form fluxes and dynamical neutralization of the cosmological constant
Raphael Bousso,Joseph Polchinski +1 more
TL;DR: In this article, it was shown that with multiple fluxes the allowed values can form a sufficiently dense ''discretuum'' for M-theory compactifications on manifolds with non-trivial three-cycles.
Journal ArticleDOI
Loop Quantum Cosmology: A Status Report
Abhay Ashtekar,Parampreet Singh +1 more
TL;DR: Loop quantum cosmology (LQC) as mentioned in this paper is the result of applying principles of loop quantum gravity to cosmological settings, where quantum geometry creates a brand new repulsive force which is totally negligible at low spacetime curvature but rises very rapidly in the Planck regime, overwhelming the classical gravitational attraction.
Journal ArticleDOI
Flux Compactification
Michael R. Douglas,Shamit Kachru +1 more
TL;DR: A survey of the landscape of string and M theory vacua can be found in this article, where the authors discuss the potential for testable consequences of this picture, such as observable effects of moduli, constraints on early cosmology, and predictions for the scale of supersymmetry breaking.
Journal ArticleDOI
Dark Energy
TL;DR: A survey of theoretical models and some aspects of numerical studies for dark energy can be found in this paper, where the authors review the problem of dark energy, including a survey of the theoretical models.