Quantum Cosmology of Kantowski-Sachs like Models

The Wheeler-DeWitt equation for a class of Kantowski-Sachs like models is completely solved. The generalized models include the Kantowski-Sachs model with cosmological constant and pressureless dust. Likewise contained is a joined model which consists of a Kantowski-Sachs cylinder inserted between two FRW half--spheres. The (second order) WKB approximation is exact for the wave functions of the complete set and this facilitates the product structure of the wave function for the joined model. In spite of the product structure the wave function can not be interpreted as admitting no correlations between the different regions. This problem is due to the joining procedure and may therefore be present for all joined models. Finally, the {s}ymmetric {i}nitial {c}ondition (SIC) for the wave function is analyzed and compared with the ``no bouindary'' condition. The consequences of the different boundary conditions for the arrow of time are briefly mentioned.Comment: 21 pages, uses LaTeX2e, epsf.sty and float.sty, three figures (50 kb); changes: one figure added, new interpretation of quantizing procedure for the joined model and many minor change

Hamiltonian dynamics and Noether symmetries in Extended Gravity Cosmology

We discuss the Hamiltonian dynamics for cosmologies coming from Extended Theories of Gravity. In particular, minisuperspace models are taken into account searching for Noether symmetries. The existence of conserved quantities gives selection rule to recover classical behaviors in cosmic evolution according to the so called Hartle criterion, that allows to select correlated regions in the configuration space of dynamical variables. We show that such a statement works for general classes of Extended Theories of Gravity and is conformally preserved. Furthermore, the presence of Noether symmetries allows a straightforward classification of singularities that represent the points where the symmetry is broken. Examples of nonminimally coupled and higher-order models are discussed.Comment: 20 pages, Review paper to appear in EPJ

The Bohm Interpretation of Quantum Cosmology

I make a review on the aplications of the Bohm-De Broglie interpretation of quantum mechanics to quantum cosmology. In the framework of minisuperspaces models, I show how quantum cosmological effects in Bohm's view can avoid the initial singularity, isotropize the Universe, and even be a cause for the present observed acceleration of the Universe. In the general case, we enumerate the possible structures of quantum space and time.Comment: 28 pages, 1 figure, contribution to the James Cushing festschrift to appear in Foundations of Physic

Decoherence, the measurement problem, and interpretations of quantum mechanics

Environment-induced decoherence and superselection have been a subject of intensive research over the past two decades, yet their implications for the foundational problems of quantum mechanics, most notably the quantum measurement problem, have remained a matter of great controversy. This paper is intended to clarify key features of the decoherence program, including its more recent results, and to investigate their application and consequences in the context of the main interpretive approaches of quantum mechanics.Comment: 41 pages. Final published versio

Stochastic Gravity: A Primer with Applications

Stochastic semiclassical gravity of the 90's is a theory naturally evolved from semiclassical gravity of the 70's and 80's. It improves on the semiclassical Einstein equation with source given by the expectation value of the stress-energy tensor of quantum matter fields in curved spacetimes by incorporating an additional source due to their fluctuations. In stochastic semiclassical gravity the main object of interest is the noise kernel, the vacuum expectation value of the (operator-valued) stress-energy bi-tensor, and the centerpiece is the (stochastic) Einstein-Langevin equation. We describe this new theory via two approaches: the axiomatic and the functional. The axiomatic approach is useful to see the structure of the theory from the framework of semiclassical gravity. The functional approach uses the Feynman-Vernon influence functional and the Schwinger-Keldysh close-time-path effective action methods which are convenient for computations. It also brings out the open systems concepts and the statistical and stochastic contents of the theory such as dissipation, fluctuations, noise and decoherence. We then describe the application of stochastic gravity to the backreaction problems in cosmology and black hole physics. Intended as a first introduction to this subject, this article places more emphasis on pedagogy than completeness.Comment: 46 pages Latex. Intended as a review in {\it Classical and Quantum Gravity

Must Quantum Spacetimes Be Euclidean?

The Bohm-de Broglie interpretation of quantum mechanics is applied to canonical quantum cosmology. It is shown that, irrespective of any regularization or choice of factor ordering of the Wheeler-DeWitt equation, the unique relevant quantum effect which does not break spacetime is the change of its signature from lorentzian to euclidean. The other quantum effects are either trivial or break the four-geometry of spacetime. A Bohm-de Broglie picture of a quantum geometrodynamics is constructed, which allows the investigation of these latter structures. For instance, it is shown that any real solution of the Wheeler-De Witt equation yields a generate four-geometry compatible with the strong gravity limit of General Relativity and the Carroll group. Due to the more detailed description of quantum geometrodynamics given by the Bohm-de Broglie interpretation, some new boundary conditions on solutions of the Wheeler-DeWitt equation must be imposed in order to preserve consistency of this finer view.Comment: 42 pages LaTeX, last version with minor corrections, being the most importants on pages 0, 6, 11, 21, 23, and 30 . The new title does not change our conclusion

Exact Hypersurface-Homogeneous Solutions in Cosmology and Astrophysics

A framework is introduced which explains the existence and similarities of most exact solutions of the Einstein equations with a wide range of sources for the class of hypersurface-homogeneous spacetimes which admit a Hamiltonian formulation. This class includes the spatially homogeneous cosmological models and the astrophysically interesting static spherically symmetric models as well as the stationary cylindrically symmetric models. The framework involves methods for finding and exploiting hidden symmetries and invariant submanifolds of the Hamiltonian formulation of the field equations. It unifies, simplifies and extends most known work on hypersurface-homogeneous exact solutions. It is shown that the same framework is also relevant to gravitational theories with a similar structure, like Brans-Dicke or higher-dimensional theories.Comment: 41 pages, REVTEX/LaTeX 2.09 file (don't use LaTeX2e !!!) Accepted for publication in Phys. Rev.

Stochastic Gravity: Theory and Applications

Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein-Langevin equation, which has in addition sources due to the noise kernel. In the first part, we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. In the second part, we describe three applications of stochastic gravity theory. First, we consider metric perturbations in a Minkowski spacetime, compute the two-point correlation functions of these perturbations and prove that Minkowski spacetime is a stable solution of semiclassical gravity. Second, we discuss structure formation from the stochastic gravity viewpoint. Third, we discuss the backreaction of Hawking radiation in the gravitational background of a black hole and describe the metric fluctuations near the event horizon of an evaporating black holeComment: 100 pages, no figures; an update of the 2003 review in Living Reviews in Relativity gr-qc/0307032 ; it includes new sections on the Validity of Semiclassical Gravity, the Stability of Minkowski Spacetime, and the Metric Fluctuations of an Evaporating Black Hol

A Low Matter Density Decaying Vacuum Cosmology from Complex Metric

A low matter density decaying vacuum cosmology is proposed on the assumption that the universe's radius is a complex quantity \hat{R} if it is regarded as having a zero energy-momentum tensor. But we find that when the radius is real, it contains matter. Using the Einstein-Hilbert action principle, the physical scale factor R(t) =|\hat{R}| is obtained as equal to (R_0^{2} + t^{2})^{1/2} with R_0 representing the finite radius of the universe at t=0. The resulting physical picture is roughly a theoretical justification of the old Ozer-Taha model. The new model is devoid of all cosmological problems. In particular, it confirms the bounds on H_p, the present value of the Hubble parameter: 0.85 < H_p t_p < 1.91 and faces no age problem. We argue that the total energy density consists of parts corresponding to relativistic/non-relativistic matter, a positive vacuum energy and a form of matter with equation of state p_K = -(1/3) rho_K (textures or generally K-matter), and the following predictions are made for the present nonrelativistic era: Omega_{M,n.rel.} \approx 2/3, Omega_{V,n.rel.} \approx 1/3, Omega_ <<1, Omega_K \approx 1, where a parameter corresponding to K-matter is taken to be unity. It is shown that the spacetime with complex metric has signature changing properties. Using quantum cosmological considerations, it is shown that the wave function is peaked about the classical contour of evolution and the minimum radius R_0 of the nonsingular model is predicted as comparable with the Planck length. PACS No(s); 98.80 Hw, 04.20, 04.60Comment: 21 pages, no figure

Stochastic Gravity: Theory and Applications

Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein-Langevin equation, which has in addition sources due to the noise kernel.In the first part, we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. In the second part, we describe three applications of stochastic gravity theory. First, we consider metric perturbations in a Minkowski spacetime: we compute the two-point correlation functions for the linearized Einstein tensor and for the metric perturbations. Second, we discuss structure formation from the stochastic gravity viewpoint. Third, we discuss the backreaction of Hawking radiation in the gravitational background of a quasi-static black hole.Comment: 75 pages, no figures, submitted to Living Reviews in Relativit