An Ermakov study of Q not zero EFRW minisuperspace oscillators

2000

The existence of a Noether symmetry for a given minisuperspace cosmological model is a sort of selection rule to recover classical behaviours in cosmic evolution since oscillatory regimes for the wave function of the universe come out. The so called Hartle criterion to select correlated regions in the configuration space of dynamical variables can be directly connected to the presence of a Noether symmetry and we show that such a statement works for generic extended theories of gravity in the framework of minisuperspace approximation. Examples and exact cosmological solutions are given for nonminimally coupled and higher-order theories.

The existence of a Noether symmetry for a given minisuperspace cosmological model is a sort of selection rule to recover classical behaviours in cosmic evolution since oscillatory regimes for the wave function of the universe come out. The so called Hartle criterion to select correlated regions in the configuration space of dynamical variables can be directly connected to the presence of a Noether symmetry and we show that such a statement works for generic extended theories of gravity in the framework of minisuperspace approximation. Examples and exact cosmological solutions are given for nonminimally coupled and higher-order theories.

Papers in honor of Charles Misner, 1993

We trace the development of ideas on dissipative processes in chaotic cosmology and on minisuperspace quantum cosmology from the time Misner proposed them to current research. We show 1) how the effect of quantum processes like particle creation in the early universe can address the issues of the isotropy and homogeneity of the observed universe, 2) how viewing minisuperspace as a quantum open system can address the issue of the validity of such approximations customarily adopted in quantum cosmology, and 3) how invoking statistical processes like decoherence and correlation when considered together can help to establish a theory of quantum fields in curved spacetime as the semiclassical limit of quantum gravity.

2010

We study Hawking-like radiation in a Friedmann-Robertson-Walker (FRW) universe using the quasi-classical WKB/tunneling method, which pictures this process as a "tunneling" of particles from behind the apparent horizon. The correct temperature of the Hawking-like radiation from the FRW space-time is obtained using a canonical invariant tunneling amplitude. In contrast to the usual quantum-mechanical WKB/tunneling problem, where the tunneling amplitude has only a spatial contribution, we find that the tunneling amplitude for FRW space-time (i.e. the imaginary part of the action) has both spatial and temporal contributions. In addition we study backreaction and energy conservation of the radiated particles and find that the tunneling probability and the change in entropy, S, are related by the relationship Γ ∝ exp[−∆S], which differs from the standard result, Γ ∝ exp[∆S]. By regarding the whole FRW universe as an isolated adiabatic system, the change in the total entropy is zero. Then, splitting the entropy between the interior and exterior parts of the horizon (∆S total = ∆S int + ∆Sext = 0), we can explain the origin of the minus sign difference with the usual result: our ∆S is for the interior region, while the standard result from black hole physics is for the exterior region.

Physics Letters A, 1996

Using as an illustrative example the p=1 operator-ordered Wheeler-DeWitt equation for a closed, radiation-filled Friedmann-Robertson-Walker universe, we introduce and discuss the supersymmetric double Darboux method in quantum cosmology. A one-parameter family of "quantum" universes and the corresponding "wavefunctions of the universe" for this case are presented. based on an essay written for the 1996 Awards of the Gravity Research Foundation (Wellesley Hills, Ma, 02181-0004) Phys. Lett. A 223, 28-30 (25 Nov 1996) PACS number(s): 98.80.Hw; 11.30.Pb Many interesting results have been obtained mostly in one-dimensional quantum mechanics by means of Darboux-Witten (DW) supersymmetric procedures; for a recent review see [1]. These are, essentially, factorizations of the one-dimensional Schrödinger differential operator, first performed in the supersymmetric context by Witten in 1981 [2], and in mathematics literature, in the broader sense of the Darboux transformation, by Darboux, as early as 1882 [3].

Nuclear Physics B, 1996

The Hawking minisuperspace model (closed FRW geometry with a homogeneous massive scalar field) provides a fairly non-trivial testing ground for fundamental problems in quantum cosmology. We provide evidence that the Wheeler-DeWitt equation admits a basis of solutions that is distinguished by analyticity properities in a large scale factor expansion. As a consequence, the space of solutions decomposes in a preferred way into two Hilbert spaces with positive and negative definite scalar product, respectively. These results may be viewed as a hint for a deeper significance of analyticity. If a similar structure exists in full (non-minisuperspace) models as well, severe implications on the foundations of quantum cosmology are to be expected.

2011

Physical Review D, 1999

The wave function of the universe is usually taken to beafunctional of the three-metric on a spacelike section, , which is measured. It is sometimes better, however, to work in the conjugate representation, where the wave function depends on a quantity related to the second fundamental form of . This makes it possible to ensure that is part of a Lorentzian universe by requiring that the argument of the wave function bepurely imaginary. We demonstrate the advantages of this formalism rst in the well-known examples of the nucleation of a d e Sitter or a Nariai universe. We then use it to calculate the pair creation rate for sub-maximal black holes in de Sitter space, which had been thought t o v anish semi-classically.

1996

We show that closed, radiation-filled Friedmann-Robertson-Walker quantum universes of arbitrary factor ordering obey the Whittaker equation. We also present the formal Witten factorization as well as the double Darboux strictly isospectral scheme for the Whittaker equation

Physical Review D, 1996

In two previous papers we have undertaken an analysis of the scalar, vectorial, and tensorial perturbations in Friedmann-Robertson-Walker ͑FRW͒ universes. A method which involved only observable, gaugeindependent perturbed quantities, considered in the framework of quasi-Maxwellian equations of gravitation, was derived. This method made it possible to obtain a Hamiltonian treatment of the perturbed FRW cosmology without the entailed ambiguities regarding gauge choices. Now we carry this Hamiltonian treatment to its full extent by advancing one step further in order to perform the quantization of all three perturbation types. This is done by following the standard semiclassical procedure and employing the quantum optics formalism to solve the Schrödinger equation and obtain all relevant quantities in this framework. ͓S0556-2821͑96͒03412-1͔ PACS number͑s͒: 98.80.Hw, 04.30.Db PHYSICAL REVIEW D