One-loop quantum cosmological correction to the gravitational constant in the closed Friedmann-Robertson-Walker universe

In this paper, we calculate the one-loop quantum cosmological corrections to the kink energy in the closed Friedmann-Robertson-Walker universe in which the fluctuation potential $V^{\prime\prime}$ has a shape invariance property. We use the generalized zeta function regularization method to implement our setup for describing quantum kink-like states. It is conjectured that the corrections lead to the renormalized gravitational constant

New Schwarzschild-like solutions in f(T) gravity through Noether symmetries

Spherically symmetric solutions for f(T) gravity models are derived by the so called Noether Symmetry Approach. First, we present a full set of Noether symmetries for some minisuperspace models. Then, we compute analytical solutions and find that spherically symmetric solutions in f(T) gravity can be recast in terms of Schwarzschild-like solutions modified by a distortion function depending on a characteristic radius. The obtained solutions are more general than those obtained by the usual solution methods.Comment: 10 pages, to appear in Phys. Rev.

Correspondence between Jordan-Einstein frames and Palatini-metric formalisms

We discuss the conformal symmetry between Jordan and Einstein frames considering their relations with the metric and Palatini formalisms for modified gravity. Appropriate conformal transformations are taken into account leading to the evident connection between the gravitational actions in the two mentioned frames and the Hilbert-Einstein action with a cosmological constant. We show that the apparent differences between Palatini and metric formalisms strictly depend on the representation while the number of degrees of freedom is preserved. This means that the dynamical content of both formalism is identical.Comment: 6 pages, to appear in Mod. Phys. Lett.

Quantum cosmology of 5D non-compactified Kaluza-Klein theory

We study the quantum cosmology of a five dimensional non-compactified Kaluza-Klein theory where the 4D metric depends on the fifth coordinate, $x^4\equiv l$. This model is effectively equivalent to a 4D non-minimally coupled dilaton field in addition to matter generated on hypersurfaces l=constant by the extra coordinate dependence in the four-dimensional metric. We show that the Vilenkin wave function of the universe is more convenient for this model as it predicts a new-born 4D universe on the $l\simeq0$ constant hypersurface.Comment: 14 pages, LaTe

Families of exact solutions of a 2D gravity model minimally coupled to electrodynamics

Three families of exact solutions for 2-dimensional gravity minimally coupled to electrodynamics are obtained in the context of ${\cal R}=T$ theory. It is shown, by supersymmetric formalism of quantum mechanics, that the quantum dynamics of a neutral bosonic particle on static backgrounds with both varying curvature and electric field is exactly solvable.Comment: 13 pages, LaTeX, to be published in JM

Canonical wave packets in quantum cosmology

We discuss the construction of wave packets resulting from the solutions of a class of Wheeler-DeWitt equations in Robertson-Walker type cosmologies, for arbitrary curvature. We show that there always exists a ``canonical initial slope" for a given initial wave function, which optimizes some desirable properties of the resulting wave packet, most importantly good classical-quantum correspondence. This can be properly denoted as a canonical wave packet. We introduce a general method for finding these canonical initial slopes which is generalization of our earlier work.Comment: 19 pages, 8 figure

Dynamical conformal transformation and classical Euclidean wormholes

We investigate the necessary condition for the existence of classical Euclidean wormholes in a conformally non-invariant gravitational model minimally coupled to an scalar field. It is shown that while the original Ricci tensor with positive eigenvalues does not allow the Euclidean wormholes to occur, under dynamical conformal transformations the Ricci tensor, with respect to the original metric, is dynamically coupled with the conformal field and its eigenvalues may become negative allowing the Euclidean wormholes to occur. Therefore, it is conjectured that dynamical conformal transformations may provide us with {\it effective} forms of matter sources leading to Euclidean wormholes in conformally non-invariant systems.Comment: 6 pages, minor revisio

Quantum Stephani Universe in vicinity of the symmetry center

We study a class of spherically symmetric Stephani cosmological models in the presence of a self-interacting scalar field in both classical and quantum domains. We discuss the construction of `canonical' wave packets resulting from the solutions of a class of Wheeler-DeWitt equations in the Stephani Universe. We suggest appropriate initial conditions which result in wave packets containing some desirable properties, most importantly good classical and quantum correspondence. We also study the situation from de-Broglie Bohm interpretation of quantum mechanics to recover the notion of time and compare the classical and Bohmian results. We exhibit that the usage of the canonical prescription and appropriate choices of expansion coefficients result in the suppression of the quantum potential and coincidence between classical and Bohmian results. We show that, in some cases, contrary to Friedmann-Robertson-Walker case, the bound state solutions also exist for all positive values of the cosmological constant.Comment: 22 pages, 19 figures, to appear in JCA