arXiv subjects
Publications and source records attributed to Luis O. Pimentel.
The quantization of closed cosmologies makes it necessary to study squared Dirac operators on closed intervals and the corresponding quantum amplitudes. This paper proves self-adjointness of these second-order elliptic operators.
The Wheeler-DeWitt equation is considered in the context of generalized scalar-tensor theories of gravitation for Bianchi type I cosmology. Exact solutions are found for two selfinteracting potentials and arbitary coupling function. The WKB wavefunctions are obtained and a family of solutions satisfying the Hawking-Page regularity conditions of wormholes are found.
The Wheeler-DeWitt equation is solved for the Bergmann-Wagoner scalar-tensor gravitational theory in the case of Friedmann-Robertson- Walker cosmological model. We present solutions for several cosmological functions: i) λ(ϕ)=0, ii) λ(ϕ)=3Λ_0ϕand iii) a more complex λ(ϕ), that depends on the choice of the coupling function, considering closed, flat and hyperbolic Friedmann universes (k=1, 0, -1). In the first two cases we show particular quantum wormhole solutions. Also, classical solutions are considered for some scalar-tensor theories, and we study the third quantization of some minisuperspace models.
We study the third quantization of a Brans-Dicke toy model, we calculate the number density of the universes created from nothing and found that it has a Planckian form. Also, we calculated the uncertainty relation for this model by means of functional Schr"odinger equation and we found that fluctuations of the third-quantized universe field tends to a finite limit in the course of cosmic expansion.
In this work cosmological models are considered for the low energy string cosmological effective action (tree level) in the absence of dilaton potential. A two parametric non-diagonal family of analytic solutions is found. The curvature is non singular, however the string coupling diverges exponentially.
The effect of a time dependent cosmological constant is considered in a family of scalar tensor theories. Friedmann-Robertson-Walker cosmological models for vacumm and perfect fluid matter are found. They have a linear expansion factor, the so called coasting cosmology, the gravitational "constant" decreace inversely with time; this model satisfy the Dirac hipotesis. The cosmological "constant" decreace inversely with the square of time, therefore we can have a very small value for it at present time.
The Wheeler-DeWitt equation is solved for some scalar-tensor theories of gravitation in the case of homogeneous and isotropic cosmological models.We present general solutions corresponding to cosmological term: (i)λ(ϕ)=0$ and $(ii) λ(ϕ)=qϕ$.
We study five dimensional cosmological models with four dimensional hypersufaces of the Bianchi type I and V. In this way the five dimensional vacuum field equations $\rm G_{AB} = 0$, led us to four dimensional matter equations $\rm G_{μν}=T_{μν}$ and the matter is interpreted as a purely geometrical property of a fifth dimension. Also, we find that the energy-momentum tensor induced from the fifth dimension has the structure of an imperfect fluid that has dissipative terms.