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Garay Elizondo, Luis Javier and Halliwel, Jonathan J. and Mena Marugán, Guillermo A. (1991) Pathintegral quantum cosmology: a class of exactly soluble scalarfield minisuperspace models with exponential potentials. Physical review D, 43 (8). pp. 25722589. ISSN 05562821

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Official URL: http://dx.doi.org/10.1103/PhysRevD.43.2572
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http://journals.aps.org  Publisher 
Abstract
We study a class of minisuperspace models consisting of a homogenous isotropic universe with a minimally coupled homogenous scalar field with a potential alpha cosh(2phi) + beta sinh(2phi), where alpha and beta are arbitrary parameters. This includes the case of a pure exponential potential exp(2phi), which arises in the dimensional reduction to four dimensions of fivedimensional KaluzaKlein theory. We study the classical Lorentzian solutions for the model and find that they exhibit exponential or powerlaw inflation. We show that the WheelerDeWitt equation for this model is exactly soluble. Concentrating on the two particular cases of potentials cosh(2phi) and exp(2phi), we consider the Euclidean minisuperspace path integral for a propagation amplitude between fixed scale factors and scalarfield configurations. In the gauge N = 0 (where N is the rescaled lapse function), the path integral reduces, after some essentially trivial functional integrations, to a single nontrivial ordinary integral over N. Because the Euclidean action is unbounded from below, N must be integrated along a complex contour for convergence. We find all possible complex contours which lead to solutions of the WheelerDeWitt equation or Green's functions of the WheelerDeWitt operator, and we give an approximate evaluation of the integral along these contours, using the method of steepest descents. The steepestdescent contours may be dominated by saddle points corresponding to exact solutions to the full Einsteinscalar equations which may be real Euclidean, real Lorentzian, or complex. We elucidate the conditions under which each of these different types of solution arise. For the exp(2phi) potential, we evaluate the path integral exactly. Although we cannot evaluate the path integral in closed form for the cosh(2phi) potential, we show that for particular N contours the amplitude may be written as a given superposition of exact solutions to the WheelerDeWitt equation. By choosing certain initial data for the pathintegral amplitude we obtain the amplitude specified by the "noboundary" proposal of Hartle and Hawking. We discuss the nature of the geometries corresponding to the saddle points of the noboundary amplitude. We identify the set of classical solutions this proposal picks out in the classical limit.
Item Type:  Article 

Additional Information:  © 1991 The American Physical Society. 
Uncontrolled Keywords:  Kaluzaklein theory; Steepestdescent contours; Wavefunction; Inflationary universe; Anisotropic universe; Gravitationalfield; Boundarycondition; Densitymatrix; Initial state; Spacetime 
Subjects:  Sciences > Physics > PhysicsMathematical models Sciences > Physics > Mathematical physics 
ID Code:  30117 
Deposited On:  19 May 2015 08:27 
Last Modified:  10 Dec 2018 15:10 
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