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Advances in Mathematical Physics
Volume 2017, Article ID 1056514, 5 pages
Research Article

Quantum Cosmology of Quadratic Theories with a FRW Metric

1Facultad de Ingeniería, Benemérita Universidad Autónoma de Puebla, 72000 Puebla, PUE, Mexico
2Facultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla, P.O. Box 165, 72000 Puebla, PUE, Mexico

Correspondence should be addressed to V. Vázquez-Báez; xm.paub.oerroc@zeuqzav.leunam

Received 1 April 2017; Accepted 17 May 2017; Published 18 June 2017

Academic Editor: Anzhong Wang

Copyright © 2017 V. Vázquez-Báez and C. Ramírez. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We study the quantum cosmology of a quadratic theory with a FRW metric, via one of its equivalent Horndeski type actions, where the dynamic of the scalar field is induced. The classical equations of motion and the Wheeler-DeWitt equation, in their exact versions, are solved numerically. There is a free parameter in the action from which two cases follow: inflation + exit and inflation alone. The numerical solution of the Wheeler-DeWitt equation depends strongly on the boundary conditions, which can be chosen so that the resulting wave function of the universe is normalizable and consistent with Hermitian operators.