Eur. Phys. J. C (2016) 76: 225
https://doi.org/10.1140/epjc/s10052-016-4087-8

Regular Article - Theoretical Physics

Wheeler–DeWitt equation and Lie symmetries in Bianchi scalar-field cosmology

¹ Instituto de Ciencias Físicas y Matemáticas, Universidad Austral de Chile, Valdivia, Chile
² Faculty of Physics, Department of Astronomy-Astrophysics-Mechanics, University of Athens, Panepistemiopolis, 157 83, Athens, Greece
³ Institute for Theoretical Physics, pl. M. Borna 9, 50-204, Wroclaw, Poland
⁴ Dipartimento di Fisica “E. Pancini”, Universita’ di Napoli Federico II, Complesso Universitario di Monte S. Angelo, Via Cinthia, 9, 80126, Naples, Italy
⁵ Istituto Nazionale di Fisica Nucleare (INFN) Sez. di Napoli, Complesso Universitario di Monte S. Angelo, Via Cinthia, 9, 80126, Naples, Italy
⁶ Gran Sasso Science Institue (INFN), Viale F. Crispi 7, 67100, L’Aquila, Italy

^* e-mail: capozziello@na.infn.it

Received: 26 January 2016
Accepted: 14 April 2016
Published online: 23 April 2016

Abstract

Lie symmetries are discussed for the Wheeler-De Witt equation in Bianchi Class A cosmologies. In particular, we consider general relativity, minimally coupled scalar-field gravity and hybrid gravity as paradigmatic examples of the approach. Several invariant solutions are determined and classified according to the form of the scalar-field potential. The approach gives rise to a suitable method to select classical solutions and it is based on the first principle of the existence of symmetries.