Eur. Phys. J. C (2016) 76: 629
https://doi.org/10.1140/epjc/s10052-016-4491-0

Regular Article - Theoretical Physics

Noether symmetries in Gauss–Bonnet-teleparallel cosmology

¹ Dipartimento di Fisica “E. Pancini”, Universita’ di Napoli“Federico II”, Complesso Universitario di Monte S. Angelo, Edificio G, Via Cinthia, 80126, Napoli, Italy
² INFN Sezione di Napoli, Complesso Universitario di Monte S. Angelo, Edificio G, Via Cinthia, 80126, Napoli, Italy
³ Gran Sasso Science Institute (INFN), Via F. Crispi 7, 67100, L’ Aquila, Italy
⁴ Tomsk State Pedagogical University, 634061, Tomsk, Russia
⁵ Institute for Theoretical Physics, Goethe University, Max-von-Laue-Str. 1, 60438, Frankfurt, Germany
⁶ Laboratory of Theoretical Cosmology, Tomsk State University of Control Systems and Radioelectronics (TUSUR), 634050, Tomsk, Russia

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

Received: 30 September 2016
Accepted: 7 November 2016
Published online: 18 November 2016

Abstract

A generalized teleparallel cosmological model, , containing the torsion scalar T and the teleparallel counterpart of the Gauss–Bonnet topological invariant , is studied in the framework of the Noether symmetry approach. As gravity, where is the Gauss–Bonnet topological invariant and R is the Ricci curvature scalar, exhausts all the curvature information that one can construct from the Riemann tensor, in the same way, contains all the possible information directly related to the torsion tensor. In this paper, we discuss how the Noether symmetry approach allows one to fix the form of the function and to derive exact cosmological solutions.