Eur. Phys. J. C (2018) 78: 447
https://doi.org/10.1140/epjc/s10052-018-5939-1

Regular Article - Theoretical Physics

Classification of the Horndeski cosmologies via Noether symmetries

¹ Dipartimento di Fisica “E. Pancini”, Universitá di Napoli “Federico II”, Naples, Italy
² Gran Sasso Science Institute, Via F. Crispi 7, 67100, L’Aquila, Italy
³ INFN Sez. di Napoli, Compl., Univ. di Monte S. Angelo, Edificio G, Via Cinthia, 80126, Naples, Italy
⁴ Institute of Physics, Kazan Federal University, Kremlevskaya Street 16a, Kazan, 420008, Russia

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

Received: 12 April 2018
Accepted: 25 May 2018
Published online: 5 June 2018

Abstract

Adopting Noether point symmetries, we classify and integrate dynamical systems coming from Horndeski cosmologies. The method is particularly effective both to select the form of Horndeski models and to derive exact cosmological solutions. Starting from the Lagrangians selected by the Noether symmetries, it is possible to derive several modified theories of gravity like f(R) gravity, Brans–Dicke gravity, string inspired gravity and so on. In any case, exact solutions are found out.