https://doi.org/10.1140/epjc/s10052-020-8258-2
Regular Article - Theoretical Physics
Noether cosmology
1
Universitá di Napoli “Federico II”, Compl. Univ. di Monte S. Angelo, Edificio G, Via Cinthia, 80126, Naples, Italy
2
INFN Sezione di Napoli, Compl. Univ. di Monte S. Angelo, Edificio G, Via Cinthia, 80126, Naples, Italy
3
Gran Sasso Science Institute, viale F. Crispi 7, 67100, L’Aquila, Italy
4
Tomsk State Pedagogical University, ul. Kievskaya, 60, 634061, Tomsk, Russia
* e-mail: capozziello@na.infn.it
Received:
19
May
2020
Accepted:
16
July
2020
Published online:
6
August
2020
We develop the n-dimensional cosmology for gravity, where 
is the Gauss–Bonnet topological invariant. Specifically, by the so-called Noether Symmetry Approach, we select 
power-law models where k is a real number. In particular, the case 
for 
results equivalent to General Relativity showing that we do not need to impose the action 
to reproduce the Einstein theory. As a further result, de Sitter solutions are recovered in the case where is non-minimally coupled to a scalar field. This means that issues like inflation and dark energy can be addressed in this framework. Finally, we develop the Hamiltonian formalism for the related minisuperspace and discuss the quantum cosmology for this model.
© The Author(s), 2020
