Eur. Phys. J. C (2020) 80: 266
https://doi.org/10.1140/epjc/s10052-020-7805-1

Regular Article - Theoretical Physics

Spectral action approach to higher derivative gravity

¹ Instituto de Física, Universidade de Brasília, Brasília, DF, 70910-900, Brazil
² International Center of Physics, C.P. 04667, Brasília, DF, Brazil
³ Department of Physics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, 11519, Prague, Czech Republic

^* e-mail: aleksandr.pinzul@gmail.com

Received: 28 January 2020
Accepted: 4 March 2020
Published online: 24 March 2020

Abstract

We study the spectral action approach to higher derivative gravity. The work focuses on the classical aspects. We derive the complete and simplified form of the purely gravitational action up to the 6-derivative terms. We also derive the equivalent forms of the action, which might prove useful in different applications, namely Riemann– and Weyl–dominated representations. The spectral action provides a rather rigid structure of the higher derivative part of the theory. We discuss the possible consequences of this rigidness. As one of the applications, we check whether the conformal backgrounds are preferred in some way on the classical level, with the conclusion that at this level, there is no obvious reason for such a preference, the space studied in earlier works being a special case. Some other possible properties of the higher derivative gravity given by the spectral action are briefly discussed.