Eur. Phys. J. C (2009) 64: 483-494
https://doi.org/10.1140/epjc/s10052-009-1154-4

Regular Article - Theoretical Physics

One-loop effective action for non-local modified Gauss–Bonnet gravity in de Sitter space

¹ Dipartimento di Fisica, Università di Trento and Istituto Nazionale di Fisica Nucleare Gruppo Collegato di Trento, Trento, Italia
² Facultat Ciències, Consejo Superior de Investigaciones Científicas (ICE/CSIC) and Institut d’Estudis Espacials de Catalunya (IEEC), Campus UAB, Torre C5-Par-2a pl, 08193, Bellaterra (Barcelona), Spain
³ Department of Physics, Nagoya University, Nagoya, 464-8602, Japan
⁴ ICREA, Barcelona, Spain
⁵ Center of Theor. Phys., TSPU, Tomsk, Russia

^* e-mail: cognola@science.unitn.it

Received: 20 July 2009
Published online: 26 September 2009

Abstract

We discuss the classical and quantum properties of non-local modified Gauss–Bonnet gravity in de Sitter space, using its equivalent representation via string-inspired local scalar-Gauss–Bonnet gravity with a scalar potential. A classical, multiple de Sitter universe solution is found where one of the de Sitter phases corresponds to the primordial inflationary epoch, while the other de Sitter space solution—the one with the smallest Hubble rate—describes the late-time acceleration of our universe. A Chameleon scenario for the theory under investigation is developed, and it is successfully used to show that the theory complies with gravitational tests. An explicit expression for the one-loop effective action for this non-local modified Gauss–Bonnet gravity in the de Sitter space is obtained. It is argued that this effective action might be an important step towards the solution of the cosmological constant problem.