Eur. Phys. J. C (2015) 75: 343
https://doi.org/10.1140/epjc/s10052-015-3562-y

Regular Article - Theoretical Physics

Gravity’s Rainbow: a bridge towards Hořava–Lifshitz gravity

¹ Dipartimento di Ingegneria e Scienze Applicate, Università degli Studi di Bergamo, Viale Marconi 5, 24044, Dalmine, Bergamo, Italy
² I.N.F.N., sezione di Milano, Milan, Italy
³ Institut d’Astrophysique de Paris, UMR 7095-CNRS, Université Pierre and Marie Curie, 98bis boulevard Arago, 75014, Paris, France
⁴ Instituto de Física, Pontificia Universidad de Católica de Valparaíso, Casilla 4950, Valparaíso, Chile

^* e-mail: remo.garattini@unibg.it

Received: 26 May 2015
Accepted: 7 July 2015
Published online: 22 July 2015

Abstract

We investigate the connection between Gravity’s Rainbow and Hořava–Lifshitz gravity, since both theories incorporate a modification in the ultraviolet regime which improves their quantum behavior at the cost of the Lorentz invariance loss. In particular, extracting the Wheeler–De Witt equations of the two theories in the case of Friedmann–Lemaître–Robertson–Walker and spherically symmetric geometries, we establish a correspondence that bridges them.