Eur. Phys. J. C (2014) 74: 3132
https://doi.org/10.1140/epjc/s10052-014-3132-8

Regular Article - Theoretical Physics

Ghost-free massive theories modeled as effective Einstein spaces and cosmic acceleration

¹ Theory Division, CERN, 1211, Geneva 23, Switzerland
² Rector’s Office, Alexandru Ioan Cuza University, Alexandru Lapuşneanu street, nr. 14, UAIC, Corpus R, office 323, 700057, Iasi, Romania

^* e-mail: sergiu.vacaru@uaic.ro

Received: 17 July 2014
Accepted: 14 October 2014
Published online: 5 November 2014

Abstract

We study how massive ghost-free gravity -modified theories, MGFTs, can be encoded into generic off-diagonal Einstein spaces. Using “auxiliary” connections completely defined by the metric fields and adapted to nonholonomic frames with associated nonlinear connection structure, we decouple and integrate in certain general forms the field equations in MGFT. Imposing additional nonholonomic constraints, we can generate Levi-Civita, LC, configurations and mimic MGFT effects via off-diagonal interactions of effective Einstein and/or Einstein–Cartan gravity with nonholonomically induced torsion. We show that imposing nonholonomic constraints it is possible reproduce very specific models of massive gravity studied in Cai et al. (arXiv:1307.7150, 2013), Klusoňet al. (Phys Lett B 726:918, 2013), Nojiri and Odintov (Phys Lett B 716:377, 2012) and Nojiri et al. (JCAP 1305:020, 2013). The cosmological evolution of ghost-free off-diagonal Einstein spaces is investigated. Certain compatibility of MGFT cosmology to small off-diagonal deformations of CDM models is established.