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Coupling matter in modified Q gravity

T. Harko, T. S. Koivisto, F. S. N. Lobo, G. J. Olmo, D. Rubiera-Garcia

Abstract
We present a novel theory of gravity by considering an extension of symmetric teleparallel gravity. This is done by introducing, in the framework of the metric-affine formalism, a new class of theories where the nonmetricity Q is nonminimally coupled to the matter Lagrangian. More specifically, we consider a Lagrangian of the form L ~ f1(Q) + f2(Q)LM, where f1 and fare generic functions of Q, and LM is the matter Lagrangian. This nonminimal coupling entails the nonconservation of the energy-momentum tensor, and consequently the appearance of an extra force. The formulation of the gravity sector in terms of the Q instead of the curvature may result in subtle improvements of the theory. In the context of nonminimal matter couplings, we are therefore motivated to explore whether the new geometrical formulation in terms of the Q, when implemented also in the matter sector, would allow more universally consistent and viable realizations of the nonminimal coupling. Furthermore, we consider several cosmological applications by presenting the evolution equations and imposing specific functional forms of the functions f1(Q) and f2(Q), such as power-law and exponential dependencies of the nonminimal couplings. Cosmological solutions are considered in two general classes of models, and found to feature accelerating expansion at late times.

Physical Review D
Volume 98, Issue 8
2018 October

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Instituto de Astrofísica e Ciências do Espaço Universidade do Porto Faculdade de Ciências da Universidade de Lisboa
Fundação para a Ciência e a Tecnologia COMPETE 2020 PORTUGAL 2020 União Europeia