Non-linear extension of non-metricity scalar for MOND

Fabio D'Ambrosio,Mudit Garg,Lavinia Heisenberg

doi:10.1016/j.physletb.2020.135970

Abstract

General Relativity enjoys the freedom of different geometrical interpretations in terms of curvature, torsion or non-metricity. Within this geometrical trinity, a simpler geometrical formulation of General Relativity manifests itself in the latter, where gravity is entirely attributed to non-metricity. In this Letter, we consider non-linear extensions of Coincident General Relativity f(Q˚) for phenomenological applications on both cosmological as well as galactic scales. The theory not only delivers dark energy on large scales but also recovers MOND on galactic scales, together with implications for the early universe cosmology. To the best of our knowledge, this represents the first relativistic, covariant, and ghost-free hybrid-formulation of MOND which recovers both, General Relativity and MOND in the appropriate limits and reconciles expected cosmological behavior. We further illustrate that previous bimetric formulations of MOND generically suffer from ghost instabilities and f(Q˚) crystalizes as a unique ghost-free theory.

Highlights

Since its inception, General Relativity is perceived as the geometrical property of spacetime
In this work we have considered a relativistic, ghostfree, and covariant hybrid-formulation of MOdified Newtonian Dynamics (MOND) in terms of a non-linear extension of the non-metricity scalar f (Q)
In the non-relativistic limit pertaining to smallvelocity sources and weak field configurations one successfully recovers the MOND phenomenology on galactic scales

Summary

INTRODUCTION

General Relativity is perceived as the geometrical property of spacetime. In this Letter we consider a non-linear extension of non-metricity scalar f (Q) within the geometrical formulation of gravity as a relativistic, covariant, Lorentz invariant, and ghost-free theory that recovers both, General Relativity and MOND in certain limits and admits ΛCDM as a cosmological evolution on large scales. In [14] it was shown that the Bimetric Modification Of Newtonian Dynamics (BIMOND) [11] corresponds to f (Q) theory in the coincident gauge if the second metric of bigravity is forced to be Minkowski We confirm this finding and further systematically show that it is not possible to have a ghost-free BIMOND theory which recovers the MOND phenomenology in the non-relativistic limit, except in the unique case where it becomes the f (Q) theory. It can even have interesting implications for early universe cosmology

THE NON-RELATIVISTIC LIMIT

COSMOLOGICAL IMPLICATIONS

The original formulation of BIMOND

Findings

CONCLUSION