Field equations and cosmology for a class of nonlocal metric models of MOND

Cédric Deffayet (1) , Gilles Esposito-Farèse (1) , Richard P. Woodard

1 IAP - Institut d'Astrophysique de Paris

We consider a class of nonlocal, pure-metric modified gravity models which were developed to reproduce the Tully-Fisher relation without dark matter and without changing the amount of weak lensing predicted by general relativity. Previous work gave only the weak field limiting form of the field equations specialized to a static and spherically symmetric geometry. Here we derive the full field equations and specialize them to a homogeneous, isotropic and spatially flat geometry. We also discuss the problem of fitting the free function to reproduce the expansion history. Results are derived for models in which the MOND acceleration a₀≈1.2×1^0-10 m.s-² is a fundamental constant and for the more phenomenologically interesting case in which the MOND acceleration changes with the cosmological expansion rate.

Keywords: 04.50.Kd; 95.35.+d; 98.62.-g; Modified theories of gravity; Dark matter; Characteristics and properties of external galaxies and extragalactic objects; Astrophysics - Cosmology and Nongalactic Astrophysics; General Relativity and Quantum Cosmology

Domains: Sciences of the Universe [physics]

Cédric Deffayet, Gilles Esposito-Farèse, Richard P. Woodard. Field equations and cosmology for a class of nonlocal metric models of MOND. Physical Review D, 2014, 90, ⟨10.1103/PhysRevD.90.064038⟩. ⟨insu-03645314⟩