The Two Body Problem in the Presence of Dark Energy and Modified Gravity: Application to the Local Group

Understand

We explore mass estimation of the Local Group via the use of the simple, dynamical `timing argument' in the context of a variety of theories of dark energy and modified gravity: a cosmological constant, a perfect fluid with constant equation of state $w$, quintessence (minimally coupled scalar field), MOND, and symmetrons (coupled scalar field).

• We explore generic coupled scalar field theories, with the symmetron model as an explicit example.
• We find that theories which attempt to eliminate dark matter by fitting rotation curves produce mass estimates in the timing argument which are not compatible with the luminous mass of the galaxies alone.
• Assuming that the galaxies are approaching their first encounter, MOND gives of around $2.7\times 10^{10} M_\odot$, roughly 10\% of the luminous mass of the LG, although a higher mass can be obtained in the case of a previous fly-by event between the MW and M31.