The dynamics of the local group as a probe of Dark Energy and Modified
  Gravity
  In this work we study the dynamics of the Local Group (LG) within the context
of cosmological models beyond General Relativity (GR). Using observable
kinematic quantities to identify candidate pairs we build up samples of
simulated LG-like objects drawing from $f(R)$, symmetron, DGP and quintessence
N-body simulations together with their $\Lambda$CDM counterparts featuring the
same initial random phase realisations. The variables and intervals used to
define LG-like objects are referred to as Local Group model; different models
are used throughout this work and adapted to study their dynamical and
kinematic properties. The aim is to determine how well the observed LG-dynamics
can be reproduced within cosmological theories beyond GR, We compute kinematic
properties of samples drawn from alternative theories and $\Lambda$CDM and
compare them to actual observations of the LG mass, velocity and position. As a
consequence of the additional pull, pairwise tangential and radial velocities
are enhanced in modified gravity and coupled dark energy with respect to
$\Lambda$CDM, inducing significant changes to the total angular momentum and
energy of the LG. For example, in models such as $f(R)$ and the symmetron this
increase can be as large as $60\%$, peaking well outside of the $95\%$
confidence region allowed by the data. This shows how simple considerations
about the LG dynamics can lead to clear small-scale observational signatures
for alternative scenarios, without the need of expensive high-resolution
simulations.
