Phase Space description of Nonlocal Teleparallel Gravity
  We study cosmological solutions in nonlocal teleparallel gravity or $f(T)$
theory, where $T$ is the torsion scalar in teleparallel gravity. This is a
natural extenstion of the usual teleparallel gravity with nonlocal terms. In
this work the phase space portrait proposed to describe the dynamics of an
arbitrary flat, homogeneous cosmological background with a number of matter
contents, both in early and late time epochs. The aim was to convert the system
of the equations of the motion to a first order autonomous dynamical system and
to find fixed points and attractors using numerical codes. For this purpose,
firstly we derive effective forms of cosmological field equations describing
the whole cosmic evolution history in a homogeneous and isotropic cosmological
background and construct the autonomous system of the first order dynamical
equations. In addition, we investigate the local stability in the dynamical
systems called "the stable/unstable manifold" by introducing a specific form of
the interaction between matter, dark energy, radiation and a scalar field.
Furthermore, we explore the exact solutions of the cosmological equations in
the case of de Sitter spacetime. In particular, we examine the role of an
auxiliary function called "gauge" $\eta$ in the formation of such cosmological
solutions and show whether the de Sitter solutions can exist or not. Moreover,
we study the stability issue of the de Sitter solutions both in vacuum and
non-vacuum spacetimes. It is demonstrated that for nonlocal $f(T)$ gravity, the
stable de Sitter solutions can be produced even in vacuum spacetime.
