Gravitational theories with stable (anti-)de Sitter backgrounds
  In this article we will construct the most general torsion-free
parity-invariant covariant theory of gravity that is free from ghost-like and
tachyonic nstabilities around constant curvature space-times in four
dimensions. Specifically, this includes the Minkowski, de Sitter and anti-de
Sitter backgrounds. We will first argue in details how starting from a general
covariant action for the metric one arrives at an "equivalent" action that at
most contains terms that are quadratic in curvatures but nevertheless is
sufficient for the purpose of studying stability of the original action. We
will then briefly discuss how such a "quadratic curvature action" can be
decomposed in a covariant formalism into separate sectors involving the tensor,
vector and scalar modes of the metric tensor; most of the details of the
analysis however, will be presented in an accompanying paper. We will find that
only the transverse and trace-less spin-2 graviton with its two helicity states
and possibly a spin-0 Brans-Dicke type scalar degree of freedom are left to
propagate in 4 dimensions. This will also enable us to arrive at the
consistency conditions required to make the theory perturbatively stable around
constant curvature backgrounds.
  This will be included as a chapter in the book entitled "At the Frontier of
Spacetime - Scalar-Tensor Theory, Bells Inequality, Machs Principle, Exotic
Smoothness" (Springer 2016)
