Post-Newtonian, Quasi-Circular Binary Inspirals in Quadratic Modified
  Gravity
  We consider a general class of quantum gravity-inspired, modified gravity
theories, where the Einstein-Hilbert action is extended through the addition of
all terms quadratic in the curvature tensor coupled to scalar fields with
standard kinetic energy. This class of theories includes
Einstein-Dilaton-Gauss-Bonnet and Chern-Simons modified gravity as special
cases. We analytically derive and solve the coupled field equations in the
post-Newtonian approximation, assuming a comparable-mass, spinning black hole
binary source in a quasi-circular, weak-field/slow-motion orbit. We find that a
naive subtraction of divergent piece associated with the point-particle
approximation is ill-suited to represent compact objects in these theories.
Instead, we model them by appropriate effective sources built so that known
strong-field solutions are reproduced in the far-field limit. In doing so, we
prove that black holes in Einstein-Dilaton-Gauss-Bonnet and Chern-Simons theory
can have hair, while neutron stars have no scalar monopole charge, in
diametrical opposition to results in scalar-tensor theories. We then employ
techniques similar to the direct integration of the relaxed Einstein equations
to obtain analytic expressions for the scalar field, metric perturbation, and
the associated gravitational wave luminosity measured at infinity. We find that
scalar field emission mainly dominates the energy flux budget, sourcing
electric-type (even-parity) dipole scalar radiation and magnetic-type
(odd-parity) quadrupole scalar radiation, correcting the General Relativistic
prediction at relative -1PN and 2PN orders. Such modifications lead to
corrections in the emitted gravitational waves that can be mapped to the
parameterized post-Einsteinian framework. Such modifications could be strongly
constrained with gravitational wave observations.
