Constraints on $f(R)$ theories of gravity from GW170817
  A novel constraint on $f(R)$ theories of gravity is obtained from the
gravitational wave signal emitted from the binary neutron star merger event
GW170817. The $f(R)$ theories possess an additional massive scalar degree of
freedom apart from the massless spin-2 modes. The corresponding scalar field
contributes an additional attractive, short-ranged "fifth" force affecting the
gravitational wave radiation process. We realize that chameleon screening is
necessary to conform with the observation. A model independent bound $\vert
f'(R_0) -1\vert < 3\times 10^{-3}$ has been obtained, where the prime denotes
the derivative with respect $R$ and $R_0$ is the curvature of our Universe at
present. Though we use the nonrelativistic approximations and obtain an order
of magnitude estimate of the bound, it comes from direct observations of
gravitational waves and thus it is worth noting. This bound is
stronger/equivalent compared to some earlier other bounds such as from the
Cassini mission in the Solar-System, Supernova monopole radiation, the observed
CMB spectrum, galaxy cluster density profile, etc., although it is weaker than
best current constraints ($\vert f'(R_0) -1\vert \lesssim 10^{-6}$) from
cosmology. Using the bound obtained, we also constrain the parameter space in
the $f(R)$ theories of dark energy like Hu-Sawicki, Starobinsky, and Tsujikawa
models.
