New Bounds on Dark Energy Induced Fifth Forces
  We consider the gravitational Wilsonian effective action at low energy when
all the particles of the standard model have decoupled. When the ${\cal R}^2$
terms dominate, the theory is equivalent to a scalar-tensor theory with the
universal coupling $\beta=1/\sqrt 6$ to matter for which we present strong
lower and upper bounds on the scalaron mass $m$ obtained by using results from
the E\"ot-Wash experiment on the modification of the inverse-square law, the
observations of the hot gas of galaxy clusters and the Planck satellite data on
the neutrino masses. In terms of the range of the scalar interaction mediated
over a distance of order $m^{-1}$, this leads to the small interval $4\,\mu m
\lesssim m^{-1} \lesssim 68\, \mu m$ within reach of future experimental tests
of deviations from Newton's gravitational inverse-square law.
