Positivity in the sky
  Positivity bounds - the consequences of requiring a unitary, causal, local UV
completion - place strong restrictions on theories of dark energy and/or
modified gravity. We derive and investigate such bounds for Horndeski
scalar-tensor theories and for the first time pair these bounds with a
cosmological parameter estimation analysis, using CMB, redshift space
distortion, matter power spectrum and BAO measurements from the Planck,
SDSS/BOSS and 6dF surveys. Using positivity bounds as theoretical priors, we
show that their inclusion in the parameter estimation significantly improves
the constraints on dark energy/modified gravity parameters. Considering as an
example a specific class of models, which are particularly well-suited to
illustrate the constraining power of positivity bounds, we find that these
bounds eliminate over 60% of the previously allowed parameter space. We also
discuss how combining positivity requirements with additional theoretical
priors has the potential to further tighten these constraints: for instance
also requiring a subluminal speed of gravitational waves eliminates all but 1%
of the previously allowed parameter space.
