The effective Lagrangian of dark energy from observations
  Using observational data on the expansion rate of the universe (H(z)) we
constrain the effective Lagrangian of the current accelerated expansion. Our
results show that the effective potential is consistent with being flat i.e., a
cosmological constant; it is also consistent with the field moving along an
almost flat potential like a pseudo-Goldstone boson. We show that the potential
of dark energy does not deviate from a constant at more than 6% over the
redshift range 0 < z < 1. The data can be described by just a constant term in
the Lagrangian and do not require any extra parameters; therefore there is no
evidence for augmenting the number of parameters of the LCDM paradigm. We also
find that the data justify the effective theory approach to describe
accelerated expansion and that the allowed parameters range satisfy the
expected hierarchy. Future data, both from cosmic chronometers and baryonic
acoustic oscillations, that can measure H(z) at the % level, could greatly
improve constraints on the flatness of the potential or shed some light on
possible mechanisms driving the accelerated expansion. Besides the above
result, it is shown that the effective Lagrangian of accelerated expansion can
be constrained from cosmological observations in a model-independent way and
that direct measurements of the expansion rate H(z) are most useful to do so.
