Riding on irrelevant operators
  We investigate the stability of a class of derivative theories known as
$P(X)$ and Galileons against corrections generated by quantum effects. We use
an exact renormalisation group approach to argue that these theories are stable
under quantum corrections at all loops in regions where the kinetic term is
large compared to the strong coupling scale. This is the regime of interest for
screening or Vainshtein mechanisms, and in inflationary models that rely on
large kinetic terms. Next, we clarify the role played by the symmetries. While
symmetries protect the form of the quantum corrections, theories equipped with
more symmetries do not necessarily have a broader range of scales for which
they are valid. We show this by deriving explicitly the regime of validity of
the classical solutions for $P(X)$ theories including Dirac-Born-Infeld (DBI)
models, both in generic and for specific background field configurations.
Indeed, we find that despite the existence of an additional symmetry, the DBI
effective field theory has a regime of validity similar to an arbitrary $P(X)$
theory. We explore the implications of our results for both early and late
universe contexts. Conversely, when applied to static and spherical screening
mechanisms, we deduce that the regime of validity of typical power-law $P(X)$
theories is much larger than that of DBI.
