Detailed balance condition and ultraviolet stability of scalar field in
  Horava-Lifshitz gravity
  Detailed balance and projectability conditions are two main assumptions when
Horava recently formulated his theory of quantum gravity - the Horava-Lifshitz
(HL) theory. While the latter represents an important ingredient, the former
often believed needs to be abandoned, in order to obtain an ultraviolet stable
scalar field, among other things. In this paper, because of several attractive
features of this condition, we revisit it, and show that the scalar field can
be stabilized, if the detailed balance condition is allowed to be softly
broken. Although this is done explicitly in the non-relativistic general
covariant setup of Horava-Melby-Thompson with an arbitrary coupling constant
$\lambda$, generalized lately by da Silva, it is also true in other versions of
the HL theory. With the detailed balance condition softly breaking, the number
of independent coupling constants can be still significantly reduced. It is
remarkable to note that, unlike other setups, in this da Silva generalization,
there exists a master equation for the linear perturbations of the scalar field
in the flat Friedmann-Robertson-Walker background.
