view of various no-go theorems, $p$-form gauge fields appear to be the only massless, higher spin fields that can be consistently coupled to gravity. Furthermore, there can be only one type of graviton [@bdgh]. With this observation in mind, the action (\[001\]) is actually quite general. The only restriction concerns the scalar sector: we assume the coupling to the dilaton to be exponential because this corresponds to the tree-level couplings of the dilaton field of string theory. Note, however, that string-loop effects are expected to generate more general couplings $\exp (\lambda \phi) \rightarrow B(\phi)$ which can exhibit interesting “attractor” behaviours [@tDaP]. We also restrict ourselves by not including scalar potentials; see, however, the end of the article for some remarks on the addition of a potential for the dilaton, which can be treated by our methods.

Two possible general, “competing" behaviours of the fields in the vicinity of the spacelike singularity have been identified[^2]:

1.  \[Kasnerbehaviour\] The simplest is the [*“generalized Kasner behaviour”*]{}, in which the spatial scale factors and the field $\exp(\phi)$ behave at each spatial point in a monotone, power-law fashion in terms of the proper time as one approaches the singularity, while the effect of the $p$-form 