  We investigate multi-field inflationary scenarios with fields that drop out
of the model in a staggered fashion. This feature is natural in certain
multi-field inflationary setups within string theory; for instance, it can
manifest itself when fields are related to tachyons that condense, or
inter-brane distances that become meaningless when branes annihilate.
Considering a separable potential, and promoting the number of fields to a
smooth time-dependent function, we derive the formalism to deal with these
models at the background and perturbed level, providing general expressions for
the scalar spectral index and the running. We recover known results of e.g. a
dynamically relaxing cosmological constant in the appropriate limits. We
further show that isocurvature perturbations are suppressed during inflation,
so that perturbations are adiabatic and nearly Gaussian. The resulting setup
might be interpreted as a novel type of warm inflation, readily implemented
within string theory and without many of the shortcomings associated with warm
inflation.
  To exemplify the applicability of the formalism we consider three concrete
models: assisted inflation with exponential potentials as a simple toy model (a
graceful exit becomes possible), inflation from multiple tachyons (a constant
decay rate of the number of fields and negligible slow roll contributions turns
out to be in good agreement with observations) and inflation from multiple
M5-branes within M-theory (a narrow stacking of branes yields a consistent
scenario).
