  Cosmological scenarios with a non-standard equation of state can involve
ultrastiff fluids, understood as primordial fluids for which $p/\rho> 1$. Their
energy densities can dominate the Universe energy budget at early times, in the
otherwise radiation dominated epoch. During that period the Universe undergoes
a faster expansion, that has implications for any decoupling process that takes
place in that era. Quintessence models or Ekpyrotic cosmologies are good
examples of such scenarios. Assuming the ultrastiff state to be thermally
decoupled at very early times, if ever coupled, its observational imprints are
left solely in the Universe expansion rate and in the radiation energy density.
We consider a complete set of ultrastiff fluids and study their signatures in
the neutrino decoupling and BBN eras. Measurements of $N_\text{eff}$ alone
place mild constraints on these scenarios, with forthcoming measurements from
the Simons Observatory in the Chilean Atacama desert being able to test regions
where still sizable effects are observable. However, when BBN data is taken
into account, those regions are proven to be barely reconcilable with
primordial helium-4 and deuterium abundances measurements. Our findings show
that measurements of the primordial helium-4 abundance imply the tightest
constraints, with measurements of primordial deuterium being -- to a certain
extent -- competitive as well. We point out that a $\sim 60\%$ improvement on
the statistical uncertainty of the primordial helium-4 abundance measurement,
will test these scenarios in the region where they can produce sizable effects.
Beyond that precision the regions that are accessible degenerate with standard
expectations. In that case, although potentially present, neither neutrino
decoupling nor BBN observables will be sensitive probes.
