No slow-roll inflation \`a la Generalized Chaplygin Gas in General
  Relativity
  The Generalized Chaplygin Gas (GCG) model is characterized by the equation of
state $P = -A \rho^{-\alpha}$, where $A>0$ and $\alpha < 1$. The model has been
extensively studied due to its interesting properties and applicability in
several contexts, from late-time acceleration to primordial inflation.
Nonetheless we show that the inflationary slow-roll regime cannot be satisfied
by most of the parameter space of the GCG model when General Relativity (GR) is
considered. In particular, although the model has been applied to inflation
with $0 < \alpha < 1$, we show that for $-1 < \alpha \le 1$ there is no
expansion of the Universe but an accelerated contraction. For $\alpha \le
-5/3$, the second slow-roll parameter $\eta_H$ is larger than unity, so there
is no sustained period of inflation. Only for $\alpha$ very close to -1 the
model produces enough $e$-folds, thus greatly reducing its parameter space.
Moreover, we show that the model is ruled out by the Planck 2018 results.
Finally, we extend our analysis to the Generalized Chaplygin-Jacobi Gas (GCJG)
model. We find that the introduction of a new parameter does not change the
previous results. We thus conclude that the violation of the slow-roll
conditions is a generic feature of the GCG and GCJG models during inflation
when GR is considered and that the models are ruled out by the Planck 2018
results.
