LAUSR

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 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 $\alpha <-1$ we prove that there is indeed an inflationary period, although the second and third slow-roll parameters $\eta_H$ and $\xi_H$ are larger than unity for $\alpha \le -5/3$. Such a behaviour of the slow-roll parameters has two significant drawbacks on the model. First, the number of $e$-folds $N$ during inflation is $N \ll 60$ for most of the parameter space, especially for $\alpha \le -5/3$. This means that the horizon and flatness problems cannot be solved during inflation. Second, the slow-roll approximations are not valid for the model during inflation when $\alpha \le -5/3$. This is relevant since some studies have relied on these approximations in order to constrain the parameter space of the GCG model. In particular we show that the approximation $z''/z \approx 2a^2 H^2$ in the Mukhanov-Sasaki equation is not valid. We extend our analysis to the Generalized Chaplygin-Jacobi Gas (GCJG) model. We find that the introduction of a new parameter does not solve the previous problems. We 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.