Is bouncing easier with a negative effective dark fluid density ?

Assuming that a cosmological model can describe the whole Universe history, we look for the conditions of a cosmological bounce thus in agreement with late time observations. Our approach involves casting such a theory into General Relativity with curvature ($\Omega_{\kappa}$), matter ($\Omega_{m}$), radiation ($\Omega_{r}$) and an effective dark fluid ($\Omega_{d}$) and formulating the corresponding field equations as a 2D dynamical system, wherein phase space points corresponding to extrema of the metric function are constrained by observational data. We show that if this effective dark fluid density is positive at the bounce, these observational constraints imply its occurrence in the future at a redshift $z<-0.81$ whatever the cosmological model (dark energy, brane, $f(R)$, etc.) corresponding to this effective dark fluid and even with a positive curvature. Hence, the effective dark fluid density must be negative at the bounce such as it arises for $z>-0.81$ and thus possibly in the past. Observations also impose that the dark fluid effective density can change sign only within the redshift range $0.54<z<0.61$. We then proceed by examining 3 cosmological models: a non linear dark fluid model, a Randall Sundrum brane model and a $f(R)=R+mR^n+\Lambda$ model. For each of them, we examine the conditions for (1) a bounce at early time, (2) with a negative effective dark fluid energy density, (3) this having to change sign within the above specified redshift interval. We find that none of these three models satisfy all three constraints. We conclude that while a negative effective dark fluid energy density required by observational constraints for a bounce at early times facilitates this bounce, the requirement for $\Omega_d$ to change sign and become positive within the above specified narrow redshift interval proves exceedingly challenging to satisfy these same constraints.
Comment: 14 pages, 6 figures