Is a non-vanishing cosmological constant really needed?

Abstract

Using consistenly the compact Friedmann-Lemaitre solutions for an open $(k=-0.580)$ universe with zero cosmological constant ($\Lambda =0$) we show that the oberved apparent accelerated expansion is compatible with a time dependent Hubble parameter $H=\dot{R}/R$ equal to $H=87.95$ km/s/Mpc at $t=10.39$ Gys, $H_0=67.9\pm 4$ km/s/Mpc at $t_o=13.7\pm 0.2$ Gyrs (present), $H=61.4$ km/s/Mpc at $t=15$ Gyrs and with an apparent global flatness given by $1={\Omega }_m+{\Omega }_r+{\Omega }_k$ at all times which, properly averaged from galaxy formation times to present, gives $<{\Omega }_m>=0.272$, $<{\Omega }_r>=0.005$, $<{\Omega }_k>=0.728$. Therefore, no cosmological constant is needed.