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.