Non-zero trilinear parameter in the mSUGRA model - dark matter and collider signals at Tevatron and LHC

New regions of the parameter space in the minimal super-gravity (mSUGRA) model with small $m_0$ and small $m_{1/2}$ consistent with the WMAP data on dark matter relic density open up if the rather adhoc assumption $A_0$=0, where $A_0$ is the common trilinear soft breaking parameter, employed in most of the existing analyses is relaxed. Since this region corresponds to relatively light squarks and gluinos which are likely to be probed extensively in the very early stages of the LHC experiments, the consequences of moderate or large negative values of $A_0$ are examined in detail. We find that in this region several processes including lightest supersymmetric particle (LSP) pair annihilation, LSP - lighter tau slepton (${\tilde \tau}_1$) coannihilation and LSP - lighter top squark (${\tilde t}_1$) coannihilation contribute to the observed dark matter relic density. The possibility that a relic density producing ${\tilde t}_1$ can be observed at the current experiments at the Tevatron is wide open. At the LHC a large number of squark - gluino events lead to a very distinctive semi-inclusive signature $\tau^\pm$+X$_\tau$ (anything without a tau lepton) with a characteristic size much larger than $e^\pm$+X$_e$ or $\mu^\pm$+X$_\mu$ events.