  An analysis of soft breaking under the constraint of modular invariance is
given. The role of dilaton and moduli dependent front factors in achieving a
modular invariant $V_{soft}$ is emphasized. Further, it is shown that in string
models $\tan\beta$ is no longer a free parameter but is determined in terms of
$\alpha_{string}$ and the other soft parameters by the constraints of modular
invariance and radiative electroweak symmetry breaking. The above framework is
then used to analyze the neutralino relic density consistent with the WMAP data
at self dual points in the Kahler and complex structure moduli. One finds that
the combined set of constraints arising from modular invariant soft breaking,
radiative electroweak symmetry breaking and WMAP lead to upper limits on
sparticle masses for $\mu>0$. These limits are investigated for a class of
models and found to lie within reach of the Tevatron and of the Large Hadron
Collider (LHC). Further, an analysis of the neutralino-proton cross section
shows that dark matter in these models can be explored in CDMS (Soudan), GENIUS
and ZEPLIN. While the analysis is carried out within the general framework of
heterotic strings, the possibility that the results of the analysis may extend
to a broader class of string models, such as models based on intersecting D
branes, is also discussed.
