the existence of a global AdS minimum of the potential which is essential for its stability. It can be seen that the resulting cosmological constant has been very finely tuned to make it compatible with the near Minkowskian but de- Sitter nature of the space-time of the present day universe. It is however worth pointing out here that the existence of the global minimum is extremely sensitive to the values of the parameters $\alpha, \alpha_1, A, {W}_0, a, k$ and $k_1$, thus rendering the model as fine tuned.

Discussions
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String theory admits of numerous vacua, but only a very few of them are compatible with phenomenologically viable models in the low energy limit. It is therefore worthwhile to investigate the possible features of string inspired supergravity models from both particle phenomenology as well as cosmological point of view. This work is an attempt to establish the required constraints on the structures of these models in order to get the desired features. In this work we have considered a general supergravity scenario which simultaneously may address the issues of early inflationary phase of the universe, smallness of the observed cosmological constant in the present epoch as well as the TeV 