  Models for structure formation attempt to predict the power spectrum of
density perturbations in the present universe from the initial power spectrum
and the nature of dark matter. Observational constraints on the power spectrum
at different scales in the present epoch can, therefore, be used to eliminate
(or choose between) different theoretical models. Such a comparison is fairly
easy at large scales (at which linear theory is valid), and one can use
observations like the MBR anisotropy, large scale steaming motions etc to
constrain the models. But to discriminate between the models effectivley, it is
necessay to constrain the power spectrum at small scales. The most reliable
constraints on the power spectra at small scales come from the predicted
abundance of bound systems which can be estimated reasonably accurately using
Press-Schecter (or similar) methods$^1$. In the past, this method has been used
in conjunction with the quasar abundance$^{2-4}$ and cluster abundance$^{5-7}$.
We show here that the abundance of damped lyman alpha systems (DLAS,
hereafter), provides a far stronger constraint on the models for structure
formation. Models with a mixture of hot and cold dark matter $^{8-11}$ (which
are consistent with large scale observations) are strongly ruled out by the
DLAS constraints while models with cosmological constant $^{12}$ are marginally
inconsistent. It is also possible to combine the constraints from the abundance
of clusters, DLAS and QSO's to obtain model-independent bounds on the power
spectrum at the nonlinear scales. These bounds are to be respected by any
viable model for structure formation.
