  Current cosmological observations show a strong signature of the existence of
a dark energy component with negative pressure. The most obvious candidate for
this dark energy is the cosmological constant (with the equation of state
w_X=p/\rho=-1), which, however, raises several theoretical difficulties. This
has led to models for dark energy component which evolves with time. We discuss
certain questions related to the determination of the nature of dark energy
component from observations of high redshift supernova. The main results of our
analysis are: (i) Even if the precise value of w_X is known from observations,
it is not possible to determine the nature of the unknown dark energy source
using only kinematical and geometrical measurements. We have given explicit
examples to show that different types of sources can give rise to a given w_X.
(ii) Although the full data set of supernova observations (which are currently
available) strongly rule out models without dark energy, the high (z>0.25) and
low (z<0.25) redshift data sets, individually, admit decelerating models with
zero dark energy. Any possible evolution in the absolute magnitude of the
supernovae, if detected, might allow the decelerating models to be consistent
with the data. (iii) We have introduced two parameters, which can be obtained
entirely from theory, to study the sensitivity of the luminosity distance on
w_X. Using these two parameters, we have argued that although one can determine
the present value of w_X accurately from the data, one cannot constrain the
evolution of w_X.
