  Taylor expanding the cosmological equation of state around the current epoch
is the simplest model one can consider that does not make any a priori
restrictions on the nature of the cosmological fluid. Most popular cosmological
models attempt to be ``predictive'', in the sense that once somea priori
equation of state is chosen the Friedmann equations are used to determine the
evolution of the FRW scale factor a(t). In contrast, a retrodictive approach
might usefully take observational dataconcerning the scale factor, and use the
Friedmann equations to infer an observed cosmological equation of state. In
particular, the value and derivatives of the scale factor determined at the
current epoch place constraints on the value and derivatives of the
cosmological equation of state at the current epoch. Determining the first
three Taylor coefficients of the equation of state at the current epoch
requires a measurement of the deceleration, jerk, and snap -- the second,
third, and fourth derivatives of the scale factor with respect to time.
Higher-order Taylor coefficients in the equation of state are related to
higher-order time derivatives of the scale factor. Since the jerk and snap are
rather difficult to measure, being related to the third and fourth terms in the
Taylor series expansion of the Hubble law, it becomes clear why direct
observational constraints on the cosmological equation of state are so
relatively weak; and are likely to remain weak for the foreseeable future.
