  We explore constraints on various forms for the effective potential during
inflation based upon a statistical comparison between inflation-generated
fluctuations in the cosmic microwave background temperature and the COBE DMR
results. Fits to the first year 53 A + B x 90 A + B cross correlation function
using an effective potential of the form V(phi) = lambda*phi^x/x!, yield upper
limits of x le 107 and x le 397 at the 1 sigma and 2 sigma confidence levels,
while the same analysis produces a power law of index of n = 1.10
^{+0.47}_{-0.64} which would imply an underestimate of x le 63 from the simple
analytic relation between x and n . We also quantify new limits on the
parameters for polynomial effective potentials. This work highlights the
importance of a careful statistical treatment when seeking constraints on the
inflation-generating effective potential.
