Measurements of the large-scale anisotropy in the cosmic microwave background (CMB) by the Cosmic Background Explorer (COBE) Differential Microwave Radiometer experiment have provided important support for the hot big bang model with inflation. A favored explanation for the generation of the observed fluctuations in the CMB temperature is by the expansion of quantum fluctuations of a scalar field during the inflationary epoch. The fact that the observed temperature fluctuations are consistent with a scale-invariant spectrum of power on various angular scales is in agreement with predictions of inflationary models. However, the COBE observations are not exactly scale invariant and neither are the predictions of inflation. This is because inflation occurs as the universe is rolling down an effective potential. Thus, the amount of inflation is slightly different for different angular scales. The change in angular anisotropy of the cosmic microwave background from scales of a few degrees to the full sky is, therefore, a measurement of the rate of change in the effective potential during that short interval of inflation for which those angular scales were stretched beyond the apparent horizon. We explore the degree to which the functional form of the potential can be constrained from the sensitivity of the variance of the quantum fluctuations to the inflation generating potential.
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