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A favored explanation for the generation of seed fluctuations in the early universe is by the expansion of quantum fluctuations of a scalar field during the inflationary epoch. The COBE observations of the angular anisotropy of the cosmic microwave background on scales from a few degrees to the full sky is therefore a measurement of a subset of these fluctuations which are dependent upon a small piece of the scalar-field effective potential which drives inflation. This is particularly true since the fluctuations resolved by COBE are for the most part larger than the horizon at recombination and not yet distorted from the inflation-generated spectrum by gravitational clustering on sub-horizon scales.
We have therefore used the COBE angular correlation function to constrain the shape of possible inflation effective potentials. Indeed, the shape of the inflation effective potential is not known. A large number of different models, with different potentials, some with many free parameters, have been proposed. While most models lead to a spectrum which is nearly scale invariant, this scale-invariance is not exact, and some models lead to significantly non-scale-invariant spectra. Although the constraints which can be placed on effective potentials are not very restrictive due to observational uncertainties, and effects of cosmic variance, these studies do provide at least some information and represent the only direct observation of the shape of the inflation effective potential.
Work performed in part under the auspices of the U.S. Department of Energy by the Lawrence Livermore National Laboratory under contract W-7405-ENG-48.
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