Constraints on Chaotic Inflation from the COBE DMR results

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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 COBE 53A+B x 90A+B angular correlation function are obtained using simple analytic forms for the effective potential in chaotic inflation models. Not surprisingly, these fits are optimized for a nearly scale-free fluctuation power spectrum. However, from the chi² distribution for the fits we can set upper limits of n le 1.2 and n le 7 at the 1 sigma and 2 sigma confidence levels, respectively, for a V(phi) = lambda phiⁿ effective potential. Similarly, new limits on parameters for polynomial effective potentials can be determined at the 1 sigma and 2 sigma confidence levels. The most stringent constraint, however, is on the overall magnitude of the effective potential.