Statistical constraints on the inflation effective potential from the COBE DMR results

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. We show that the confidence limits of fits to the angular correlation are more sensitive to the inflation generating potential than implied by the uncertainty in the spectral index alone. This is because the cosmic variance diminishes both as contributions from higher multipoles become important, and as the tensor and scalar contributions become comparable. Fits to the first year 53A+B90A+B cross correlation function using an effective potential of the form V () =^x/x! yield upper limits of x35 and x266 at the 1 and 2 confidence levels, while the same analysis produces a power law of index of n=1. 10-₀. ₆₄^+0. 47 which would imply an overestimate of x63 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.