Abstract
We investigate the ability of current cosmic microwave background data to reliablyconstrain the form of the primordial power spectrum generated during inflation. Weattempt to identify more exotic power spectra that yield equally good fits to the data assimple power-law spectra. In order to test a wide variety of spectral shapes, we combine theflow formalism, which is a method of stochastic model generation, with a numericalintegration of the mode equations of quantum fluctuations. This allows us to handleinflation models that yield spectra that are not well described by the standard spectralparameterization. Using the latest WMAP data set, we find a high degree of variation inpossible spectral shapes. In particular, we find strongly running spectra arising fromfast-rolling inflaton fields providing equally good fits to the data as power-law spectraarising from slowly rolling fields. Current data poorly constrains the spectrum on scalesk<0.01h Mpc−1, where the error due to cosmic variance is large. Among the statistically degeneratemodels, we identify spectra with strong running on these larger scales, but with reducedrunning at smaller scales. These models predict values for the tensor-to-scalar ratio,r, that lieoutside the 2-σ confidence interval obtained from SDSS + WMAP (Sloan Digital Sky Survey plusWilkinson Microwave Anisotropy Probe) data for spectra that are parameterized as powerlaws or spectra with constant running. By considering more generalized powerspectra, we therefore open up regions of parameter space excluded for simplermodels.
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