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Register a new userCMB Constraints on Principal Components of the Inflaton Potential
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We place functional constraints on the shape of the inflaton potential from the cosmic microwave background through a variant of the generalized slow roll approximation that allows large amplitude, rapidly changing deviations from scale-free conditions. Employing a principal component decomposition of the source function G~3(V/V)^2 - 2V/V and keeping only those measured to better than 10% results in 5 nearly independent Gaussian constraints that maybe used to test any single-field inflationary model where such deviations are expected. The first component implies < 3% variations at the 100 Mpc scale. One component shows a 95% CL preference for deviations around the 300 Mpc scale at the ~10% level but the global significance is reduced considering the 5 components examined. This deviation also requires a change in the cold dark matter density which in a flat LCDM model is disfavored by current supernova and Hubble constant data and can be tested with future polarization or high multipole temperature data. Its impact resembles a local running of the tilt from multipoles 30-800 but is only marginally consistent with a constant running beyond this range. For this analysis, we have implemented a ~40x faster WMAP7 likelihood method which we have made publicly available.
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We study the conditions under which simple relations between the inflaton couplings and CMB observables can be established. The crucial criterion is to avoid feedback effects during reheating, which tend to introduce a complicated dependence of the CMB observables on a large number of microphysical parameters that prohibits the derivation of meaningful constraints on any individual one of them. We find that the inflaton coupling can be measured with cosmological data when the effective potential during reheating can be approximated by a parabola, and when the coupling constants are smaller than an upper bound that it determined by the ratios between the inflaton mass and the Planck mass or the scale of inflation. The power at which these ratios appear is determined by the power at which the inflaton appears in a given interaction term, and the value of the upper bound is largely independent of the type of produced particle. Our results show that next generation CMB observatories may be able to constrain the inflaton couplings for various types of interactions, providing an important clue to understand how a given model of inflation may be embedded into a more fundamental microphysical theory of nature.
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