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Abstract: We update constraints on the Hubble function Hphi during inflation, usingthe most recent cosmic microwave background CMB and large scale structureLSS data. Our main focus is on a comparison between various commonly usedmethods of calculating the primordial power spectrum via analyticalapproximations and the results obtained by integrating the exact equationsnumerically. In each case, we impose naive, minimally restrictive priors on theduration of inflation. We find that the choice of priors has an impact on theresults: the bounds on inflationary parameters can vary by up to a factor two.Nevertheless, it should be noted that within the region allowed by the minimalprior of the exact method, the accuracy of the approximations is sufficient forcurrent data. We caution however that a careless minimal implementation of theapproximative methods allows models for which the assumptions behind theanalytical approximations fail, and recommend using the exact numerical methodfor a self-consistent analysis of cosmological data.

Autor: Jan Hamann, Julien Lesgourgues, Wessel Valkenburg


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