The precision of slow-roll predictions for the CMBR anisotropies

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  • 12 November 1999
Abstract
Inflationary predictions for the anisotropy of the cosmic microwave background radiation (CMBR) are often based on the slow-roll approximation. We study the precision with which the multipole moments of the temperature two-point correlation function can be predicted by means of the slow-roll approximation. We ask whether this precision is good enough for the forthcoming high precision observations (error < 1%) by means of the MAP and PLANCK satellites. The error in the multipole moments due to the slow-roll approximation is demonstrated to be bigger than the error in the power spectrum. For power-law inflation with n_S = 0.9 the error from the leading order slow-roll approximation is ~ 5% for the amplitudes and ~ 20% for the quadrupoles. For the next-to-leading order the errors are within a few percent. The errors increase with |n_S - 1|. To obtain a precision of 1% it is mandatory to use the next-to-leading order. For a general model of inflation the next-to-leading order does not guarantee 1% precision. In the case of power-law inflation this precision is obtained for the spectral indices if |n_S - 1| > 0.02 and for the quadrupoles if |n_S - 1| > 0.15 only. The slow-roll approximation cannot be improved beyond the next-to-leading order in the slow-roll parameters.

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