1999/11/30 by Jerome Martin, Jérôme Martin, Dominik J. Schwarz +1 · 3 citations
Mathematics · Physics and Astronomy · #Amplitude #Anisotropy #Approx #Computational physics #Cosmic background radiation #Cosmic microwave background #Cosmology and Gravitation Theories #Dark Matter and Cosmic Phenomena #Galaxies: Formation, Evolution, Phenomena #Inflation (cosmology) #Mathematics #Multipole expansion #Order (exchange) #Physics #Quadrupole #Quantum mechanics #Slow roll #Spectral density #Statistics #astro-ph #gr-qc #hep-ph
paper · pdf · doi:10.1103/physrevd.62.103520
published as Phys.Rev. D62 (2000) 103520 · 3 important additions: 1. discussion of higher multipoles, 2. comparison of error from the slow-roll approximation with the error from the cosmic variance, 3. suggestion for improvement of slow-roll approximation; two figures and a table added; 15 pages, 14 figures, RevTeX; accepted for publication in Phys. Rev. D
arxiv created 2000/05/25 · openalex publication_date 2000/10/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Inflationary predictions for the anisotropy of the cosmic microwave background radiation 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 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 nS=0.9 the error from the leading order slow-roll approximation is \ensuremath≈5% for the amplitudes and \ensuremath≈20% for the quadrupoles. For the next-to-leading order the errors are within a few percent. The errors increase with |nS\ensuremath-1|. To obtain a precision of 1% it is necessary, but in general not sufficient, to use the next-to-leading order. In the case of power-law inflation this precision is obtained for the spectral indices if |nS\ensuremath-1|<0.02 and for the quadrupoles if |nS\ensuremath-1|<0.15 only. The errors in the higher multipoles are even larger than those for the quadrupole, e.g. \ensuremath≈15% for l=100, with nS=0.9 at the next-to-leading order. We find that the accuracy of the slow-roll approximation may be improved by shifting the pivot scale of the primordial spectrum (the scale at which the slow-roll parameters are fixed) into the regime of acoustic oscillations. Nevertheless, the slow-roll approximation cannot be improved beyond the next-to-leading order in the slow-roll parameters.