  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 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 $\approx 5%$ for the amplitudes and $\approx 20%$ 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
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 $|n_S - 1| < 0.02$ and for the quadrupoles if $|n_S - 1| < 0.15$
only. The errors in the higher multipoles are even larger than those for the
quadrupole, e.g. $\approx 15%$ for l=100, with $n_S = 0.9$ 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.

Astrophysics;General Relativity and Quantum Cosmology;High Energy Physics - Phenomenology