Determination of Inflationary Observables by Cosmic Microwave Background Experiments.

Inflation produces nearly Harrison-Zel'dovich scalar and tensor perturbation spectra which lead to anisotropy in the cosmic microwave background (CMB). The amplitudes and shapes of these spectra can be parametrized by Q _sp{S}{2}, r equiv Q_sp {T}{2}/Q_sp{S }{2}, n_S and n_T where Q _sp{S}{2} and Q _sp{T}{2} are the scalar and tensor contributions to the square of the CMB quadrupole and n_S and n _T are the power-law spectral indices. Even if we restrict ourselves to information from angles greater than half of a degree, three of these observables can be measured with some precision. The combination 100^{1-n_S} Q_sp{S}{2} can be known to better than +/-0.3%. The scalar index n_S can be determined to about +/-0.01. The ratio r can be known to about +/-0.1 for n _S ~eq 1 and slightly better for smaller n_S. The precision with which n_T can be measured depends weakly on n_{S } and strongly on r. For n_ {S} ~eq 1 n_{T } can be determined with a precision of about +/-0.056(1.5 + r)/r. A full-sky experiment with a half-degree beam using technology available today, similar to those being planned by several groups, can achieve the above precision. Good angular resolution is more important than high signal-to-noise ratio; for a given detector sensitivity and observing time a smaller beam provides more information than a larger beam. This conclusion holds for any model in which the perturbations obey Gaussian statistics. The uncertainty in n_S is roughly proportional to the beam size. We briefly discuss the effects of uncertainty in the Hubble constant, baryon density, cosmological constant and ionization history.