Determination of Inflationary Observables by Cosmic Microwave Background Anisotropy 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 $Q_S^2$, $r\equiv Q_T^2/Q_S^2$,$n_S$and$n_T$where$Q_S^2$and$Q_T^2$ are the scalar and tensor contributions to the square of the CMB quadrupole and $n_S$ and $n_T$ are the power-lawspectral indices. Even if we restrict ourselves to information from angles greater than one third of a degree, three of these observables can be measured with some precision. The combination ${130}^{1-n_S}{Q}_S^2$ can be known to better than $\pm 0.3\mathrm{\%}$. The scalar index $n_S$ can be determined to better than $\pm 0.02$. The ratio $r$ can be known to about $\pm 0.1$ for $n_S \simeq 1$andslightlybetterforsmaller$n_S$\mathrm{.}Theprecisionwithwhich$n_T$canbemeasureddependsweaklyon$n_S$andstronglyon$r$\mathrm{.}For$n_S \simeq 1$ $n_T$ can be determined with a precision of about $\pm 0.056(1.5+r)\mathrm{/}r$. A full-sky experiment with a ${20}^{\mathrm{\prime }}$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 significantly more information than a larger beam. The uncertainties in $n_S$ and $r$ are roughly proportional to the beam size. We briefly discuss the effects of uncertainty in the Hubble constant, baryon density, cosmological constant and ionization history.