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Inflation produces nearly scale-invariant 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 Qₒ^2, rQₓ^2/Qₒ^2, nₒ, and nₓ where Qₒ^2 and Qₓ^2 are the scalar and tensor contributions to the square of the CMB quadrupole and nₒ and nₓ are the power-law spectral 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 105ₒ^1-nQₒ^2 can be known to better than 0. 3%. The scalar index nₒ can be determined to better than 0. 02. The ratio r can be known to about 0. 1 for nₒ1 and slightly better for smaller nₒ. The precision with which nₓ can be measured depends weakly on nₒ and strongly on r. For nₒ1, nₓ can be determined with a precision of about 0. 056 (1. 5+r) /r. A full-sky experiment with a 20 arc min 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. The uncertainties in nₒ 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.
Lloyd Knox (Sun,) studied this question.