Determination of Inflationary Observables by Cosmic Microwave Background Anisotropy Experiments

Lloyd Knox

doi:10.1103/PhysRevD.52.4307

paper

Determination of Inflationary Observables by Cosmic Microwave Background Anisotropy Experiments

arXiv:astro-ph/9504054 · doi:10.1103/PhysRevD.52.4307

Abstract

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 $13 0^{1 - n_{S}} Q_{S}^{2}$ can be known to better than $\pm 0.3%$ . 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 $n_{S} ≃ 1$ 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 $n_{S} ≃ 1$ $n_{T}$ can be determined with a precision of about $\pm 0.056 (1.5 + r) / r$ . A full-sky experiment with a $2 0^{'}$ 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.

28 pages of uuencoded postscript with 8 included figures. A postscript version is also available by anonymous ftp at ftp://astro.uchicago.edu/pub/astro/knox/fullsim.ps

Determination of Inflationary Observables by Cosmic Microwave Background Anisotropy Experiments

Abstract

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