Mathematics – Logic
Scientific paper
Jan 1995
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995phdt.........9k&link_type=abstract
Thesis (PH.D.)--THE UNIVERSITY OF CHICAGO, 1995.Source: Dissertation Abstracts International, Volume: 56-03, Section: B, page: 1
Mathematics
Logic
2
Scientific paper
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}, nS and nT where Q _sp{S}{2} and Q _sp{T}{2} are the scalar and tensor contributions to the square of the CMB quadrupole and nS 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-nS} Q_sp{S}{2} can be known to better than +/-0.3%. The scalar index nS 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 nS. The precision with which nT 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 nS 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.
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