The Amplitude and Spectral Index of the Large Angular Scale Anisotropy in the Cosmic Microwave Background Radiation

In many cosmological models, the large angular scale anisotropy in the cosmic microwave background is parameterized by a spectral index, $n$, and a quadrupolar amplitude, $Q$. For a Peebles-Harrison-Zel'dovich spectrum, $n=1$. Using data from the Far Infra-Red Survey (FIRS) and a new statistical measure, a contour plot of the likelihood for cosmological models for which $-1 < n < 3$ and $0 \le Q \le 50~\mu{\rm K}$ is obtained. We find that the likelihood is maximum at $(n, Q) = (1.0, 19 uK)$. For constant $n$ the likelihood falls to half its maximum at $Q \approx 14 uK$ and $25 uK$ and for constant $Q$ the likelihood falls to half its maximum at $n \approx 0.5$ and $1.4$. Regardless of $Q$, the likelihood is always less than half its maximum for $n < -0.4$ and for $n > 2.2$, as it is for $Q < 8 uK$ and $Q > 44$.