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 \leq Q \leq 50 ~ { } \mu { K } is obtained .
We find that the likelihood is maximum at ( n,Q ) = ( 1.0 , 19 ~ { } ~ { } \mu { K } ) .
For constant n the likelihood falls to half its maximum at Q \approx 14 ~ { } ~ { } \mu { K } and 25 ~ { } ~ { } \mu { K } 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 ~ { } ~ { } \mu { K } and Q > 44 ~ { } ~ { } \mu { K } .