Introduction to Cosmology

178 Cosmic Microwave Background

Making use of Equations (6.10) and (8.5), the distribution at time푡′becomes

d푛′훾(휈′)=^8 휋

3 푐^3

d휈′^3

eℎ휈′∕푘푇′− 1

, (8.7)

which is precisely the blackbody spectrum at temperature푇′.
Although several accurate experiments since Penzias and Wilson have confirmed
the temperature to be near 3K by measurements at different wavelengths, the conclu-
sive demonstration that the spectrum is indeed also blackbody in the region masked
by radiation from the Earth’s atmosphere was first made by a dedicated instrument,
the Far Infrared Absolute Spectrophotometer (FIRAS) aboard the COBE satellite
launched in 1989 [2]. The present value of the photon temperature,푇 0 , is from mea-
surements in 2009,

푇 0 = 2. 7255 ± 0 .0006 K. (8.8)

The spectrum reported by the COBE team in 1993 [3] matches exactly the the-
oretical prediction for blackbody radiation remaining from the hot Big Bang. The
measurement errors on each of the 34 wavelength positions have not been added to
the theoretical blackbody curve because they could not be distinguished It is worth
noting that such a pure blackbody spectrum had never been observed in laboratory
experiments. All theories that attempt to explain the origin of large-scale structure
seen in the Universe today must conform to the constraints imposed by these COBE
measurements.
The vertical scale in Figure 8.1 gives theintensity퐼( 1 ∕휆)of the radiation, that is, the
power per unit inverse wavelength interval arriving per unit area at the observer from

1.2

1.0 Theory and observation agree

Intensity, 10

-^4
ergs/cm

2 sr sec cm

-^1

0.8

0.6

0.4

0.2

0.0

0510

Waves/cm

15 20

Figure 8.1 The theoretical blackbody spectrum from Equation (6.13). From D. J. Fixsen,
E. S. Cheng, J. M. Gales, J. C. Mather, R. A. Shafer, and E. L. Wright, The Cosmic Microwave
Background Spectrum from the Full COBE* FIRAS Data Set.Astrophys. J., 473 , 576, published
20 December ©1996. AAS. Reproduced with permission.