What are the Cosmological monopole and dipole?

[jordy1113]

Hi there I'm currently studying cosmology but I'm having a hard time grasping that concept of the cosmological monopole and dipole (quadrupole etc) and was wondering if someone could explain what they are conceptually and physically. Thanks : )

 

[kimbyd]

The monopole is just the average temperature of the CMB. The dipole is dominated by our motion with respect to the CMB: the CMB gets blue-shifted in the direction of our motion, and redshifted opposite to our motion.

The higher multipoles are all from primordial variations in temperature from place to place in the early universe.

 

[Ibix]

Similar to the way you can write a 1d function $f(x)$ as a sum of polynomials, or Fourier decompose it and write it as a sum/integral of $\sin$ functions, you can decompose a function $g(\theta,\phi)$ defined on the surface of a sphere as an infinite sum of the spherical harmonics. The CMB temperature as a function of position on the sky is a function defined on a sphere, so can be decomposed in this way. The first terms in these sums are the monopole and dipole terms, which have the interpretations @kimbyd gave.

 

[jordy1113]

The monopole is just the average temperature of the CMB. The dipole is dominated by our motion with respect to the CMB: the CMB gets blue-shifted in the direction of our motion, and redshifted opposite to our motion.

The higher multipoles are all from primordial variations in temperature from place to place in the early universe.

Hey thanks this actually really helps me think about it better