I What are the Cosmological monopole and dipole?

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The cosmological monopole represents the average temperature of the Cosmic Microwave Background (CMB), while the dipole reflects the effects of Earth's motion relative to the CMB, resulting in blue-shifting in the direction of motion and red-shifting in the opposite direction. Higher multipoles, such as quadrupoles, arise from primordial temperature variations in the early universe. The CMB temperature can be analyzed using spherical harmonics, allowing for a mathematical decomposition of its temperature distribution across the sky. Understanding these concepts is crucial for studying the universe's early conditions and cosmic structure.
jordy1113
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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 : )
 
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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.
 
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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.
 
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kimbyd said:
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
 
https://en.wikipedia.org/wiki/Recombination_(cosmology) Was a matter density right after the decoupling low enough to consider the vacuum as the actual vacuum, and not the medium through which the light propagates with the speed lower than ##({\epsilon_0\mu_0})^{-1/2}##? I'm asking this in context of the calculation of the observable universe radius, where the time integral of the inverse of the scale factor is multiplied by the constant speed of light ##c##.
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Hi, I’m pretty new to cosmology and I’m trying to get my head around the Big Bang and the potential infinite extent of the universe as a whole. There’s lots of misleading info out there but this forum and a few others have helped me and I just wanted to check I have the right idea. The Big Bang was the creation of space and time. At this instant t=0 space was infinite in size but the scale factor was zero. I’m picturing it (hopefully correctly) like an excel spreadsheet with infinite...
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