CMB Angular Distribution: Understanding Gaussian Random Fields

[Madster]

Dear all,

I don't understand why the Cosmic Microwave Background's angular distribution is considered to to a Gaussian random field initially.
The rest of the analysis is roughly clear to me, COBE/WMAP/PLANCK measure the CMB Photons and show the temperature fluctuations w.r.t. the mean temperature. On this data a spherical analysis is applied... But where does the GRF come from? What is b.t.w. a geometrical meaning of a GRF?

Thank you very much

 

[Mordred]

This article may help you hope your math is good lol

http://www.astro.rug.nl/~weygaert/tim1publication/lss2007/computerIII.pdf

the main usage in the CMB is in measurements of the CMB power spectrum.

 

[Madster]

This article may help you hope your math is good lol

http://www.astro.rug.nl/~weygaert/tim1publication/lss2007/computerIII.pdf

the main usage in the CMB is in measurements of the CMB power spectrum.

thanks, my math is sufficient enough to get the script. So still what mechanism makes the CMB a gaussian random field, or to be more precise, let's us initially approximate the description with a GRF and look for fluctuations?

 

[Mordred]

Gaussian random fields is an area I'm weak in however I did take bit of time researching its usages in CMB. I have some related articles in my data base that I plan on studying at some point.

http://background.uchicago.edu/~whu/Presentations/cmblens.pdf

http://background.uchicago.edu/~whu/papers/hudedval06.pdf

http://physics.stackexchange.com/questions/9106/what-exactly-is-meant-by-the-gaussianity-of-cmbr

http://www.lorentz.leidenuniv.nl/~vitelli/ThomasPNAS.pdf

hope those help

 

[sardar]

for your question. The Cosmic Microwave Background (CMB) is a remnant radiation from the early universe, and its angular distribution is considered to be a Gaussian random field due to the nature of its origin and the statistical properties of the universe.

To understand this, we need to look at the early universe and the processes that led to the formation of the CMB. In the early stages of the universe, the temperature and density fluctuations were small and random, and they were amplified by inflation and gravitational collapse. This resulted in a homogeneous and isotropic distribution of matter and energy, which is a fundamental property of the universe known as the cosmological principle.

The CMB is created as the universe cools down and becomes transparent to radiation. At this point, the photons in the universe are decoupled from matter and travel freely. The temperature fluctuations in the CMB are a direct result of the density fluctuations in the early universe, and they follow a Gaussian distribution due to the central limit theorem. This means that the temperature fluctuations are random and can be described by a Gaussian probability distribution.

The concept of a Gaussian random field is a mathematical representation of this random distribution. It describes a field that is randomly distributed in space and has a Gaussian probability distribution at each point. In the case of the CMB, this field represents the temperature fluctuations at different points in the sky.

The geometrical meaning of a GRF is that it describes the spatial distribution of a random field. In the case of the CMB, it represents the variation in temperature across the sky. The spherical analysis applied to the CMB data is used to study the statistical properties of this random field and to compare it with theoretical predictions from inflationary models.

I hope this helps to clarify the concept of a Gaussian random field and its relevance to the CMB angular distribution. Please let me know if you have any further questions. Thank you.