# Why is the CMB fluctuations (two-point correlation) approximately Gaussian?

I was learning about the Inflaton model and by quantizing it ,I can derive a $$1/k^3$$ power spectra , which is the Fourier transform of the fluctuation correlation function. But that doesn't give a Gaussian. I must have some wrong understanding.

• The CMB was produced around 300,000 years after the end of inflation. As such, inflation almost certainly isn't the only contributor (and probably isn't even the dominant contributor either). – probably_someone May 28 at 17:24
• OK. I'm completely new to this field. So can you help me clarify a few statements: (1) Why do we assume the fluctuation be Gaussian? If they are uncorrelated it should be a delta function. (2) I found many papers saying that their new inflaton models can predict observables in the CMB spectra. What does that mean if the current single scalar inflaton model can't explain the observed fluctuation correlation (which is claimed Gaussian)? – Jason Tao May 28 at 17:48
• I'm not an expert in this field either, so definitely don't take my word for it on the last comment. I'll step back and let someone who knows what they're talking about handle this instead. – probably_someone May 28 at 18:21
• @probably_someone thank you – Jason Tao May 28 at 18:48
• OK. I've realized this is related to the Gaussian random field hypothesis of correlation functions. But anyone can clarify for me how that works in a single quantum realization of the universe like the one we live in? – Jason Tao May 30 at 16:55