Gaussian vs. non-Gaussian fluctuations

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Discussion Overview

The discussion revolves around the nature of Gaussian and non-Gaussian fluctuations in the context of cosmic inflation. Participants explore the implications of these fluctuations for the cosmic microwave background (CMB) and their relationship to the mechanisms of inflation, particularly the inflaton potential.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions whether the fluctuations refer to those of inflation itself and seeks clarification on their relation to the inflaton potential.
  • Another participant explains that Gaussian fluctuations in the CMB correspond to a random distribution of photons, while non-Gaussian fluctuations indicate a preferred distribution, potentially linked to topological defects in the universe.
  • A participant inquires about the mechanisms that could generate non-Gaussianity during inflation.
  • Responses suggest various mechanisms for generating non-Gaussianity, including multiple fields, non-slow roll evolution, strong higher-order couplings, non-trivial vacuum/initial states, and non-canonical kinetic terms.
  • One participant notes that non-Gaussianity can also arise in the amplitude distribution of fluctuations in the temperature power spectrum, potentially without violating isotropy.

Areas of Agreement / Disagreement

Participants express differing views on the implications and mechanisms of Gaussian versus non-Gaussian fluctuations, with no consensus reached on the nature of these fluctuations or their significance in cosmology.

Contextual Notes

Some discussions may depend on specific definitions of Gaussianity and non-Gaussianity, and the implications of these concepts may vary based on the assumptions made about the inflationary model.

Einj
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Hello everyone,
I know this is a very basic question but I was wondering, in the context of inflation, what does it mean to have gaussian or non-gaussian fluctuations.
First of all, are we talking about the fluctuations of the inflation?
Second of all, how is the nature of the fluctuations related to the mechanism of inflation, say e.g. the inflaton potential?

Thanks!
 
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Gaussian, wrt to the CMB, refers to a distribution of CMB photons that is consistent with a gaussian probability curve [i.e., random]. A non-guassian distribution suggests a preferred distribution of CMB photons [i.e., corresponding to topological defects in the universe]. Most cosmologists are suspicious of non gaussianity because it violates the cosmological principle.
 
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Thanks for the reply! How can non-gaussianity be generated at the level of inflation?
 
Einj said:
Thanks for the reply! How can non-gaussianity be generated at the level of inflation?
All sorts of ways: multiple fields, non-slow roll evolution, strong higher-order couplings, non-trivial vacuum/initial state, non-canonical kinetic terms (e.g. DBI inflation), etc...
 
Chronos said:
Gaussian, wrt to the CMB, refers to a distribution of CMB photons that is consistent with a gaussian probability curve [i.e., random]. A non-guassian distribution suggests a preferred distribution of CMB photons [i.e., corresponding to topological defects in the universe]. Most cosmologists are suspicious of non gaussianity because it violates the cosmological principle.
Nongaussianity can also arise in the distribution of the amplitude of fluctuations (the a_{\ell m}) in the temperature power spectrum. I believe this can happen without violating isotropy.
 

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