Linear vs non linear matter power spectrum

Click For Summary

Discussion Overview

The discussion revolves around the differences between linear and non-linear matter power spectra, particularly in the context of large scale structure formation in cosmology. Participants seek to clarify the mathematical definitions and implications of these terms, exploring their relevance in different scales of cosmic structure.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant expresses confusion about the definitions of linear and non-linear power spectra, noting that both are described as the Fourier transform of the 2-point correlation function of the density field.
  • Another participant attempts to clarify the distinction by discussing general characteristics of linear versus non-linear relationships, but this may not directly address the specific context of power spectra.
  • A participant acknowledges the need for a mathematical description of large scale structure formation and references a book by Peebles for further details, indicating a lack of accessible definitions in the literature.
  • One participant suggests that the non-linear power spectrum should be used at scales where differences between linear and non-linear approximations become significant, though they express uncertainty about the exact limits of this transition.
  • A link to an external resource is provided, which discusses the linear versus non-linear power spectrum in relation to large scale structure, although its relevance to the specific questions raised is not confirmed by other participants.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the definitions or implications of linear and non-linear power spectra. There are multiple viewpoints and some uncertainty regarding the transition between the two types of spectra.

Contextual Notes

Participants note the lack of clear definitions in the literature and the potential for varying interpretations of the terms based on different scales of cosmic structure. There is also mention of the need for further investigation into non-linear power spectrum approximations.

Jip
Messages
20
Reaction score
2
Hi,

I have troubles understanding the difference between linear and non linear matter power spectrum. These words are commonly used in the litterature, but I have found no definitions yet.

My understanding is that there is one definition of the power spectrum for matter distribution, basically as the Fourier transform of the 2-point correlation function of the density field.

It covers both very large scales where linear approximation for the dynamics should be accurate, while at small scales the non linear gravitational collapse heavily impacts the dynamics.
Still, we have only one power spectrum.

So, what does linear or nonlinear power spectrum refers to? (in terms of maths, I mean)

Thanks for your help!
 
Space news on Phys.org
If you graph a linear relation the graph will show a straight line whether or not its flat, diagonal or vertical. This is described as value a is directly or indirectly proportional to value b.
A non linear relation will be a curve, examples include bell curves, sinusoidal wave forms
etc. Hence non linear.
value a is exponentially proportional to b. This type of relation will give a bell curve
 
Yes, I'am aware of this, but I'm rather talking about mathematical description of large scale structure formation! I have found that details can be found in peeble's book, 1980. But I don't have it. Any other ref is welcome! :)
 
Ah ok wasn't sure on what you were unclear on. I may have an article that will help but I'll have to dig around in my archives to find it.
 
Jip said:
Hi,

I have troubles understanding the difference between linear and non linear matter power spectrum. These words are commonly used in the litterature, but I have found no definitions yet.

My understanding is that there is one definition of the power spectrum for matter distribution, basically as the Fourier transform of the 2-point correlation function of the density field.

It covers both very large scales where linear approximation for the dynamics should be accurate, while at small scales the non linear gravitational collapse heavily impacts the dynamics.
Still, we have only one power spectrum.

So, what does linear or nonlinear power spectrum refers to? (in terms of maths, I mean)

Thanks for your help!
Well, I think the general idea is to start using the non-linear power spectrum at the scales in which there is a noticeable difference between the linear power spectrum and the non-linear approximations. I doubt there is a firm limit on precisely where this occurs, but the best way to investigate it is probably to start investigating some nonlinear power spectrum approximations.
 

Similar threads

Undergrad I'm slightly confused about the power spectrum of matter
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Angular power spectrum dependence in redshift z and k
  • · Replies 5 ·
Replies
5
Views
2K
Graduate Relation between Matter Power spectrum and Angular power spectrum
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Computing sig8 for correction in non-linear regime
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Understanding the Linear Power Spectrum: How Do BAOs Create Wiggles?
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Cross-correlations: what size to select for the matrix?
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Is my calculation of the power spectrum correct?
  • · Replies 17 ·
Replies
17
Views
3K
How is the Power Spectrum of Matter Density Field Defined?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Bremsstrahlung single photon or spectrum
  • · Replies 1 ·
Replies
1
Views
1K
High School Dark matter can be cold warm or hot
  • · Replies 2 ·
Replies
2
Views
2K