Density perturbations made simple

[resurgance2001]

Hi

I know that this question has been answered in other threads, but those threads seemed to be closed now, and what I am looking for is a real "for beginner - real dummies" type answer.

I understand that there are ripples in the background microwave radiation. The textbook (OU) I am reading at the moment, then goes on to start talking about variations in the density of matter. So my first question is (please excuse the basic level of these questions) is there assumed to be a connection between the variations in matter density and CMB? If so, why is that? Do the surveys of the CMB reflect the distribution of galaxies in the universe?

Also can anyone explain in really simple terms, how Fourier series and Fourier transforms get involved with all of this? I kind of understand what Fourier series are.

Is there any decent literature that someone could point me in the direction of in order to better understand this topic? I generally like the Open University and have had little but praise for them in the past, but the four pages related to this topic are among the most incomprehensible I have ever come across.

Thanks in advance for any help.

Cheers and seasons greetings to all you.

 

[mfb]

So my first question is (please excuse the basic level of these questions) is there assumed to be a connection between the variations in matter density and CMB?

The CMB variations are the matter density variations at the time (and place) the CMB we see today was emitted. More dense matter was hotter.

Do the surveys of the CMB reflect the distribution of galaxies in the universe?

The galaxies we see today were not formed out of the material that emitted the CMB radiation we see today, and there are billions of years in between. If you start with the CMB distribution we see and simulate billions of years of time-evolution in the computer, the result looks very similar to the galaxy distributions we see. One prominent example was the millenium simulation, but there were more and better simulations afterwards.

 

[Chalnoth]

Also can anyone explain in really simple terms, how Fourier series and Fourier transforms get involved with all of this? I kind of understand what Fourier series are.

The short of it is: it makes the math easier.

If you make use of certain approximations, approximations which are valid for large length scales, you can make the differential equations that describe how these perturbations evolve linear. If you have a linear differential equation, then you can decompose the solution into sinusoidal waves, each of which evolves independently of all of the others. So instead of having a huge number of interacting particles that all impact one another, you reduce the problem to the behavior of individual waves whose behavior is (comparatively) easy to calculate.

 

[George Jones]

For more details, try Wayne Hu's website,
http://background.uchicago.edu/

In particular, look at the first three links.

 

[Mordred]

For the particle physics aspects read

http://arxiv.org/pdf/hep-th/0503203.pdf "Particle Physics and Inflationary Cosmology" by Andrei Linde
http://www.wiese.itp.unibe.ch/lectures/universe.pdf:" Particle Physics of the Early universe" by Uwe-Jens Wiese Thermodynamics, Big bang Nucleosynthesis

 

[Mordred]

For the particle physics aspects read

http://arxiv.org/pdf/hep-th/0503203.pdf "Particle Physics and Inflationary Cosmology" by Andrei Linde
http://www.wiese.itp.unibe.ch/lectures/universe.pdf:" Particle Physics of the Early universe" by Uwe-Jens Wiese Thermodynamics, Big bang Nucleosynthesis

Though both articles cover the SO(5) rather than the SO(10)

 

[George Jones]

Though both articles cover the SO(5) rather than the SO(10)

While these articles may be nice, they are not at the level for which the original poster is looking.

 

[resurgance2001]

The CMB variations are the matter density variations at the time (and place) the CMB we see today was emitted. More dense matter was hotter.The galaxies we see today were not formed out of the material that emitted the CMB radiation we see today, and there are billions of years in between. If you start with the CMB distribution we see and simulate billions of years of time-evolution in the computer, the result looks very similar to the galaxy distributions we see. One prominent example was the millenium simulation, but there were more and better simulations afterwards.

Thanks that is a great help.

 

[resurgance2001]

The short of it is: it makes the math easier.

If you make use of certain approximations, approximations which are valid for large length scales, you can make the differential equations that describe how these perturbations evolve linear. If you have a linear differential equation, then you can decompose the solution into sinusoidal waves, each of which evolves independently of all of the others. So instead of having a huge number of interacting particles that all impact one another, you reduce the problem to the behavior of individual waves whose behavior is (comparatively) easy to calculate.

thanks - that's clear

 

[resurgance2001]

Thanks George - I will check this out.

For more details, try Wayne Hu's website,
http://background.uchicago.edu/

In particular, look at the first three links.

 

[ChrisVer]

Hi

I know that this question has been answered in other threads, but those threads seemed to be closed now, and what I am looking for is a real "for beginner - real dummies" type answer.

I understand that there are ripples in the background microwave radiation. The textbook (OU) I am reading at the moment, then goes on to start talking about variations in the density of matter. So my first question is (please excuse the basic level of these questions) is there assumed to be a connection between the variations in matter density and CMB? If so, why is that? Do the surveys of the CMB reflect the distribution of galaxies in the universe?

Also can anyone explain in really simple terms, how Fourier series and Fourier transforms get involved with all of this? I kind of understand what Fourier series are.

Is there any decent literature that someone could point me in the direction of in order to better understand this topic? I generally like the Open University and have had little but praise for them in the past, but the four pages related to this topic are among the most incomprehensible I have ever come across.

Thanks in advance for any help.

Cheers and seasons greetings to all you.

Hi,

I will start from a book recommendation. If I recall well, Dodelson's book is a good one to look into the topic of CMB fluctuations.

The variations in matter density can take into account weird behaviors in the thermal evolution of the universe, because the distribution then is not taken to be the Fermi-Dirac but a perturbed version of it. CMB is already (a little) anisotropic in temperatures, of $\delta T/T \sim 10^{-5}$. This small variation can also lead in matter anisotropies.

Fourier series come into play because they make things more easy to deal with.

 

[bapowell]

The review article by Liddle and Lyth is quite clear and comprehensive: http://arxiv.org/abs/astro-ph/9303019. It forms the basis of their textbook on perturbations and inflation.

 

[resurgance2001]

Hi,

I will start from a book recommendation. If I recall well, Dodelson's book is a good one to look into the topic of CMB fluctuations.

The variations in matter density can take into account weird behaviors in the thermal evolution of the universe, because the distribution then is not taken to be the Fermi-Dirac but a perturbed version of it. CMB is already (a little) anisotropic in temperatures, of $\delta T/T \sim 10^{-5}$. This small variation can also lead in matter anisotropies.

Fourier series come into play because they make things more easy to deal with.

Thanks - I will see if I can find the book you have recommended. Typically, with a course like the one I currently doing, only a small amount of time is spent on each topic before moving on to the next. So it is doubly frustrating if you find yourself not being able to understand anything at all. Cheers

 

[resurgance2001]

I keep seeing the word 'constraints' used - eg. "The fact that constraints on one parameter can correlate with constraints on another is known as 'parameter degeneracies'

Please excuse again the basic level of my question, but I am confused by what they mean in this context by the word 'constraints' and 'parameters' I keep seeing these two words used over and over again. I am used to using them in ordinary every day speech but I just don't get what they are saying in terms of cosmology. Does constraints mean limiting range? And does parameter mean factor or variable? Cheers

 

[ChrisVer]

Does constraints mean limiting range? And does parameter mean factor or variable?

yes. Contraints are either put by theory or experimental data and they are limits. In the parameter space they correspond to an area/volume that your theory can still exist in. An example, is the cosmological contraint on the sum of neutrino mass which comes from asking for neutrinos not to close the universe density. So you know that their masses sum should not exceed eg $12~eV$. It can be as well $11~eV$ or $0.1~eV$ (in this context).

Parameters are parameters. You can see them as variables. But if I recall well, variables are dynamical objects, whereas parameters can be just numbers that are put into your theory and are in general unknown. Eg take the coupling of an unknown dark matter particle X to photons. When you search for the interaction of X with photons, and you find nothing, you can say that the coupling constant (the model parameter) is very small , and give some limits.

Are you OK with the "parameter degeneracies" term?

These examples can work with almost everything concerning contraints and parameters, you just have to change the language and look into the technicalities.

 

[resurgance2001]

Thanks Chris. That is a great help again. cheers

 

[cristo]

The review article by Liddle and Lyth is quite clear and comprehensive: http://arxiv.org/abs/astro-ph/9303019. It forms the basis of their textbook on perturbations and inflation.

I would second this article. @resurgance2001, is this the sort of level that you are looking at (it's not clear what course you are studying...)?