What is the mathematical equation for the best-fit model of CMB power spectrum?

[awu]

I am not a physics major, just interested in the discussions about cosmology. But many times get lost in the discussions.

 

Many people show the beautiful fit of the model and the observed CMB power spectrum (~ like the one below copied from Wikipedia). But I can not find the mathematical equation(s) of this best-fit lambda CDM model... Could anyone help??? Thanks a lot!

 

[Sato]

Isn't that the equation, written vertically, describing the y axis?

[awu]

There are 6 basic parameters in the Lambda CDM model. Change each of them will make the curve change accordingly. I found some very interesting interactive tool on NASA website: http://map.gsfc.nasa.gov/resources/camb_tool/

But I am wondering what are the rules (or mathematical formulas) behind the changes? This my real question.

[Mordred]

there is no way to cover that in a single post, you need to look at full textbooks to fully understand the LCDM models 6 parameters.

 

here is a basic entry level article on universe geometry

http://cosmology101.wikidot.com/universe-geometry

page 2

http://cosmology101.wikidot.com/geometry-flrw-metric/

 

here is some free textbook style articles

 

http://arxiv.org/pdf/hep-ph/0004188v1.pdf :"ASTROPHYSICS AND COSMOLOGY"- A compilation of cosmology by Juan Garcıa-Bellido
http://arxiv.org/abs/astro-ph/0409426 An overview of Cosmology Julien Lesgourgues

http://cosmo.torun.pl/~boud/Observational_cosmology_-_30h_course.pdf

 

my signature contains more articles that will help your studies the cosmology101 link as well as the the two links on the calculator, (handy for seeing the expansion history). the cosmocalc/start link

is the tutorial some of the metrics can be found within the links from that site

 

personally I would recommend buying textbooks

Scott Dodelsons "Modern Cosmology" is excellent (particularly in regards to the CMB)

also a good introduction is Barbera Ryden's "Introduction to cosmology" this one covers how the FLRW metric works extremely well and how the 6 parameters are derived

Edited June 4, 2014 by Mordred

[awu]

Thanks a loooooooooooooooot !!!

[Mordred]

lol sorry there isn't an easier way, the 6 parameters of the FLRW metric can be used to calculate numerous parameters. For example just from the temperature of the CMB one can calculate how each particle species contributes to its black-body temperature, (including the density of each particle species) This article takes 3 chapters to do it in. It also has a good review section prior to getting into the thermodynamics,

 

http://www.wiese.itp.unibe.ch/lectures/universe.pdf:" Particle Physics of the Early universe" by Uwe-Jens Wiese Thermodynamics, Big bang Nucleosynthesis

 

LCDM is an extremely involved model,

[awu]

Thanks Mordred. Actually I feel good knowing it is such a complicated problem...I thought I was asking a stupid question which everyone else knows the answer.

 

I read some of the text. Of course, there are many concepts and equation I do not understand. But I have the impression that different scientists have different ideas about how to treat the CMB data and what the major cosmological parameters are. For example,

(1) some people think the 6 parameters in the lambda CDM model can allow the fitting of data;

(2) others say the Friedman universe entirely depend on the 4 parameters: density of radiation, density of matter, density of dark energy and hubble's constant;

(3) some others say the anisotropy spectrum depends on the 4 fundamental parameters: curvature, density of baryonic matter, density of dark energy and density of matter.

(4) some others present some more parameters which I have not yet looked to see what they are.

......

I do not know if scientists today have a common agreement already. I am confused by how these parameters play in making the curve in the temperature power spectrum, or to say it in a bigger picture, in making up our universe.