Talk:Friedmann equations

Context

The author of this article says that the Friedmann equations relate certain cosmological parameters in the context of general relavity. I would like to modify this statement to say that these equations define certain cosmological models in general relativity, usually called the Friedmann dusts (or matter domninated Friedmann models) and Friedmann radiation fluids (or radiation dominated Friedmann models). The equations themselves arise in the course of deriving these models in a comoving coordinate chart.

Omega

I just hunted for 20 minutes and didn't find an article specifically on Omega, the density parameter. I put in a blurb about it on the Omega page, and created two new redirect articles, density of the universe and density parameter. I feel Omega deserves its own page, but I can't do it. --zandperl 13:42, 21 March 2006 (UTC)

Or it could go under either Omega (cosmology) or Omega (astronomy). --zandperl 13:47, 21 March 2006 (UTC)

I agree that we need an Omega (cosmology) article, and density parameter should redirect to it instead of this page. I also can't do it now, but maybe at the end of this semester. --Keflavich 01:45, 16 April 2006 (UTC)

Shouldn't "Density of the Universe" have its own page with discussion of:

-Variation in density.

-large scale variation and structure ~ link to page.

-Talk about steady state universe's that call for creation of matter to maintain constant density of universe.

-Why we think we know what the density is and how we found it. -Why we could be wrong.

Alejandr013 21:05, 4 August 2006 (UTC)

Development

There should be some more development of where the equations come from. I may add some straightforward derivation. Alejandr013 21:02, 4 August 2006 (UTC)

It would be nice to include the actual value of the cosmic density of matter here. I've been searching the web for days trying to find a value, it seems to be one of the values that everybody else knows but never bothers to write down. AJH

speed of light

I may be braindead, but I can't for the life of me see how ρ and $p/c^{2}$ have the same units. –Joke 02:27, 14 August 2006 (UTC)

ρ is density, Kilograms over Meters cubed ρ=:${\frac {Kg}{m^{3}}}$

$p/c^{2}$ is Pressure over velocity squared, or Force over area over velocity squared so

${\frac {p}{c^{2}}}={\frac {F}{Ac^{2}}}={\frac {F/A}{(m/s)^{2}}}={\frac {\frac {Kg*(m/s^{2})}{m^{2}}}{(m/s)^{2}}}={\frac {kg}{m^{3}}}$

Differentiating ρ, P, and p in physics can be difficult (did you catch the pun?). I thought it was standard to put pressure P capitalized and p little as momentum, and rho as density. What are the conventions on Wikipedia? Alejandr013 20:49, 14 August 2006 (UTC)

I think you left out a $c^{2}$ factor at the beginning -- I've taken the liberty of correcting it. Yes, it all comes down to the naming conventions for GR. Is $\rho$ the mass density or the energy density? In non-GR physics $\rho$ is normally mass density, but since c=1 is normally set by Geometrized unit system it doesn't matter most of the time. Of course a general audience will not necessarily know of these unit conventions -- and according to WP policy articles should written with the general public in mind as well as the experts.

There is an unoffical set of naming conventions in GR: User:Hillman/WikiProject GTR/Policies. --Michael C. Price ^talk 01:25, 15 August 2006 (UTC)

The $\rho$ which appears in the equations is mass-density, as noted above, but later in the article there is talk of energy density and vacuum energy. This is confusing, at least it was to me; the first time I read it I assumed $\rho$ was indeed energy density, but then noticed the dimensions of the equation wouldn't balance. I think it should be clarified by specifically saying 'mass density' when ρ is introduced. Or, perhaps by changing to $\rho$ being energy density which seems to be used on other pages (e.g. cosmological constant). Then the term becomes

${\frac {4\pi G}{c^{2}}}\left(\rho _{e}+3p\right)$

The subscript e for energy density would be nice, but I guess this is no place to introduce new notation? E4mmacro 04:17, 9 April 2007 (UTC)

mistake

I think, there is a mistake in the equations from the beginning. Instead of a² in the last term on the r.h.s. there should be R², where R = R(t) = a(t).R₀. The dimension of the first equation is then s^-2- same for all terms on the left and right hand side of the equation...

Whoplaysdice 09:56, 29 May 2007 (UTC)

If you are speaking of this equation:

$H^{2}\equiv \left({\frac {\dot {a}}{a}}\right)^{2}={\frac {8\pi G\rho +\Lambda }{3}}-K{\frac {c^{2}}{a^{2}}}$,

then the right-most term already has units of reciprocal seconds squared. The Gaussian curvature when a=1, K has units of reciprocal meters squared. c has units of meters per second. a has units of one (i.e. arbitrary units or unit-less). So it is: m^-2·m²s^-21 = s^-2. Is that OK? JRSpriggs 10:26, 29 May 2007 (UTC)

Thanks for the explanation very much. I haven't noticed that K has units of reciprocal meters squared... I'm sorry. Whoplaysdice 10:32, 29 May 2007 (UTC)

As a matter of fact, if the curvature is constant within a polygon, the area of the polygon times that curvature is just the "spherical" excess (in radians) of the sum of the interior angles of the polygon relative to the value in Euclidean space. JRSpriggs 04:38, 30 May 2007 (UTC)