Friedmann Definition and 86 Threads

I have some misunderstanding about Fridman models of University. Friedman equation: ## \begin{array}{l} {\left( {\frac{{\dot a}}{a}} \right)^2} = \frac{{8\pi G}}{3}\rho - \frac{{k{c^2}}}{{{a^2}}}\\ \frac{1}{a}\frac{{{d^2}a}}{{d{t^2}}} = - \frac{{4\pi G}}{3}\left( {\rho + \frac{{3p}}{{{c^2}}}}...

Homework Statement Consider a universe with Cold Matter, Radiation, and Dark Energy satisfying an equation of state p = w\rho. Variables: p is the pressure of the universe, w is a constant, and \rho is the density of the universe. a) Show that the Friedmann equation can be rewritten as...

Homework Statement To relate E to the total energy of the expanding sphere, we need to integrate over the sphere to determine its total energy. These integrals are most easily carried out by dividing the sphere into shells of radius r, and thickness dr, so that each shell has a volume dV...

I had a discussion regarding the region of spacetime visible to an observer falling into aSchwarzschild black hole. Using Eddington-Finkelstein coordinates this is rather straightforward, at least graphically. However the situation is rather artificial b/c the BH exists externally. So my...

Homework Statement Rewrite Friedmann equation using conformal time and density parameters \Omega_m and \Omega_r. Is there a relation between the two? How many parameters define the problem? Homework Equations Friedmann equation \left(\frac{\dot{a}}{a}\right)^2=\frac{8\pi...

Hi I am using the metric ds^{2}=c^{2}dt^{2}-a^{2}(t)[\frac{dr^{2}}{1-kr^{2}}+r^{2}(dθ^{2} + sin^2θd^{2}∅)] and am subsequently trying to derive the christoffel symbols: \Gamma^{\sigma}_{\mu\nu}=\frac{1}{2}g^{\sigma\rho}(\partial_{\nu}g_{\rho\mu} +\partial_{\mu}g_{\rho\nu}...

I am having a trouble finding relationship between 'a' and 't' by integrating friedmann equation in a multi-component universe. It would be very helpful if you can help me with just matter-curvature only universe and matter-lambda only universe. The two integrals looks like following...

Homework Statement the first friedmann equation is: (\frac{\dot{a}}{a})^2=\frac{8\pi G\rho}{3}-\frac{kc^2}{a^2}+\frac{\Lambda}{3} In the case of a closed Universe (k > 0) containing only non-relativistic matter and no cosmological constant, write the Friedmann equation in terms of, H(a), H0...

Looking at the Friedmann equation H^2=\left[\frac{\dot{a}}{a}\right]^2=\frac{8\pi G\rho}{3}-\frac{kc^2}{a^2} and considering positive curvature, then for the limit where the second term dominates, we're left with \left[\frac{\dot{a}}{a}\right]^2=-\frac{kc^2}{a^2} This implies a complex...

(i) Obtain the scale factor a(t) and redshift z when the energy density of matter and radiation were equal. (ii) Next use the a(t) relation for a matter-only universe to estimate the time of matter-radiation equality. (iii) Repeat (ii) but using the a(t) relation for a radiation-only universe...

I'm just beginning to look into loop quantum cosmology, and I've recently run into some fundamental confusion concerning how exactly the Friedmann equation fits in. Is it just that the application of loop quantum gravity yields a modified/effective Friedmann equation, or is it the other way...

Are you confortable with the demonstration in page 19 of Introduction to Modern Cosmology - A. Liddle ? My problem is in particular eq. (3.4) when he writes the potential energy of a test particle. I think there is a factor of 2 missing in the denominator.

I'm a little confused about the density \rho in the equation: H^2 = \left(\frac{\dot{a}}{a}\right)^2 = \frac{8 \pi G}{3}\rho - \frac{kc^2}{a^2} Measuring \rho at a single instant in time seems easy. But \rho changes with time. The time dependence of \rho is given as...

Homework Statement The universe is expanding as shown by a Hubble constant H of 75 Km s^-1 Mpc^-1, but a constant density of matter of 10^-26 kg m^-3 is maintained by the continuous creation of hydrogen atoms as the universe expands. Find the rate of creation of hydrogen atoms per unit...

Hello everyone, Its been 4 years now since I posted, Last time i was asking for school homework and now I'm about to finish my physics master degree with 1 exam left in cosmology. As I'm sure you are aware, the k term in the Friedmann equation represents the curvature term k = 0, -1 & +1...

Hey! I'd like to see an easy way to arrive to Friedmann equation by using Newton's Mechanics. I've seen many ways but they skip many steps so I don't understand the whole. THANKS!

Homework Statement Solve for the age of the universe as a function of scale factor in a cosmology with \Omega_{M}=0.3, \Omega_{\Lambda}=0.7.Homework Equations The Attempt at a Solution (\frac{\dot{a}}{a})^2=H_0^2(0.3a^{-3}+0.7) \frac{da}{a\sqrt{0.3a^{-3}+0.7}}=H_0dt At this point, Maple seems...

Here is the homepage of the event -- to be held from Jun 19 to Jul 05 2008, in João Pessoa, Brazil: http://www.fisica.ufpb.br/eventos/friedmann2008/friedmann2008new2.htm http://www.fisica.ufpb.br/eventos/friedmann2008/friedmann2008new2_arquivos/page0016.htm" are the current scheduled...

:confused: could anyone please help me with this coursework,i am soo confused with maths,thanks 1) Start with friedmann equation for case for flat universe k=0 with mass density total p =p(m) + p(cosmo constant). how can i derive integral relating scale factor to time in form...

The purpose of this thread is to describe certain interesting aspects that are explicit or implicit in the “standard model” of cosmology for a flat universe, by reference to the Friedmann equations. I hope to provoke more interest and constructive dialogue about the substance of this topic...

Anybody like to help a physics student who did their BSc six years ago and has forgotten all their maths! Its a problem from Andrew Liddle's Introduction to cosmology 5.5 The Friedmann eqn is (a'/a)2 = 8TTG/3 P - k/a2 Consider the case k>o, with the universe containing matter only, so...

MTW section 27.7 states: It then proceeds to derive the relationships: \rho_m a^3 = constant and \rho_v a^4 = constant that pervect has shown before. My question: does this mean one cannot push the basic Friedmann equations that were discussed so exhaustively in the locked thread...

Hi Pervect, Since you deleted my last post, and gave me a 3rd warning, the Forum readers no may longer have a context for what this post is about. So I need to make it clear, in the interest of intellectual integrity, that I am confessing my errors and apologizing for misstating the...

Hi folks. Is there any laboratory demonstration or theoretical model for the proposition that a fundamental attribute of the “fabric of space” is its ability to expand forever just because it got a single expansionary “kick in the pants” from inflation? In other words, why didn’t space stop...

Does the metric of the Friedmann model yield an unbouded universe? I mean, are the geodesics of this metric closed?

Homework Statement Show that a lambda-dominated euclidean universe entails an exponential expansion. Homework Equations Equation of state is P=-E (E=epsilon) There is no curvature (i.e. a flat universe) The Friedmann equation is then ((a(dot)/a)^2)=((8piG)/3c^2)E + lambda/3...

Hello everybody, could somebody tell me how to get the scale factor as a function of time [R(t)] from the Friedmann Equations for a simple dust, pressureless universe when k != 0, \Lambda = 0. Mathematica 5.2 doesn't want to give me any solution and wherever I searched the best thing I got...

Homework Statement A closed Friedmann universe contains a single perfect fluid with an equation of state of the form p=w\rho c^2. Transforming variables to conformal time \tau using dt=a(t)d\tau, show that the variable y=a^{(1+3w)/2} is described by a simple harmonic equation as a function of...

Homework Statement By substituting in \left( \frac{\dot{a}}{a_0} \right)^2 = H^2_0 \left(\Omega_0 \frac{a_0}{a} + 1 - \Omega_0 \right) show that the parametric open solution given by a(\psi)=a_0 \frac{\Omega_0}{2(1-\Omega_0)}(\cosh{\psi} - 1) and t(\psi)=\frac{1}{2H_0} \frac{\Omega_0}{(1 -...

I'm trying to derive Friedmann's equation for cosmology using Newtonian physics. I've got the force equation F=ma for the case without a cosmological constant. But now I'm trying to incorporate the cosmological constant into this force equation. But I'm having trouble seeing how the...

Hi does anyone know a website or paper where the friedmann equation is derived from the robertson walker metric? it should have the calculation of atleast a few of the christoffel symbols etc thanks blumfeld

http://www-gap.dcs.st-and.ac.uk/~history/Biographies/Friedmann.html You may have heard people say that we live in a Friedmann universe. Why do they say that instead of saying "deSitter universe" or "Lemaître universe" didnt these other people also come up with an expanding universe...

Got stuck in this question, the question asked to use friedmann equation to show that the age of an empty universe (average density = 0) is τ=1/H₀ where H₀ is the present day value of Hubble's Constant. Well, i got the friedmann equation by put the value ρ(average)=0 but the trouble is...

arXiv:astro-ph/0503715 v2 31 Mar 2005 Late time failure of Friedmann equation Alessio Notari* Physics Department, McGill University, 3600 University Road, Montr´eal, QC, H3A 2T8, Canada (Dated: March 31, 2005) It is widely believed that the assumption of homogeneity is a good zeroth...

Please show me how to solve this paradox cos the Friedmann equation is: H^{2}= \frac{8*pi*G*rho}{3}-\frac{k*c^{2}}{R^{2}} but the concordance model says that k=0, so we can eliminate the last term of the equation then we isolate rho, the density of energy: rho=\frac{3*H^{2}}{8*pi*G}...

What is your preferred way of remembering and writing down the Friedmann equations and in what form do you include dark energy in them? Heres the way that seems best to me. It is a balance between making them uncluttered but not so simplified as to lose intelligibility. For one bit of...