Friedmann Definition and 86 Threads

First, "Energy is not conserved" as e.g. explained by Sean Carroll in https://www.preposterousuniverse.com/blog/2010/02/22/energy-is-not-conserved/ . Second, the Friedmann Equations are expressed in energy conservation, e.g. https://core.ac.uk/download/pdf/25318877.pdf equation (16). Do we...

"Tsinghua students, true to form, protesting lockdowns with the Friedmann Equation: the basic reality of the universe is constant, eternal expansion, or put another way, opening up." [Moderator's note: chinese twitter link removed.]

If it is known that such an equation exists, I would much appreciate seeing a link to a reference. If it is known that such an equation does not exist, I would much appreciate seeing a reference with an explanation of implications regarding the compatibility of general relativity with a...

The empty FRW-universe with curvature parameter ##k = -1## and expanding linearly is well known. Also that it is mathematically equivalent (after a coordinate transformation) with the Milne universe which also expands linearly. I wonder if the Friedmann Equations have another solution (I...

I was shown that adot^2/a^2 = c/a^3, adot = c / √(a), then da/dt = c / √(a) . Then I was told that I have to integrate this, but I don't understand where to go from there or how this will show me that the scale factor grows as t^(2/3).

The thread title is the title of a recently published paper: https://iopscience.iop.org/article/10.3847/1538-4357/ab32da The paper claims to resolve an ambiguity in "cosmological backreaction" models, which are models that take into account spatial inhomogeneity to derive correction terms to...

The Friedman Equations is based on the cosmological principle, which states that the universe at sufficiently large scale is homogeneous and isotropic. But what if, as an hypothesis, the universe was anisotropic and the clustering of masses are aligned to an arbitrary axis (axial pole), how...

Required Equations Note: Includes inequalities. [1] H(s) = 0, and [2] H’(s) = 0? [3] [4] H = a’/a [5] a(t0) = a0 =1 [6] H0 = H(t0) [7] ΩR = 0 [8] Ωk<0, Ωk = -K, K > 0 [9] ΩM>1, ΩM = M, M > 1 [10] ΩΛ = 1-Ωk- ΩM = 1+K-M > 0 → M-1 < K Solution Note: I have assigned this problem to myself...

We need to prove that a3(t)= ρo/2Λ [cosh(sqrt(24πGΛ)*t) -1] by changing into a variable of u, where u=2Λa3/ρo From Friedmann's second equation we know that Λ= ρm/ 2 Also ρm= ρo/ a3 [First attempt] I begin from Friedmann's equation where (for here), ρtotal= ρm + Λ and k=0; a'2/a2 = 8πG(ρm +...

Does the Friedmann vacuum equation have a linear solution rather than an exponential one? Using natural units one can write Friedmann's equation for the vacuum as $$ \begin{eqnarray*} \left(\frac{\dot a}{a}\right)^2 &=& \frac{8\pi G}{3}\rho_{vac}\\\tag{1} &=& L^2 \left(\frac{\rho_0}{L^4}\right)...

One simple question whether the k in the friedmann equation H(t)2=∑8πGε(t)/3c2-k/a2 is something related to curvature or is simply constt.?? If related to curvature whether it is 1/R where R is the radius of the 3-sphere.??

Homework Statement Assume that the universe today is flat with both matter and a cosmological constant, the latter with energy density which remains constant with time. Integrate Eq. (1.2) to find the present age of the universe. That is, rewrite Eq. (1.2) as: dt = H0-1 da / a [ΩΛ + (1 - ΩΛ )...

My discussion of the Friedmann metric comes from the derivation presented in section 4.2.1 of the reference: https://www1.maths.leeds.ac.uk/~serguei/teaching/cosmology.pdf I have a couple of simple questions on the derivation. The are placed at points during the derivation.I note the...

Hello. I've been doing some reading about Friedmann's three types of GR solution that yield closed, open and flat universes. I think I can grasp the closed solution best. As far as I understand it a closed universe is finite in both time and space. It begins, grows and then collapses in upon...

Greg Bernhardt submitted a new PF Insights post This article is part of our student writer series. The writer Arman777, is an undergraduate physics student at METU A Journey Into the Cosmos - FLRW Metric and The Friedmann Equation Continue reading the Original PF Insights Post.

Greg Bernhardt submitted a new PF Insights post Coordinate Dependent Statements in an Expanding Universe Continue reading the Original PF Insights Post.

Friedmann Equation without the cosmological constant can be written as; $$H^2=\frac {8πρG} {3}-\frac {1} {a^2(t)}$$ for ##Ω>1## (which in this case we get a positive curvature universe), and for a matter dominant universe; $$ρ=\frac {1} {a^3(t)}$$ so in the simplest form the Friedmann equation...

Greg Bernhardt submitted a new PF Insights post A Journey Into the Cosmos - The Friedmann Equation Continue reading the Original PF Insights Post.

while deriving the friedmann equation using Newtonian Mechanics the 2nd term of the r.h.s is coming to be 2^U/(r^2*a^2) where U is a constt,but it is replaced by -kc^2/(r^2*a^2)?

From time to time I come across some text in a Wikipedia article that is quite misleading to a naive reader. The following is an example: https://en.wikipedia.org/wiki/Friedmann_equations The problem is that the sign of Ω0,k is backwards. That is the sign is positive for a universe with...

Homework Statement Question attached My method was going to be: set ##r=R## and solve for ##n(R)## set ##r=2GM## and solve for ##n(2GM)## I was then going to integrate proper time ##s## over these values of ##r##: ##\int\limits^{n=cos^{-1}(\frac{4GM}{R}-1)}_{n=cos^{-1}(1)=0} s(n) dn ###...

Homework Statement Use Friedmann equations to show that if ##\dot{a} > 0##, ##k<0## and ##\rho>0## then there exists a ##t*## in the past where ##a(t*)=0## Homework Equations [/B] Friedmann : ##(\frac{\dot{a}}{a})^2=\frac{8\pi G}{3}\rho-\frac{k}{a^2}##The Attempt at a Solution [/B]...

Friedmann's Eq can be viewed here https://ned.ipac.caltech.edu/level5/March08/Frieman/Equations/paper1x.gif What I don't get is that all the texts/analyses of Friedmann's equation say that if the right hand side is negative it means that the universe will expand reach a critical point and then...

Hello, I was just wondering about the method for integrating Friedmann equation for k=1 and w=1/3 ∫(8πρ/a^(2)-1)^-1/2thank you

Hi everyone, I want to derive the Friedmann equations from Einstein Field Equations. However, I have a problem that stems from the energy-momentum tensor. I am also trying to keep track of ## c^2 ## terms. FRW Metric: $$ ds^2= -c^2dt^2 + a^2(t) \left( {\frac{dr^2}{1-kr^2} + r^2 d\theta^2 + r^2...

It has occurred to me that the Friedmann equation allows for a solution H = H0 = 0 . This seems to say that independently of the value of the scale factor a, and the various Ωs, a static universe is possible. I am guessing that this solution is spurious and is a side effect of the...

The first Friedmann equation for a flat Universe is given by: $$\bigg(\frac{\dot{a}(t)}{a(t)}\bigg)^2 = \frac{8 \pi G}{3} \rho(t)$$ The energy density ##\rho(t)## is given by: $$\rho(t) \propto \frac{E(t)}{a(t)^3}$$ where ##E(t)## is the energy of the cosmological fluid in a co-moving...

Good day all, A question that I haven't really found the answer for yet: "Whom did first come up with the idea of the cosmological principle?" I almost looked everywhere for the answer but still cannot find it. Was it Friedmann or Lemaitre? Or was it some other great physicist? But there...

Hi all I want to ask a question about NFE(Newtonian Friedmann Equation).I know that NFE is not usefull to describe universe.But we can have a general idea about universe to use that formula. I know that the only spatial coordinate system is CMB referance frame and NFE is derived from...

What if the Friedmann equation told how the (square of) fractional growth rate of spatial volume relates to the energy density, instead of describing how the (square of) fractional growth rate of spatial distance relates to energy density? Just two slightly different ways of describing the...

Homework Statement (a) Show the relation between frequency received and emitted (b) Find the proper area of sphere (c) Find ratio of fluxes Homework EquationsThe Attempt at a Solution Part (a) Metric is ##ds^2 = -c^2dt^2 + a(t)^2 \left( \frac{dr^2}{1-kr^2}+ r^2(d\theta^2 + \sin^2\theta)...

In friedmann equation we start to make a model kinetic energy-potantial energy=U kinetic energy depends observer and referance frame so what's the referance frame and observer in this calculation. Thanks

I am studying general relativity from Hobson and came across the term 'lifetime' of a closed (k>0) universe, ##t_{lifetime}##. I suppose at late times the curvature dominates and universe starts contracting? Are they simply referring to ##\int_0^{\infty} dt##? If so, would the bottom expression...

Homework Statement (a)Sketch how the contributions change with time (b)For no cosmological constant, how long will this universe exist? (c)How far would a photon travel in this metric? (d)Find particular density ##\rho_E## and scale factor (e)How would this universe evolve?[/B] Homework...

I'm utterly confused by co-moving distance, transverse comoving distance and proper distance. Is comoving distance = proper distance? Then what is transverse comoving distance? Here's what I know so far: The FRW metric can either be expressed as ds^2 = c^2dt^2 - a^2(t) \left[ \frac{dr^2}{1-kr^2}...

Hi, I have been studying general relativity using Hobson's lately, particularly about the FRW universe. I know that for a matter universe with curvature, H^2 = \left( \frac{\dot a}{a} \right)^2 = \frac{8\pi G}{3} \rho_m -\frac{kc^2}{a^2} Another expression I came across is also 1 = \Omega_m +...

Homework Statement (a)Find how ##\rho## varies with ##a##. (b) Show that ##p = \frac{2}{\lambda^2}##. Find ##B## and ##t_0##. (c) Find ##w## and ##q_0##. What values of ##\lambda## makes the particle horizon infinite? Find the event horizon and age of universe. (d) Find luminosity distance...

Homework Statement [/B] (a) Find the value of A and ##\Omega(\eta)## and plot them. (b) Find ##a_{max}##, lifetime of universe and deceleration parameter ##q_0##. Homework Equations Unsolved problems: Finding lifetime of universe. The Attempt at a Solution Part(a)[/B] FRW equation is...

Homework Statement (a) Find the FRW metric, equations and density parameter. Express the density parameter in terms of a and H. (b) Express density parameter as a function of a where density dominates and find values of w. (c) If curvature is negligible, what values must w be to prevent a...

Taken from Hobson's book: Metric is given by ds^2 = c^2 dt^2 - R^2(t) \left[ d\chi^2 + S^2(\chi) (d\theta^2 + sin^2\theta d\phi^2) \right] Thus, ##g_{00} = c^2, g_{11} = -R^2(t), g_{22} = -R^2(t) S^2(\chi), g_{33} = -R^2(t) S^2(\chi) sin^2 \theta##. Geodesic equation is given by: \dot...

You know friedmann equations derived from kinetic energy and potantial energy conservation.I found these shell model for universe.Here I am curious about something. This shell is like a surface of sphere isn't it.I mean it has only surface and that surface mass is m.And we made our equations...

Currently reading Peter Coles, Cosmology a very short introduction. There is a bit I don't understand. In a section discussing Friedmann Models, and how going on the cosmological principle density of the universe is the same in every place, and therefore space must be warped in the same way at...

Hi, I'm looking at 'Lecture Notes on General Relativity' by Sean M.Carroll. I have a question about p. 227, solving for ##a(t)## in the dark energy case. So for dust and radiation cases it was Friedmann equations you solve. But in the case of a non-zero cosmological constant Eienstien equation...

This thread is meant to give a basic introduction to the equation that governs distance growth, how it changes over time. If you've worked with Jorrie's calculator ("Lightcone") you may know that the present distance growth rate is about 1/144 of a percent per million years, and the longterm...

Hi! I'm struggling to derive the accelerated Friedmann equation (shame on me!)... I'll tell you what I'm doing and maybe you can find where the mistake is. First of all, we know that: H^2 = \frac{\rho}{2M^2_p}+\frac{\Lambda}{3} Now, using the Einstein Equations and doing the trace of...

Homework Statement For the equation H^2 = \frac{8 \pi G \rho_m}{3} + \frac{H}{r_c} how do I find the value of H for scale factor a \rightarrow \infty , and show that H acts as though dominated by \Lambda (cosmological constant) ? Homework Equations \rho_m \propto \frac{1}{a^3} H > 0...

Definition/Summary The Friedmann equation is a dynamical equation that describes the expansion of the universe. Equations H^2 = \left( \frac{\dot{a}}{a}\right)^2 = \frac{8\pi G}{3} \rho - \frac{kc^2}{a^2} Extended explanation The Friedmann equation is derived from the 0-0...

Definition/Summary While the Friedmann equation can demonstrate a flat universe, the Friedmann acceleration equation, in conjunction, can demonstrate a flat yet accelerating universe. Equations Friedmann acceleration equation- \dot{H}+H^2=\frac{\ddot{a}}{a}=-\frac{4\pi...

The Hubble's Law v=H0D LHS of The Friedmann equation H2/H02 I am a bit confused with the following: 1: The Hubble constant H0 is the current universe velocity/distance ratio, it is basically a constant, so galaxies in the universe with a further distance, move away from each other at a...

Hello! I'm a senior at San Francisco State University, and I'm currently enrolled in a cosmology class. It's a GWAR class, meaning General Writing Assessment Requirement- I didn't expect much math. In fact, the first half of the class was basically an anthropology course, which is more in line...