# What is Friedmann: Definition and 86 Discussions

Friedman, Friedmann, and Freedman are surnames of German origin, and from the 17th century were also adopted by Ashkenazi Jews. It is the 9th most common surname in Israel (8th among Jews) and most common exclusively Ashkenazi name.
They may refer to:

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1. ### I "Energy is not conserved" vs. energy is conserved: Friedmann Equations

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...
2. ### How Are Tsinghua Students Using the Friedmann Equation to Protest Lockdowns?

"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.]
3. ### I Is there a Friedmann equation form with inflation?

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...
4. ### I Is Minkowski spacetime a solution of the Friedmann Equations?

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...
5. ### How Can Separating Variables Show Scale Factor Growth in Friedmann Equation?

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).
6. ### A Implications of Symmetry and Pressure in Friedmann Cosmology

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...
7. ### A Anisotropic Universe and Friedmann Equations

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...
8. ### Find the Metastatic Conditions for Omegas in the Friedmann Equation

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...
9. ### Friedmann's equation for a^3 with Λ, ρm

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 +...

26. ### Question regarding Friedmann equation

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...
27. ### Definition of Energy in Friedmann equations?

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...
28. ### Who First Conceived the Idea of the Cosmological Principle?

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...
29. ### Newtonian Friedmann Equation, Referance frame, Homogeneity

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...
30. ### Just for fun: recast the Friedmann eqn. to be about volume instead

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...
31. ### How is Frequency Redshift Related to Sphere's Proper Area and Flux Ratio?

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)...
32. ### Referance Frame Calculating Newtonian Friedmann Equation

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
33. ### Lifetime of Universe: Limits & Expansion Explained

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...
34. ### How do I find the scale factor of cosmological constant?

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...
35. ### Comoving/Proper distance, transverse comoving distance

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}...
36. ### Redshift in Terms of k | General Relativity

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 +...
37. ### What Are the Steps to Solve the FRW Cosmological Model?

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...
38. ### What Is the Lifetime of the Universe According to the FRW Model?

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...
39. ### What Is the FRW Metric and How Is It Applied in General Relativity?

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...
40. ### What is the Geodesic Equation for FRW Metric's Time Component?

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...
41. ### Calculating Surface Density of the Universe Using the Shell Model

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...
42. ### Space Curvature: Friedmann Models Explained

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...
43. ### Solving Friedmann Equations with Cosmological Constant

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...
44. ### What is the key equation for distance growth in Kindercosmos?

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...
45. ### Why Is the Accelerated Friedmann Equation Giving Incorrect Signs?

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...
46. ### Solving expansion rate for a variant of the Friedmann equation

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...
47. ### What Describes the Expansion of the Universe?

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...
48. ### What is the Friedmann acceleration equation

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...
49. ### Questions on Hubble's law and Friedmann equation

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...
50. ### Help understanding the Friedmann equations?

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...