# What is Frw metric: Definition and 29 Discussions

The Friedmann–Lemaître–Robertson–Walker (FLRW; ) metric is an exact solution of Einstein's field equations of general relativity; it describes a homogeneous, isotropic, expanding (or otherwise, contracting) universe that is path-connected, but not necessarily simply connected. The general form of the metric follows from the geometric properties of homogeneity and isotropy; Einstein's field equations are only needed to derive the scale factor of the universe as a function of time. Depending on geographical or historical preferences, the set of the four scientists – Alexander Friedmann, Georges Lemaître, Howard P. Robertson and Arthur Geoffrey Walker – are customarily grouped as Friedmann or Friedmann–Robertson–Walker (FRW) or Robertson–Walker (RW) or Friedmann–Lemaître (FL). This model is sometimes called the Standard Model of modern cosmology, although such a description is also associated with the further developed Lambda-CDM model. The FLRW model was developed independently by the named authors in the 1920s and 1930s.

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1. ### I Expansion of the Universe and the cosmological principle

Wikipedia states the following in their article about the expansion of the universe: If the cosmological principle was discovered to be false in our universe, i.e. our universe was discovered to be inhomogeneous or anisotropic or both on very large scales and the FLRW metric does not hold for...
2. ### B Solve General Geodesics in FLRW Metric w/ Conformal Coordinates

Once having converted the FLRW metric from comoving coordinates ##ds^2=-dt^2+a^2(t)(dr^2+r^2d\phi^2)## to "conformal" coordinates ##ds^2=a^2(n)(-dn^2+dr^2+r^2d\phi^2)##, is there a way to facilitate solving for general geodesics that would otherwise be difficult, such as cases with motion in...
3. ### Does anyone know which are Ricci and Riemann Tensors of FRW metric?

I just need to compare my results of the Ricci and Riemann Tensors of FRW metric, but only considering the spatial coordinates.
4. ### How to calculate the four-momentum of a photon in FRW Metric

I have calculated the Christoffel symbols for the above given metric, but I don't understand how to calculate a photon's four-momentum using this information. I believe it has something to do with the null geodesic equation but I can't understand how to put that information into the problem...
5. ### I Ricci scalar for FRW metric with lapse function

I need the Ricci scalar for the FRW metric with a general lapse function ##N##: $$ds^2=-N^2(t) dt^2+a^2(t)\Big[\frac{dr^2}{1-kr^2}+r^2(d\theta^2+\sin^2\theta\ d\phi^2)\Big]$$ Could someone put this into Mathematica as I don't have it?

24. ### Understanding the FRW Metric: Exploring Physical and Comoving Coordinates

Hello everyone, I already know that the solution to this question is obvious but I can't find it. Consider an expanding universe following the FRW metric ds^2=-dt^2-a^2(t)dx^2 (1 space dimension for simplicity). We know that the physical spatial distance x_p is related to the comoving spatial...
25. ### The present epoch in FRW metric

In an expanding universe that is modeled by the FRW metric we assume that scale factor of the "present epoch" is unity which is equivalent to a zero redshift. Therefore, most observed galaxies with nonzero redshifts are in our past light cone. But it is unclear to me how much back in time or...
26. ### Ricci scalar and curveture of FRW metric

hi we know that our universe is homogenous and isotropic in large scale. the metric describe these conditions is FRW metric. In FRW, we have constant,k, that represent the surveture of space. it can be 1,0,-1. but the the Einstan Eq, Ricci scalar is obtained as function of time! and this...
27. ### Origins of Scale Factor of FRW Metric and Misc Questions of GR Equations

In the context of Friedmann's time, 1922, how did he know to make the metric scale factor, a, a function of time when Hubble's redshifts were not yet published? I understand that he took the assumption that the universe is homogenous and isotropic, but does that naturally imply that the universe...
28. ### FRW metric for closed universe

Hi, I'm new to Physics Forum and wasn't really sure where to post this since its not strictly speaking a homwork question. So if it happens to be in the wrong place I apologise. I was looking through some lecture notes from when I did my Physics degree years ago and come across a problem...
29. ### Exploring FRW Metric Symmetries in Spacetime

What are the symmetries determined by FRW spacetime? I guess they include Lorentz symmetry, rotationally and translationally symmetries, but not time symmetry. Is this right? Thanks