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My understanding of cosmological principle is this:
Space looks same in all directions and is homogeneous. But this principle was under heading of Observational Evidence for expansion of space in this article:

https://en.wikipedia.org/wiki/Expansion_of_the_universe#Observational_evidence

My question is, how does Cosmological Principle imply an expanding space?
If it's my understanding of cosmological principle which is flawed, I would highly appreciate if someone corrects me. Thanks in advance!!

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  • $\begingroup$ The cosmological principle states that at any given time the Universe is isotropic and homogeneous - which allows for constant curvature. In general relativity, there are typically 3 choices for curvature, $k=1,0,-1$. As far as an expanding universe is concerned, it's by fiat. It's consistent with Big Bang Theory - which is consistent with the Old Testament of the Bible. The Hubble data, however, looks like random sequence - it's not clear that red shifts imply velocity - and quasars which were believed to be on the "edge" of the Universe are actually in our Local Super Cluster. $\endgroup$ – Cinaed Simson Apr 4 '19 at 7:28
  • $\begingroup$ It does if combined with other hypothesis or observations. $\endgroup$ – Alchimista Apr 4 '19 at 8:51
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Since according to Cosmological Principle (CP) every point is space is equivalent to every other point, if the galaxies appear to be rushing away from an observer in the Milky way galaxy, the same would also appear to be to an observer from the Andromeda galaxy. So if the CP is true, the Universe must be expanding.

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The Cosmological Principle doesn't actually imply that the universe is expanding, instead, what this principle implies that the spatial part of the space-time manifold is maximally symmetric. What this actually means that the spatial manifold has a constant curvature everywhere given by Ricci Scalar, $R=-6\kappa$ using this principle along with defining the cosmological standard time $t$ as the time co-ordinate for co-moving cosmological fluids, we can construct metric given by:

$$d s^{2}=- d t^{2}+R^{2}(t)\left[\frac{d r^{2}}{1-\kappa r^{2}}+r^{2}\left(d \theta^{2}+\sin ^{2} \theta d \phi^{2}\right)\right]$$

where $R(t)$ is the scaling factor. Now, whether the universe is contracting/expanding depends on this scaling factor. In order to determine $R(t)$, we have to solve Einstein's field equation which is given by the Friedmann Equation for this metric: $$\frac{\dot{R}}{R}=-\frac{4 \pi}{3} G (\rho+3p)+\frac{1}{3} \Lambda c^{2}$$ and $$\left(\frac{\dot{R}}{R}\right)^{2}-\frac{8}{3} \pi G \rho=-\frac{\kappa c^{2}}{R^{2}}$$ $\rho$ being energy density and $p$ being the pressure for cosmological fluids.

So, in short, it is actually the behavior of cosmological fluids that determines the expansion/contraction of the universe. Also, in the above answer, it might be possible that the galaxies have peculiar velocities due to which can't really say "if the galaxies appear to be rushing away from an observer in the Milky Way galaxy, the same would also appear to be to an observer from the Andromeda galaxy".

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