• #### Cosmological Principle-Homogenous and Isotropic

From Savin Beniwal@21:1/5 to All on Sat Oct 10 10:14:42 2020
On Wednesday, 17 July 2019 05:17:51 UTC+5:30, Phillip Helbig (undress to reply) wrote:
Savin Beniwal <darshanbeniwal11@gmail.com> writes:

I have questions regarding the Cosmological Principle that usually we
study universe is SPATIALLY homogeneous and isotropic(around every
point) at large scale (>150MPC). Here homogenous means--> No special location and Isotropic means-->No special point. Also, this was
confirmed by Hubble in 1929 that if distances are expanding (or contracting), the speed must be proportional to distance =E2=80=93 Hubble=
's Law
is inevitable.

But my questions is that if there were a proportionality relation
between velocity and square of distance rather than a linear relation between r and v. Even then can we understand the homogenous and
isotropic concept from Hubble's law under this nonlinear relation?

No.

Say you are at the origin, at distance 1 velocity is 1, at distance 2 velocity is 4, at distance 3 velocity is 9, and so on. For an observer
at distance 1, your distance 2 is just 1 unit of distance away, but its
speed relative to the observer at 1 is 3 (4-1), whereas it should be 1
if the distance is 1.

Is this way correct to add/subtract velocities as velocities of
galaxy is about the speed of light? If we consider the velocity of
galaxy is equal or greater then speed of light (Not a surprise at
all), even then there will be a linear relation between velocity
and distance as Hubble stated?

[[Mod. note -- No. -- jt]]

In short, homogeneity and isotropy demand a linear velocity--distance
law, since otherwise homogeneity and isotropy couldn't persist. (Note
that this is purely kinematics, no dynamics, hence this does not depend
on general relativity in any way.)

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