Blueshift in case of the Big Crunch scenario

[hedgehug]

According to the FLRW metric which is used to model the expanding universe, if at present time we receive light from a distant object with a redshift of $z$, then the scale factor at the time the object originally emitted that light is $a(t)=1/(z+1)$.

https://en.wikipedia.org/wiki/Scale_factor_(cosmology)#Detail

Radiation emitted at the time of the expansion reversal and observed later during the collapse would be blueshifted, but this formula definition accounts only for the redshift.

Does it mean that the FLRW metric is valid only for the expanding universe?

 

[Ibix]

$1+z=a_\mathrm{received}/a_\mathrm{emit}$ in any FLRW model including a closed one that collapses. You can see this by considering the Killing fields and remembering that $p_a\xi^a=\mathrm{const}$ along a geodesic.

 

[hedgehug]

If the radiation was emitted at the time of the expansion reversal and observed during the collapse, then $a_{rec}/a_{emit}<1$. How about $1+z$?

 

[Ibix]

$1+z$ is always the ratio of scale factors at reception and emission.

 

[hedgehug]

$z$ is no longer redshift if $z+1<1$.

 

[Ibix]

It's a negative redshift, which is a blueshift.

 

[Ibix]

The point is that $1+z$ is the ratio of wavelengths measured locally at emission and reception, so when this is greater than 1 then $z$ is positive and you have redshift. When it's less than one then $z$ is negative and you have blueshift.

 

[hedgehug]

True. It's just a matter of the words used in the definition. Formula remains valid.

Your explanations are correct. Just note that there was a Blushift in the title of the thread since the beginning.

 

[Jaime Rudas]

Radiation emitted at the time of the expansion reversal and observed later during the collapse would be blueshifted, but this formula definition accounts only for the redshift.

Does it mean that the FLRW metric is valid only for the expanding universe?

No, that doesn't follow from what Wikipedia says. Wikipedia states that the FLRW metric is used to model the expanding universe, but it doesn't say that it can't be used to model a contracting one.

 

[hedgehug]

No, that doesn't follow from what Wikipedia says. Wikipedia states that the FLRW metric is used to model the expanding universe, but it doesn't say that it can't be used to model a contracting one.

Yeah, I already know it from Ibix. Thank you very much.