Blueshift in case of the Big Crunch scenario

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Discussion Overview

The discussion revolves around the implications of the FLRW metric in the context of a potential Big Crunch scenario, specifically addressing the behavior of redshift and blueshift of radiation emitted during different phases of the universe's expansion and contraction. Participants explore whether the FLRW metric is exclusively applicable to an expanding universe or if it can also describe a contracting universe.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant notes that the FLRW metric, which models the expanding universe, defines the scale factor at the time of emission as ##a(t)=1/(z+1)##, raising questions about its validity during a contraction phase.
  • Another participant asserts that the relationship ##1+z=a_\mathrm{received}/a_\mathrm{emit}## holds in any FLRW model, including closed models that may collapse.
  • A participant queries the implications of observing radiation emitted during the expansion reversal, specifically regarding the ratio of scale factors and the resulting value of ##1+z##.
  • It is stated that ##1+z## is always the ratio of scale factors at reception and emission, regardless of the universe's expansion or contraction.
  • Concerns are raised about the interpretation of ##z## when ##z+1<1##, suggesting that it indicates a blueshift rather than a redshift.
  • Another participant clarifies that when ##1+z## is greater than 1, ##z## is positive (redshift), while if it is less than 1, ##z## is negative (blueshift).
  • One participant emphasizes that the formula remains valid regardless of the terminology used to describe the shifts in wavelength.
  • There is a reiteration that the FLRW metric can model both expanding and contracting scenarios, countering the initial assumption that it is limited to expansion.

Areas of Agreement / Disagreement

Participants express differing views on the applicability of the FLRW metric to contracting scenarios, with some asserting it can model both expansion and contraction, while others question its validity in non-expanding contexts. The discussion remains unresolved regarding the implications of blueshift and redshift in these scenarios.

Contextual Notes

Participants reference the definitions and relationships between scale factors and redshift/blueshift without resolving the mathematical implications or assumptions underlying these concepts.

hedgehug
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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?
 
Last edited:
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##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.
 
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##?
 
##1+z## is always the ratio of scale factors at reception and emission.
 
##z## is no longer redshift if ##z+1<1##.
 
It's a negative redshift, which is a blueshift.
 
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.
 
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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.
 
Last edited:
hedgehug said:
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.
 
  • #10
Jaime Rudas said:
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.
 

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