How Does Supernova Light Dimness Indicate Universal Acceleration?

[cosmos1111]

I have a simple question regarding the acceleration of the universe.

My textbook says that the acceleration was discovered through the supernova's light appearing dimmer than expected. In a constant expanding universe, it would be brighter.

My textbook also tells me that the supernova was extremely far away, and so I'm wondering that shouldn't because it being so far away that it should be expected that it's very dim? The stretching that's occurring due to the distance would have the same affect, would it not?

 

[Orodruin]

The distances to the supernovae are of course accounted for when stating that far away supernovae are dimmer than expected in a non-accelerating universe.

 

[cosmos1111]

The distances to the supernovae are of course accounted for when stating that far away supernovae are dimmer than expected in a non-accelerating universe.

Thank you.

I wasn't questioning their discovery. I was kind of just checking up to make sure that I understood it! Appreciate the feedback in such a fast manner.

 

[Jorrie]

My textbook says that the acceleration was discovered through the supernova's light appearing dimmer than expected. In a constant expanding universe, it would be brighter.

The operative word is "expected". The 'dimness' expectation was based on decelerating expansion. The most likely reason for it to be dimmer than the expectation was lack of deceleration and quite possible acceleration of the expansion. It put the supernova at a larger comoving distance than a decelerating model would predict. A number of other independent observations later confirmed that the most likely cause is acceleration of expansion (positive $\ddot a$).

 

[Dr. Strange]

The operative word is "expected". The 'dimness' expectation was based on decelerating expansion. The most likely reason for it to be dimmer than the expectation was lack of deceleration and quite possible acceleration of the expansion. It put the supernova at a larger comoving distance than a decelerating model would predict. A number of other independent observations later confirmed that the most likely cause is acceleration of expansion (positive $\ddot a$).

Deceleration has nothing to do with it. The 'expected' value was based on the FLRW metric, which is a linear relation. People suspected the universe was decelerating, but there was no 'law' to my knowledge that created an expected value.

 

[Jorrie]

Deceleration has nothing to do with it. The 'expected' value was based on the FLRW metric, which is a linear relation. People suspected the universe was decelerating, but there was no 'law' to my knowledge that created an expected value.

How does the 'gravity law' of GR sound as a basis? The FLRW metric represents an exact solution of the Einstein field equations and without dark energy, the expansion decelerates. I do not know what you meant by 'linear relation', but FLRW does not give linear cosmic expansion over time.

 

[Dr. Strange]

How does the 'gravity law' of GR sound as a basis? The FLRW metric represents an exact solution of the Einstein field equations and without dark energy, the expansion decelerates. I do not know what you meant by 'linear relation', but FLRW does not give linear cosmic expansion over time.

In the graph below, the blue line represents FLRW without Λ, which was our 'expected' value before 1998. After the discovery that SNe Ia did not follow this relation, we added "Einstein's Greatest Blunder" back into the metric and got the red line. While you are technically right, practically the exponent on this curve is 1.1, making it a (near) linear relation with red shift.

 

[Jorrie]

While you are technically right, practically the exponent on this curve is 1.1, making it a (near) linear relation with red shift.

Yes, luminosity distance vs. redshift gives a near linear relation without Lambda, but the same is not true for the expansion curve of scale factor vs. time. The latter is the context for decelerated or accelerated expansion, contrary to what you stated before.

 

[marcus]

Yes, luminosity distance vs. redshift gives a near linear relation without Lambda, but the same is not true for the expansion curve of scale factor vs. time. The latter is the context for decelerated or accelerated expansion, contrary to what you stated before.

How does the 'gravity law' of GR sound as a basis? The FLRW metric represents an exact solution of the Einstein field equations and without dark energy, the expansion decelerates. I do not know what you meant by 'linear relation', but FLRW does not give linear cosmic expansion over time.

Just to emphasize what you say very clearly here:
We could get a curve for scale factor as a function of time, to show the deceleration you get from GR (our "law of gravity") e.g. with Λ = 0, so that the spatially flat case is with Ω_m = 1. Observation supports near spatial flatness, so that is the case to look at---the dark dashed curve labeled (1,0) here:

AFAICS what the other poster pointed out, about near LINEAR relation between present-day observation of luminosity distance versus redshift is MEANINGLESS here. It does not give us the expansion history. If we look at the expansion history as predicted by GR (via the simplified version FRW) we can see the deceleration clearly enough.
The figure is from Lineweaver's 2003 article "Inflation and the CMB"
We could also get plots of scale factor history a(t) under different assumptions about Lambda by using Lightcone calculator since that embodies the standard FRW-based model. I should try that, just for practice.

 

[Chronos]

This points out the difficulties inherent to getting the parameters right in the FLRW model and why using a variety of measurement approaches is important. Even tiny inaccuracies propagate exponentially when extrapolated across billions of years. The approach being used - continue to constrain the parameters as more and better data emerges - appears entirely reasonable.