COSMIC ACCELERATION Please forgive a probably naïve question from a lay person.
I understand that galaxies are all moving away from us in every direction we look.  And for any given distance the speed is the same.  And the greater the distance, the greater the speed.
From which it is inferred that the speed is not constant but accelerating.
Now the further away an object is from the observer, the longer ago it emitted its light.  But also. the further away it is the older it is - or rather was.  We have no way of predicting what happened to it in the intervening (for example) 8 billion years.
My naïve question is how it is known that the correlation between distance/age and speed does not have the opposite implication?  Everything nearer to us is moving away more slowly than everything further away.
I found a short article by Hao-Ran Yu of Cornell, (https://arxiv.org/abs/1311.2363). describing (back in 2013) the measurement of acceleration as “indirect”.  It seems to involve radio telecopy in some way.


*

*Is there a lay way of explaining how it is done?

*how reliable is this method?

 A: The most direct evidence for the acceleration of the expansion of the universe comes from the observation of type Ia supernovae. Specifically, their luminosity is measured to determine their distance from us, and their spectrum is measured to determine their redshift. The way that the distance is found to depend on the redshift is what would be expected if the expansion is accelerating, not if it is decelerating.
Type Ia supernovae are useful “standard candles” for determining distance because they have consistent peak luminosity. This is due to the relatively uniform mass of the white dwarfs that explode to produce them.
The experimental errors in the redshift are very low, but the errors in luminosity distance are on the order of 10%.
Confirmatory evidence for accelerating expansion comes from observing baryon acoustic oscillations, the cosmic microwave background, gravitational lensing of galaxies, the large scale distribution of galaxies, and the abundance and evolution of galactic clusters. The fact that a single cosmological model can explain all of these different observations makes the $\Lambda$CDM model compelling.
This paper from 2011 reviews the observational evidence.
A: The speed of the receding galaxies is inferred from their red shift. Gravity should be slowing them down, and this was thought to be the case until relatively recently, but by examining the redshift of distant supernovae it was discovered that the expansion of the universe is speeding up. This unexpected acceleration is caused by a mysterious force dubbed 'dark energy', or at least, that is the current interpretation. There are some doubters who believe that either experimental error has crept in or the evidence has been misinterpreted, so the matter is not yet fully settled. The reason some cosmologists have doubts is that the current speeded-up-by-dark-energy universe would be a one-off event which materialised out of nowhere for no fathomable reason, and will expand for ever. The alternative Big Bang-Big Crunch-Big Bounce universe would be slowed by gravity, finally coming to a halt and collapsing on itself to form a blue shifted, shrinking universe which would end in a fireball and singularity like the one it was born from, to be recycled in a Big Bounce. The theory has it that this pulsating, cyclic universe had no beginning and will never end.
A: There are a few things to clarify:


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*inside galaxies, space is not expanding, gravity dominates

*between galaxy clusters, space is expanding, dark energy dominates over gravity. Now the rate of expansion is faster as you go from between galaxy clusters to the voids of space between superclusters

*the universe is expanding at a uniform rate on the large scale, but if you go from the space between galaxy clusters to the voids of space between galaxy superclusters, the rate (of expansion) is increasing
