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This is a conceptual question and has probably been asked before in many guises and forms. Mine has a little twist to it.

I realize the Hubble Law tells us the farther back in time and space we look the faster the universe appears to be receding from us and the more of a red shift is observed...after all we are looking back and getting closer to when the universe first began the acceleration.

It normally would be accelerating faster farther back in time so how can one distinguish between that acceleration and what is happening now?

They only thing I can come up with is that acceleration between us and a closer "spot" in space is faster then can be explained given the acceleration that is observed much farther in the past. In other words the acceleration as you look farther back in time is actually slower than expected as compared from us to closer locations.

So the standard candles are the mechanism to get at the acceleration from us to a "close" object. Comparing the expansion rate given by Hubble the closer object is moving faster than it should given the speed of the object farther back in time so we conclude we are speeding up relative to the past.

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    $\begingroup$ The Hubble law relates distances to speeds not accelerations. The fact that the universe's expansion is accelerating rather than decelerating is the indication for dark energy as a universe with no dark energy should theoretically be decelerating in its expansion. $\endgroup$ – enumaris Sep 24 '18 at 22:14
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    $\begingroup$ See my answer here where the plot shows that the universe was decelerating until not too long ago and only since then began accelerating: physics.stackexchange.com/questions/428231/… $\endgroup$ – safesphere Sep 24 '18 at 23:42
  • $\begingroup$ Both comments put me on the right track. enumaris...I had it wrong after looking at safesphere's excellent links. Obviously I had some confusion on the basics of Hubble's law. Both links have actually answered the question. Can I accept the comment as an answer? $\endgroup$ – Sedumjoy Sep 25 '18 at 15:04
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According to the Hubble's Law, distant galaxies recede from us with the speed directly proportional to the distance. The law says nothing about acceleration. According to the current $\Lambda\text{CDM}$ cosmological model, since the Big Bang, the universe has gone through the phases of a brief initial expansion and inflation, then radiation dominance for about 70,000 years, then mater dominance for most of its life, and now is in the phase of a dark energy dominance. "Matter dominance" implies gravitational attraction and deceleration. "Dark energy dominance" implies acceleration due to the repulsive effect of the dark energy.

First, the universe accelerated initially in a fraction of a second to tremendous speeds, then it was decelerating due to gravity for billions of years, and now when the gravity is reduced by increased distances, the universe is accelerating again pushed by the dark energy. You can see the applicable solution of the Friedmann equations with the scale factor and acceleration chart in my earlier answer.

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