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Please read this http://www.researchgate.net/publication/282157370_VALUE_OF_THE_UNIVERSE%27S_ACCELERATION

Your ideas are welcome.

Qmechanic
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MAXIMILLION
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    Please copy the relevant portions of the document to the post, rather than linking it. – Kyle Kanos Sep 30 '15 at 15:56
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    Dear MAXIMILLION: Are you in any way associated with the author of the linked article? For your information, Physics.SE has a policy that it is OK to cite oneself, but it should be stated clearly and explicitly in the post itself, not in attached links. – Qmechanic Sep 30 '15 at 17:06
  • That is my publication. – MAXIMILLION Oct 02 '15 at 17:10

1 Answers1

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The universe is described by a scale factor, normally indicated by the symbol $a(t)$, that is a function of time. We take the scale factor to be one right now, so in the past $a$ was less than one and in the future $a$ will be greater than one.

Roughly speaking, if $a$ has the value $\tfrac{1}{2}$ it means everything was half as far apart as it is now, and if $a$ has the value $2$ it means everything is twice as far apart as it is now. So the scale factor measures the expansion of the universe.

If dark matter didn't exist we would expect the variation of $a$ with time to be:

$$ a(t) \propto t^{2/3} $$

So the rate of change of $a$ with time (we write this as $\dot{a}(t)$) would be given by:

$$ \dot{a}(t) \propto \frac{1}{t^{1/3}} $$

So as $t$ increases the rate of the expansion, $\dot{a}(t)$, will decrease. This is what we mean by a decelerating expansion, and as I mentioned above if dark energy didn't exist we would expect the expansion to decelerate.

However the presence of dark energy adds a term to the rate of expansion that is something like:

$$ \dot{a}(t) \propto e^{bt} $$

where $b$ is a constant. So dark energy makes the rate of expansion, $\dot{a}(t)$, increase not decrease. This is what we mean by an accelerating expansion.

If you're interested I go into the maths in more detail in my answer to How does the Hubble parameter change with the age of the universe?.

So the acceleration of the expansion is represented by the change in $\dot{a}(t)$, and we know this to reasonable precision. The paper you cite is attempting to construct a rate of acceleration from the velocities of distant objects. However this does not correspond to what cosmologists mean by the acceleration of the expansion.

Community
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John Rennie
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  • John, It would be better if you put down the value. – MAXIMILLION Oct 02 '15 at 17:15
  • @MAXIMILLION: what value? The value of $\dot{a}$ at the current time? The point is that there isn't a single value that we can point to and say "this is the acceleration of the universe". – John Rennie Oct 02 '15 at 17:19
  • John, Physicists discovered that distant galaxies are moving faster than their meant.That clearly assures you that such a value exists. – MAXIMILLION Oct 02 '15 at 17:28
  • Hubble's law says the galaxies at a distance $d$ should be moving at a velocity $v = H_0d$. What the SN1a surveys found was that $v \gt H_0d$. How you would extract a single value for the acceleration from this data escapes me. – John Rennie Oct 02 '15 at 17:35
  • John, the positions of different galaxies in the Universe without dark energy can be mapped out, then the current positions of the galaxies are also mapped out. You can use this to calculate the velocities in each case with their corresponding time. This gives you the value of the accelerating expansion of the Universe. – MAXIMILLION Oct 02 '15 at 17:51