# Beginning of accelerating expansion

1. Oct 2, 2014

### hendoS

I've been trying to find the latest, best guess, as to how long ago the universe's expansion began to accelerate (post-inflation). I've seen various estimates on websites from 5 billion to 8 billion years ago.

Is there any kind of consensus in the community that studies these things as to a more limited time range for this acceleration to have started? What is the latest observational evidence used to support these estimates?

2. Oct 2, 2014

### phinds

I don't know the answer but am curious as to why it matters to you.

3. Oct 2, 2014

### marcus

It depends on what parameters you plug into the model, mainly on H0, and Lambda. You can go get your favorite parameters, e.g. the Planck report gives you a choice of whether they depend on just Planck data or a mix of theirs with various other studies.

Once you decide on the two parameters you can plug them into some version (like Jorrie's calculator) of the standard LCDM cosmic model and it will tell you. I will work an example for you. Suppose you want to use Jorrie's DEFAULT parameters which he essentially got from 2013 Planck mission report.
Then it is very simple. You click on the Lightcone link (in my sig) and you narrow the time range say make Supper = 3 and Slower=1 (which is the present, or z=0)
and you might want to increase the number of steps N = 20 (and later even higher for better resolution, but lets start with 20)
and then you go to column select menu and check the "R0a'(t)" which gives you the TIME DERIVATIVE OF A REPRESENTATIVE DISTANCE.
And then you press "calculate" and you will get among other things the growth speed of a sample distance and it will INITIALLY DECLINE and then around say year 7 billion it will BEGIN TO INCREASE. And that's your answer.

Last edited: Oct 2, 2014
4. Oct 2, 2014

### marcus

I did exactly what I suggested you do and got this:
$${\scriptsize\begin{array}{|c|c|c|c|c|c|}\hline R_{0} (Gly) & R_{\infty} (Gly) & S_{eq} & H_{0} & \Omega_\Lambda & \Omega_m\\ \hline 14.4&17.3&3400&67.9&0.693&0.307\\ \hline \end{array}}$$ $${\scriptsize\begin{array}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline a=1/S&S&T (Gy)&R (Gly)&D_{now} (Gly)&D_{then}(Gly)&D_{hor}(Gly)&a'R_{0} (c) \\ \hline 0.333&3.000&3.2851&4.8024&17.294&5.765&11.260&0.9995\\ \hline 0.352&2.840&3.5592&5.1793&16.494&5.809&11.615&0.9791\\ \hline 0.372&2.688&3.8546&5.5797&15.679&5.833&11.967&0.9602\\ \hline 0.393&2.544&4.1726&6.0033&14.847&5.836&12.316&0.9428\\ \hline 0.415&2.408&4.5145&6.4498&14.001&5.814&12.660&0.9271\\ \hline 0.439&2.280&4.8815&6.9183&13.141&5.765&12.998&0.9131\\ \hline 0.463&2.158&5.2749&7.4072&12.269&5.686&13.327&0.9010\\ \hline 0.490&2.042&5.6956&7.9146&11.386&5.575&13.647&0.8909\\ \hline 0.517&1.933&6.1448&8.4377&10.494&5.428&13.957&0.8828\\ \hline 0.546&1.830&6.6229&8.9733&9.594&5.243&14.253&0.8770\\ \hline 0.577&1.732&7.1307&9.5174&8.691&5.017&14.536&0.8735\\ \hline 0.610&1.639&7.6686&10.0656&7.784&4.748&14.804&0.8726\\ \hline 0.644&1.552&8.2365&10.6131&6.879&4.432&15.057&0.8743\\ \hline 0.681&1.469&8.8344&11.1548&5.976&4.068&15.292&0.8788\\ \hline 0.719&1.390&9.4618&11.6855&5.079&3.653&15.511&0.8863\\ \hline 0.760&1.316&10.1179&12.2004&4.192&3.185&15.713&0.8968\\ \hline 0.803&1.246&10.8017&12.6948&3.316&2.662&15.897&0.9106\\ \hline 0.848&1.179&11.5121&13.1648&2.456&2.082&16.065&0.9276\\ \hline 0.896&1.116&12.2475&13.6072&1.612&1.444&16.216&0.9482\\ \hline 0.947&1.056&13.0065&14.0193&0.788&0.746&16.351&0.9723\\ \hline 1.000&1.000&13.7872&14.3999&0.000&0.000&16.472&1.0000\\ \hline \end{array}}$$

The growth speed for this sample distance is given in units of the speed of light. You can see that it gets as low as 0.8726 c. You can see the inflection point is around year 7.67 billion. You can make the inflection point change by choosing a slightly different H0 hubble rate. The way you control that is by controlling its reciprocal the Hubble distance R0 = c/H0
The default hubble distance is 14.4 billion LY as you an see at the top. You can type in a slightly different R0 and that will change H0 and that will change the numbers that the model computes, including the inflection point.

It is important for you to find the "column definition and selection" menu so that you can select "a'(t) R0" the distance growth speed of a sample distance. You can also UNselect various columns so the output table will not be so wide and distracting. When I did it I unchecked a couple of source recession velocity columns Vnow and Vthen because they are not relevant to your question and might be distracting.

One other thing I did, forgot to tell you, was when I opened "column definition and selection" menu to check the distance growth speed a'R0 at that point I also BUMPED UP THE NUMBER OF DECIMAL PLACES in that column from 2 to 4, so we could see the result in 4 decimal precision.
If you go to that menu you can see how the precision of each column can be varied as you wish.

I wanted to see how changing the model parameters would move the inflection point so I made R0 less (14.0 billion LY) which makes H0 slightly larger as you can see if you try it. And that then made the inflection come slightly EARLIER. Closer to 7.6 than to 7.7.

If you are familiar with the cosmological constant Lambda you know that it determines the longterm value of the Hubble radius namely Rinfinity, which viceversa determines Lambda by a simple formula. So you can try varying that too. I suppose increasing Lambda means decreasing Rinfinity (increasing the longterm growth rate H(t)) and probably makes the inflection come EARLIER, i.e. acceleration starts earlier if you reduce the Rinfinity parameter, you can try that with the calculator if you want.

Last edited: Oct 2, 2014