# Accelerating Expansion and Mediocrity Priniciple

1. Dec 30, 2015

### DaveC426913

https://en.wikipedia.org/wiki/Metric_expansion_of_space#/media/File:Universe.svg

I am possibly misreading the graph, but it seems to suggest that, if we are in an expanding universe (large dotted line), and curvature is currently zero, then its expansion was decelerating in the past (as presumably, it would under the sole influence of gravity).

But this means that we are in (or at least, near) a unique time it the universe, when curvature is crossing from negative to positive.

Does this not go against the Principle of Mediocrity? Sure, it is usually applied to observers in space, but can it not equally apply to observers in time? Are we just lucky to be at the one unique point in the universe's evolution where we see two opposing phenomena in near balance on a cosmic scale?

2. Dec 31, 2015

### Bandersnatch

Don't take that graph too literally - not without reason there are no scales on its axes.
The parts of the graph except the line marked 'accelerated expansion' represent effects of curvature in a universe without cosmological constant. I.e., those were the possible cosmologies considered before the discovery of accelerated expansion. With cosmological constant, even a flat (Ω=1 on the graph) universe would be expanding in an accelerated fashion in the long term.

The accelerated expansion line is pretty much tacked on for visualisation purposes only - the inflection point could have been placed anywhere else before or after now.
The actual moment of change from deceleration to acceleration in our universe lies around 5Gy in the past.

I suppose you could still argue that that's in conflict with the mediocrity principle - there's infinitely more time in the future as compared to the 5 Gy to the inflection point, so why are we this 'close' to it, but then you could counter that with the anthropic principle - we exist in a time conductive to our existence, and that time is likely finite.

3. Dec 31, 2015

### DaveC426913

Inflection point, That's the word I was looking for. I kept thinking of nodes in bezier curves.

Isn't the inflection point being now == our universe is currently thought to be flat?

Does that imply we have an open universe i.e. curvature < 0?

4. Dec 31, 2015

### marcus

That graph in wikipedia is very bad. Somebody should tell them about it. Charles Lineweaver, a reputable cosmologist, has a more realistic alternative in a 2003 paper of his:
http://ned.ipac.caltech.edu/level5/March03/Lineweaver/Figures/figure14.jpg

You can see, I think, that according to his numbers the inflection point came around year 8 billion. That is about 6 billion years ago.

The inflection point, with standard numbers in the standard model does not come right near the present year 13.8 or 14 billion.

If you want to see the inflection point in a table of numbers you can use Jorrie's calculator which uses present-day (Planck2015) parameters and gets approx the same answer as Lineweaver, around year 8 billion.

5. Dec 31, 2015

### marcus

DaveC, that's certainly a question that needs to be asked if one takes the WikiP figure literally. But Bander is right to advise not taking it seriously. In the above figure the dark line (labeled 0.27, 0.73) is the one to follow and look for the inflection. The 2003 Lineweaver article is titled something like "Inflation and the CMB" if you want to look it up.
http://arxiv.org/abs/astro-ph/0305179
or just google "lineweaver inflation and the CMB".
Present day Planck parameters are more like (0.31, 0.69) which corresponds to the default in Jorrie's "Lightcone" calculator, but it doesn't change the inflection time (onset of distance growth acceleration) very much. I'm always considering the spatially flat case, because whether perfectly or not it appears to be nearly flat.
http://www.einsteins-theory-of-relativity-4engineers.com/LightCone7/LightCone.html
It's kind of overkill to use Lightcone calculator on this, but it is a good exercise. One can either get Lightcone to print a table or draw a graph.

This is what happens if you go to Lightcone and set the S range to be from 10 to 0.1---S is the reciprocal of the scale factor. So type in 10 and 0.1 to the boxes labeled Supper and Slower. And say 20 for the number of steps.
$${\scriptsize\begin{array}{|c|c|c|c|c|c|}\hline T_{Ho} (Gy) & T_{H\infty} (Gy) & S_{eq} & H_{0} & \Omega_\Lambda & \Omega_m\\ \hline 14.4&17.3&3400&67.9&0.693&0.307\\ \hline \end{array}}$$ $${\scriptsize\begin{array}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline a=1/S&T (Gy)&V_{gen}/c \\ \hline 0.100&0.545390&1.757\\ \hline 0.126&0.770729&1.567\\ \hline 0.158&1.088593&1.399\\ \hline 0.200&1.536225&1.253\\ \hline 0.251&2.164577&1.126\\ \hline 0.316&3.041177&1.020\\ \hline 0.398&4.250006&0.939\\ \hline 0.501&5.882847&0.887\\ \hline 0.631&8.015105&0.873\\ \hline 0.794&10.668537&0.908\\ \hline 1.000&13.787206&1.000\\ \hline 1.259&17.257193&1.158\\ \hline 1.585&20.956083&1.391\\ \hline 1.995&24.788750&1.707\\ \hline 2.512&28.694196&2.120\\ \hline 3.162&32.638034&2.651\\ \hline 3.981&36.601471&3.325\\ \hline 5.012&40.574846&4.179\\ \hline 6.310&44.553231&5.257\\ \hline 7.943&48.534134&6.615\\ \hline 10.000&52.516301&8.326\\ \hline \end{array}}$$

In the "column select" menu I selected T (the year) and a(the scale factor) and a generic distance expansion speed vgen/c. This tracks the expansion speed of a distance which is arbitrarily chosen so that its expansion speed at the present moment is c.
You can see that the expansion speed is minimum at around year 8 billion, where the inflection point in the scale factor curve would be if we plotted it. The sample distance SLOWS until that point and thereafter GROWS.

Last edited: Dec 31, 2015
6. Dec 31, 2015

### marcus

Here's what Lightcone does if you leave the same columns selected as in the previous post and tick the "Chart" button.

Here I also limited the vertical scale to 4, for compactness. I think the default is 20. I limited the horizontal scale to 32 and told it to make 8 divisions just so that
year 8 billion would show up on the time axis. That is about where the inflection in the scale factor (blue) comes and where the distance growth speed curve (red) has a minimum.

Last edited: Dec 31, 2015
7. Jan 2, 2016

### Ken G

Remember that the mediocrity principle doesn't say we should be at a random place or a random time, it says we should be at a random place and times chosen from the set of workable possibilities. Using that version of the mediocrity principle, Dicke was able to calculate that the age of the universe when intelligent beings would first ask "what is the age of the universe" must come close to a time that can be derived from basic parameters found by Dirac (Dicke, R. H., 1961,Nature (London) 192, 440), and later Weinberg found that given the baryonic density we have, we should be somewhere close to the inflection point that inflation would have given (if the universe is to be flat), so being near the inflection point doesn't violate the mediocrity principle, it comes from it.

8. Jan 2, 2016

### marcus

That's a really good point! And we are "near" in a vague sense. The expansion age is roughly 14 billion and inflection occurred around year 8 billion, some 6 billion years ago.
One way to make more precise what we mean by "near" would be to take the inflection time as a unit. now the age is 14/8 = 1.75 units. That is much closer to one than if the current age were 80 billion years---then it would be 10 units, instead of 1.75.

9. Jan 3, 2016

### Ken G

Yes I agree completely-- there are other parameters that seem much more finely tuned than the time of inflection. We've all heard about it, this parameter or that parameter being a few percent different would mess up life completely, and so on. That dark matter and dark energy would be within a factor of a few of each other during the era of life is probably not all that shocking.