I Flatness Problem: Critical and Actual Density

[windy miller]

I have heard the flatness problem stated as the initial expansion rate of the early universe has to be fine tuned to many decimal places, I've also heard it expressed as the critical density and actual density have to be the same to within some large number of decimal places.
I presume that these two different ways of expressing the problem is because one depends on the other , is that correct or...?

 

[Simon Bridge]

I have heard the flatness problem stated as the initial expansion rate of the early universe has to be fine tuned to many decimal places,

Where? Citation please.
This is especially important in this case because the phrase "fine tuned" is almost always from creationist literature so it is a "red flag" phrase: you can safely ignore anything these folks say about any kind of science.
How we can reply to these kinds of questions depends heavily on the source.
ie. wikipedia talks about the flatness problem as a fine tuning problem for models of the early universe ... in which case I'd just direct you to a better description.

I've also heard it expressed as the critical density and actual density have to be the same to within some large number of decimal places.

Again - where? Citation please.
Similar to above - the reliance on the number of decimal places can indicate a pseudoscience source (though folk like Feynman sometimes talks about the accuracy of QED in terms of decimal places when he wants to impress a lay audience with the accuracy and reliability of the theory). The number of decimal places depends on the units used to express something ... i.e. in unified units the speed of light is 1.000... to infinite decimal places. It is usually more useful to express the precision of something in terms of a ratio.

I presume that these two different ways of expressing the problem is because one depends on the other , is that correct or...?

Without the source it is impossible to tell if the two statements are talking about the same thing or not.

Consider the following lay description of the "flatness problem":
http://hyperphysics.phy-astr.gsu.edu/hbase/astro/cosmo.html#c6
... notice how the red-flag phrases do not come up in that article?
I suspect it will also answer your questions.

 

[windy miller]

My source for this is Alan Guth. I don't think he's a creationist. He describes it as the ratio of the two densities here:
https://arxiv.org/pdf/hep-th/0702178v1.pdf
but as the expansion rate of the early universe here:

about 3 minute into the above film.

So I can only presume the two are either two sides of the same coin or one causes the other or something like that, and am looking for guidance.

On a side note:
I think its true that creationists solve the fine tuning problems by invoking god, but I don't agree that creationists are the only ones who talk about fine tuning, there's plenty of talk of fine tuning in the physics literature and I think a way to ensure creationists don't own this topic is for scientists to address it. One way to address it, is to deny its there, and that may be a legitimate approach, another is to look for solution like inflation or other mechanisms. Personally, I am happy with either approach.
But I don't see how refusing to discuss it because creationists raise the issue, helps the scientific cause. If anything it makes scientists appear closed minded and it boosts the image of creationists ;I can easily imagine them saying :"see our arguments our so strong they won't allow you to discuss it".
If my only source for this claim was a creationists spreading misinformation, surely a physics forum would be the place to correct that misinformation, rather than refusing to answer the question.

 

[George Jones]

Where? Citation please.
This is especially important in this case because the phrase "fine tuned" is almost always from creationist literature so it is a "red flag" phrase: you can safely ignore anything these folks say about any kind of science.

Sorry, but you are very, very wrong here. The term "fine-tuning" often is used in the contexts of cosmology and quantum field theory/elementary particle physics. I have at least three graduate/research-level books (e.g., "Quantum Field Theory and the Standard Model" by Schwartz has a subsection with this title) here at home that use the term, and I probably have about a dozen in my office.

 

[windy miller]

Where? Citation please.
This is especially important in this case because the phrase "fine tuned" is almost always from creationist literature so it is a "red flag" phrase: you can safely ignore anything these folks say about any kind of science.
How we can reply to these kinds of questions depends heavily on the source.
ie. wikipedia talks about the flatness problem as a fine tuning problem for models of the early universe ... in which case I'd just direct you to a better description.

Again - where? Citation please.
Similar to above - the reliance on the number of decimal places can indicate a pseudoscience source (though folk like Feynman sometimes talks about the accuracy of QED in terms of decimal places when he wants to impress a lay audience with the accuracy and reliability of the theory). The number of decimal places depends on the units used to express something ... i.e. in unified units the speed of light is 1.000... to infinite decimal places. It is usually more useful to express the precision of something in terms of a ratio.Without the source it is impossible to tell if the two statements are talking about the same thing or not.

Consider the following lay description of the "flatness problem":
http://hyperphysics.phy-astr.gsu.edu/hbase/astro/cosmo.html#c6
... notice how the red-flag phrases do not come up in that article?
I suspect it will also answer your questions.

Reading your article didn't really help I am afraid. It seemed to just restate the flatness problem as the issue of the ratio of densities. But it does explain how this relates to the issue of the expansion rates.

 

[George Jones]

Expansion rate and density are related via the Friedmann equation, (8.36) in

http://ned.ipac.caltech.edu/level5/March01/Carroll3/Carroll_contents.html

This gives
$$\dot{a}^2 = \frac{8\pi G}{3} a^2 \rho - k.$$
Equation (8.40) gives
$$\frac{8 \pi G}{3} = \frac{H^2}{\rho_{crit}} = \frac{ \dot{a}^2}{a^2 \rho_{crit}}.$$
Combining these equations results in
$$\dot{a}^2 = \dot{a}^2 \frac{\rho} {\rho_{crit}} - k,$$
which gives
$$\dot{a}^2 = \frac{-k}{1 - \frac{\rho}{\rho_{crit}}}.$$
Consequently, fine-tuning the expansion rate $\dot{a}$ is equivalent to fine-tuning the ratio of the density $\rho$ to the critical density $\rho_{crit}$.

 

[windy miller]

Thanks, George, a reply that was actually an answer! Much appreciated.