What does the cosmic inflation theory actually say about flatness?

[overzealous]

TL;DR Summary

A question has arisen in my mind about what cosmic inflation actually predicts about flatness-- actual perfect flatness or merely its appearance.

I just read an article by Natalie Wolchover (a smart and knowledgeable writer as far as I can tell) in Quanta about the new analysis supporting a closed universe. In the article she makes this comment, "The leading theory of the universe’s birth, known as cosmic inflation, yields pristine flatness. And various observations since the early 2000s have shown that our universe is very nearly flat and must therefore come within a hair of this critical density — which is calculated to be about 5.7 hydrogen atoms’ worth of stuff per cubic meter of space, much of it invisible."

Prior to reading that comment by Natalie, my understanding was that the idea of cosmic inflation occurred to Alan Guth to account for several characteristics of the universe that we observe today, including its APPARENT flatness, i.e. to have the universe expand so exponentially in the first instant that all the otherwise puzzling features we currently observe could be neatly explained: its homogeneity, its isotropic appearance, as well as its flatness. The idea regarding flatness was simple-- inflate a basketball to unimaginably enormous size and its curvature will no longer be perceptible. But it still will be curved. I thought that's all that inflation was saying about the universe-- not that what Natalie Wolchover calls 'pristine flatness' would be a result. 'Pristine flatness' seems to be indicating that the cosmic inflation theory predicts PRECISE flatness, whereas I thought that it simply accounted for the APPEARANCE of approximate flatness while by no means asserting any sort of ideal, perfect flatness was necessarily the case.

Please clarify whether a theoretical consequence of cosmic inflation is perfect flatness. And if perfect flatness is not a theoretical consequence, and if the universe turns out to be in fact perfectly flat after another thousand years of increasingly accurate measurements, does that mean that we need a new theory in which perfect flatness IS a theoretical consequence?

 

[PeterDonis]

I just read an article by Natalie Wolchover

What article? Please give a link.

in Quanta

Which means it's not an actual peer-reviewed paper, it's a pop science article. So it's not a good source if you want to actually understand what the science says.

In the article she makes this comment, "The leading theory of the universe’s birth, known as cosmic inflation, yields pristine flatness

If by that she actually means exact flatness, no, that is not a prediction of inflationary models. They only predict what you are calling apparent flatness. More precisely, the models have key parameters adjusted (the main one being the number of e-foldings that happen during the inflation phase, i.e., the factor by which the universe expands exponentially) in order to ensure that they predict a high enough degree of flatness to be consistent with our observations. Then other predictions of the models are checked against data for consistency.

 

[overzealous]

Thank you Peter for your response-- I suspected that perhaps Natalie should not have chosen the word 'pristine', given its implication of perfection. Now could you try your hand at my closing question: "And if perfect flatness is not a theoretical consequence, and if the universe turns out to be in fact perfectly flat after another thousand years of increasingly accurate measurements, does that mean that we need a new theory in which perfect flatness IS a theoretical consequence?" Let me add that it seems impossibly coincidental for perfect flatness to occur by chance, and not be mandated by a theory. Don't you think?

Oh, and here's a link to Natalie's article-- https://www.quantamagazine.org/what-shape-is-the-universe-closed-or-flat-20191104/. Yes, it admittedly is what you disparage as 'pop science'. But if it weren't for pop science-- especially the kind that appears in Quanta-- the general public (and that includes me!) would be even more abysmally ignorant about science and mathematics than they unfortunately are! In the spectrum of pop science and math, Quanta is a gloriously radiant ultraviolet!

 

[PeterDonis]

if the universe turns out to be in fact perfectly flat after another thousand years of increasingly accurate measurements

No matter how accurate our measurements get, we will never be able to conclude that the universe is perfectly flat. Concluding perfect flatness would require infinite accuracy of measurements, which is not achievable. Some departure from flatness will always be within the error bars of our measurements.

it seems impossibly coincidental for perfect flatness to occur by chance, and not be mandated by a theory

This sort of reasoning is very chancy. The universe does not have to respect our human intuitions for what seems "impossibly coincidental".

 

[Orodruin]

does that mean that we need a new theory in which perfect flatness IS a theoretical consequence?

No. You can never establish that the universe is perfectly flat for a number of reasons. Hence, you can never completely rule out a small deviation from flatness.

We also just had a thread on this subject.
https://www.physicsforums.com/threads/does-euclidean-geometry-require-initial-fine-tuning.979189/

 

[overzealous]

Orodruin and Peter: I recognize that, of course, technically a determination of perfect flatness can never be established by mortal man, so let me rephrase it. If there's an unbroken string of ever tighter constraints that are aymptotically approaching perfect flatness, I think every astrophysicist worth his salt will begin to suspect that the measurements are being driven by a law of nature, even if they haven't yet figured out what that law is.

Orodruin, Peter, I recommend that you read for enlightenment on this subject not a physics book but a very amusing short story called "Inflexible Logic" by Russell Maloney. [You can find it in a wonderful old volume, A Subtreasury of American Humor.] In the story, a fellow with a lot of time on his hands and even more money in his hands decides to empirically test the popular saying that a hundred monkeys randomly striking the keys of a hundred typewriters will eventually produce flawless copies of every book in the British Museum. But in the story, the hundred monkeys start producing flawless copies right from the start-- not so much as a comma is out of place in any of the volumes they type.

And the fellow who sponsored this experiment enjoyed reading the naughty parts that had been expurgated from his copy of Samuel Pepys' diaries that he had at home. And that's my point-- after checking a large amount of the monkeys' output and finding it impeccably reproduced the works in question-- with not a single mistaken letter or punctuation mark!-- he came to feel he could rely on the fact that the 'naughty parts' of the Diaries typed by the monkeys were real, even though he couldn't check those parts. And, analogously, I think that after a thousand years and a hundred experiments that ever more narrowly zeroed in on perfect flatness for the universe, I think physicists would come to feel that they could rely on the fact that perfect flatness was real, even though they could never absolutely prove it. And realize that a theoretical explanation for perfect flatness was demanded.

 

[Orodruin]

Orodruin and Peter: I recognize that, of course, technically a determination of perfect flatness can never be established by mortal man, so let me rephrase it. If there's an unbroken string of ever tighter constraints that are aymptotically approaching perfect flatness, I think every astrophysicist worth his salt will begin to suspect that the measurements are being driven by a law of nature, even if they haven't yet figured out what that law is.

I recommend that you read the other thread.

 

[timmdeeg]

I just read an article by Natalie Wolchover (a smart and knowledgeable writer as far as I can tell) in Quanta about the new analysis supporting a closed universe.

This was discussed here

https://www.physicsforums.com/threads/the-universe-is-now-closed-and-curved.980068/

 

[Orodruin]

If there's an unbroken string of ever tighter constraints that are aymptotically approaching perfect flatness, I think every astrophysicist worth his salt will begin to suspect that the measurements are being driven by a law of nature, even if they haven't yet figured out what that law is.

Also, let us remember that this already happened. The resulting theory is called ”inflation”. I do not think you have grasped how unobservably close to flatness that inflationary models can drive you. So close in fact that the issues mentioned in the other thread means you can practically never tell the difference.

 

[PeterDonis]

I recommend that you read for enlightenment on this subject not a physics book...

This is a physics forum. We do not discuss philosophy or personal opinions here. That doesn't mean you can't have them, it just means we don't discuss them since they're not physics.

Thread closed.