The flatness problem

I am doing a reasonable amount of reading in inflationary cosmology at the moment, thanks to a talk I went to with a German Dr of Cosmology last week – so thought that I would write something in this area. One of the catalysts for the recent(ish) interest in inflationary universe theories was the very old flatness problem. The reason I say ish, is because this is an area that has been pondered by the giants of cosmology for many decades – but really the acceptance of the theory as mainstream is a little more recent.

There always have been a number of issues with the traditional big bang theory, however the ability of the model to describe the world around us often led to these little issues being ignored. One of the biggest senses of unease with the model is the fact that the conditions needed to create a universe with the mass density we have are so finely tuned the idea that this just happened by chance seems a violation of the logic which has seen us discover so much. Indeed a flutter away from this magic number of a tiny magnitude brings us to some fairly outstanding results, when magnified over the scales of interest in cosmology.

Now let me begin by noting that the universe is expanding – hopefully this is something you are familiar with. In fact we can be a little more rigorous and say the universe is homogeneously expanding. What does that look like?


Just pay attention in the above diagram to the sphere – what you can see is that the sphere has increased in volume in the same proportions. Now conceptually the important thing to realise is that the sphere isn’t expanding into anything – what is actually happening is that space and time itself is expanding. The sharp minded might ask if that means they are too expanding – if the spacetime they occupy is expanding – and in short, no because you are held together by forces (some of us weaker than others!). So when we say that the universe is expanding, what we mean is if we were to pick two points in spacetime, for example two galaxies, then the distance between these two galaxies is increasing because the spacetime itself is increasing. If thinking about this kind of stuff does not bring you great joy, we should not drink together. Considering the universe, staring into space and wondering why and how is the most human endeavour there is – something which I guarantee your ancient ancestors did.

Okay great so we have an expanding universe but what on Earth is flatness and why is it a problem. To address this we need to define three types of universe – and they really are quite simple. The first is called an open universe, the second is called a closed universe and the final is called a flat universe. In the open universe model the universe expands for ever and ever and eventually the galaxies become so dispersed from each other and all the lights go out and the universe becomes cold. The closed universe however is a different model. In this model, like throwing a ball in the air the acceleration decreases and decreases until it stops and then contracts back in on itself due to the gravitational lure of the matter within. The final type? Well it is fairly obvious I hope – the flat universe is the middle ground. In this model we have the expansion decreasing asymptotically to zero – hence effectively the universe stops expanding.

Now the rate at which inflation increases depends upon the mass density within it. Clearly  the density of mass also has a profound impact on the strength of the gravitational force – so really it is the matter distribution which is the crux of the critical value – the value at which we live in a flat universe. The value Ω is used to denote the actual mass density divided by the critical mass density – so clearly a value of 1 here corresponds to a flat universe. Efforts to calculate Ω for our universe have put it anywhere from 0.2 up to 2 (and I have read other amounts from other sources) – but the value isn’t that important to the problem. The problem is, when you smooth little movements in Ω out over the entire cosmic history (we know we have 13.82bn years right now for starters) the magnitude of any differences give an Ω value very different to our own. Take a look at this graph, from Alan Guth –

Screen Shot 2016-05-28 at 14.33.27

If you are finding this article interesting I recommend you read Guth’s legendary book here. I am currently reading it and it is thrilling – Guth is the father of many inflationary theories and has a wonderful lecture series from MIT Openware available on YouTube. Guth answers the flatness problem, along with many other holes in the Big Bang theory.

Anyhow we digress – the point is this – in order to achieve a value of Ω that is even remotely close to any of the estimated values we have today the universe must have been very close to the flatness critical value – why? Dicke was the first person to point this out – the fact that if we can have any Ω, which we can – it should really only be in mathematical construction we have one so close to 1 – it is just too improbable. The values of Ω one second after the big bang in that graph can only differ by and order of 10 to the -16! This is an astounding result which led, eventually, scientists to look for a better reason as to why the universe is the way it is. It had to be one that incorporated elements of the big bang, which it does but also allowed for things to be created from effectively nothing and explained the flatness problem. It also needed to overcome the other big issue with the big bang, which is the homogeneous nature of the universe.

This is why inflationary theory was born and to date is the most accurate and compelling pieces of evidence we have for the formation of our universe. If I have not convinced you already – it contains multiverses. Does not get sexier than that.

13 responses to “The flatness problem

  1. I have been watching some programmes about cosmology quite recently and in all of them they stated that we are living in the open universe. So it is very interesting to learn that the science is still not sure about it.

    Liked by 3 people

    • We do not know that yet – although the future is not brighter if we live in an open or a closed one if I am honest! We know so much about cosmology – but at the same time we have so much ground to cover. To be fair to the cosmologists – it’s a tough gig

      Liked by 2 people

  2. Innocent thought provocation from worst through best…

    In a purely energetic universe demonstrably without any pure linearity, how can it possibly remain linearly flat in terms of inflation stoppage?

    Also (memory serving), I believe prominent minds (e.g. Dr. Brian Greene) are looking for signs of our universe interacting with other universes to verify multiverse theory, but I’m curious about your input on this front.

    Dark energy demonstrates an acceleration to universal expansion, so am I right to assume (given the impossibility otherwise) flatness is achieved by a diminishing of that mysterious form of energy? If so, is there a basis for that diminishing effect?

    Given the highly energetic nature of our universe and all of the wild coloration (style, etc.) of energy formations resulting from it (including roughly many millions of living species here on Earth), my hypothesis is the relative simplicity of observed inflation over billions (and apparently ultimately trillions) of years is likely to often encounter a high degree of the ‘devil in the details’ effect where an unimaginable number of factors impact inflationary results and universal shaping overall (inclusively within a universe where scientists have not firmly established the total number of dimensions — although it apparently has to be more than 4). In short, “hold on tight”, humanity.

    In the simple name of my curiosity, is any of that addressed in Dr. Guth’s book?

    Liked by 2 people

    • To be clear the inflation never actually stops in a flat universe – the inflation just decreases and decreases in rate until it is effectively zero. It sounds really fancy, but it isn’t it is actually just a very finely balanced equilibrium.

      The multiverse theory isn’t really a theory in its own right, it is more a direct consequence of the emerging theories around the creation of our own – and the fact that if we believe a certain set of conditions created our own then we accept that the law of probability makes it increasingly unlikely that we are in the only universe. That said – I think we are a long way off looking for signs and the most fruitful methods of progression (which I believe Greene is doing) is to bottom down how this one happened and see if it is logical and correct that there can be other universes.

      Is your hypothesis that there is no distinction between mass and energy within the universe? If so this is mainstream science and something that is very well proven you will be pleased to know!

      As to the devil in the detail – you are right in a sense, because that is the whole crux of the argument. The smallest of changes can result in the largest of errors – and even though we cannot calculate omega to any high level of accuracy, because of this detail issue – what we can say is that we MUST of had a value very close to the holy 1 value to be anywhere within range of what we see today.

      As to what you will find in Guths book – it depends on how much you already know – which I am not sure. Are you a Physics student? If you have sat college level cosmology you might find it interesting but only in a biographical sense. However if you don’t have any formal Physics training I would say it is a marvelous journey of discovery from a man who understands the universe frighteningly well.

      Thanks as ever for your comments – I love to bounce ideas around!


      Liked by 1 person

      • My scientific credibility comes from being an entertainer (yes, I’m being facetious) — but I’m passionate about the scientific method (for over two decades) at its most fundamentally logical level (and love testing my understanding here), because I believe I’ve authored a totally grounded and complete theory of everything “beneath” the complexity of math (albeit nicely fits with literally all well-established science — obviously including that math).

        The absence of a distinction between mass and energy is not my hypothesis.

        The absence of distinction between space and energy is my (apparently unique) hypothesis.

        Since no objective distinction has ever been discovered (please verify, but I remain humbly confident here due to blurry particle distinction), logic suggests that space is energetic, so its properties (obviously including dimensionality) modulate in all possible ways.

        Based upon the apparently non-energetic application of space (e.g. as carefully needed to fit relativity and quantum mechanics — 11 dimensions in M Theory — as opposed to a much (much) higher number of dimensions given apparently oceanic spatial modulating possibilities), I believe scientists are not yet seeing the dimensional complexity needed to mathematically reach the location of dark matter (and gravitons in general), dark energy, where virtual particles come and go, the ability to dive deeper into the digitally quantized edge in a reality energetically incapable of actualized/pure linearity, and anything else offhand that my morning state is preventing despite some caffeine kick-in.

        Science expands understanding with the human vicinity as its source.

        My theory (Reality Waveform Theory) is logically sourced at the base of reality itself and reaches “up” to connect with that science — but it concludes no objective distinction exists, so reality is purely physically energetic — e.g. science is energy, so scientific distinction must be taken less seriously (challenging due to distinction being needed for scientific leverage) to increase human understanding.

        This comment is long, so I’ll basically stop here, but I hope you don’t mind that I bounce my logical view around here sometimes when fitting.

        If my theory is wrong, then so be it, but so far, I’ve seen nothing in science that debunks it (quite the contrary).

        In reference to your post, I want to be the guy that you could respectably have that drink with (although a big “pond” apparently challenges here), but not the guy that drives you to drink (so always keep it real/objective — I condemn pseudo/junk science).

        Liked by 1 person

      • I don’t think the hypothesis is wrong or indeed misguided, I think it is a question of if you believe that dark energy is something within space – and at which point the space remains “empty” and you have difficult to detect matter within it – or if the dark energy is a part of the space itself in which case energy and space have an equivalence which is outside the realms of modern Physics and the laws we know and would represent the largest paradigm shift known. I agree entirely that there is nothing in science that can debunk your view, because in truth if it is correct we do not have and idea how to look for it. We will get there but we would need centuries of advances (I predict). Currently we are best at looking at what we know best – trying to find a particulate version of this hidden mass/energy that has been evading us.

        I fear that neither of us may see the answer to this question in our lifetimes – but I will do my best. I give myself around 60 more years on Earth, which is in human terms quite a long time.

        And I would happily have a drink with you!

        Liked by 1 person

      • “…or if the dark energy is a part of the space itself in which case energy and space have an equivalence which is outside the realms of modern Physics and the laws we know and would represent the largest paradigm shift known.”

        Is there anything mathematically preventing a space to energy conversion equation similar to the very popular mass to energy one?

        In other words, how is space mathematically factored in these days? Am I right to assume that’s a loaded question?

        I’m not a mathematician (which is frankly a bit frustrating), but if I were a physicist, your words starting this comment would be my guiding light, and I would be looking into the mathematics of space as compared to that of energy to mathematically bring out a more energetic quality of space.

        If ‘spatial energy’ (if you will) can be mathematically established, then energetic (apparently oceanic) dimensionality likely greatly increases the energetic range of math to preferably illuminate (perhaps many) more directions towards mathematically revealing those currently hidden energy constructs (e.g. dark energy).

        Another area I would consider adding to this scientific pursuit is leveraging the brilliantly successful wave function in quantum physics with respect to spatial formation.

        If I could only choose one math function to understand, the wave function would probably be it. Would you be interested in authoring (and your audience interested in reading) a post on that function, or have you already authored such a post?

        Bottom’s up!

        Liked by 1 person

      • It is hard to really say if there is anything mathematically preventing something that we cannot currently comprehend. It is a bit like the situation in which Newton had to invent the mathematics, because if at the time you asked if there was anything mathematically preventing certain phenomena requiring integral calculus it would of been quite difficult.

        That said there is increased interest in looking at the vacuum – the inflationary universe touches on vacuum fluctuation and the fact that it is possible to create a seemingly large amount of energy from “nothing” due to the cancelling effects of negative gravitational energies.

        The wave function is certainly a good topic for discussion and one that I will look to once I have finished refreshing myself on certain areas – I am currently working through important areas of the Feynman lectures which includes wave functions.

        Have you considered getting some wither formal or informal Physics and Mathematics training? You interest is clearly there it seems a shame not to channel it.

        Liked by 1 person

      • Creating and/or adapting math involving space and energy to find a conversion formula similar to E=mc2 is apparently a doable (and worthwhile) goal in the mathematical community.

        As a busy entertainer, entrepreneur, technologist, and personal caregiver (with many more other tasks on my now middle-aged plate), I have to be careful and creative in my expansion of scientific understanding.

        Many years ago, after seeing the Elegant Universe and other surface level documentaries, I watched the Cassiopeia Project videos, which (frankly after seeing them multiple times for mental grasping) took me a level deeper into understanding many scientific areas, including the very basics of the Feynman diagrams and other areas of physics, chemistry, biology, and cosmology.

        My next level will be to pinpoint a fitting mathematical entry point (e.g. learn what I can about wave functions —, study other relevant Wikipedia entries and videos, and engage on blogs such as yours (please let me know, if you believe there is any other blog(s) that fits my basic scientific level and interest).

        I already tried to focus on math.

        Due to the logically purely sinusoidal reality (think Fourier analysis, etc., in a purely energetic reality), my initial focus was on the sine wave function in trigonometry, because reality is apparently the output of that function seamlessly feeding the input of itself (albeit in all possible ways due to objectively shapeless nature of sine waves without perception — basically think an infinite number of such ways — so a dead end on this front).

        I don’t know how (or if) the sine wave function fits in the wave function (my educated guess is it must be inherent within that latter function).

        Anyway, my mathematical pursuit so far has been terribly weak due to my busy status elsewhere.

        In short, I need to focus most strongly upon my natural ability (raison d’etre) in entertainment (specifically audio), but leverage that ability to (preferably inspirationally) interact with scientists basically the same way they leverage entertainment to engage the public.

        Bouncing my logical thoughts in your comments section has already helped me.

        I’ve cleared out some of my RSS feeds to make room for reading other material (e.g. I’ll be reading your blog more frequently).

        I believe observation/perception is energy, and the shape of that energy is the shape of reality (observation is an energetic lens).

        Relative to humanity, there are dominating currents of observation, and those have been (and are being) successfully mapped to mathematical frames.

        If scientists can figure out how to leverage distinction without taking it too seriously (which they’re already apparently doing via the uncertainty principle), understanding the growing human reach of waveform mathematics logically should come to light and seriously break humanity free from the many obstacles preventing a stronger scientific advancement.

        Overall, we’ll just naturally experience where the energetic currents modulate us all.

        I believe it’s safe to say that it promises to be an interesting ride for worst through best.


  3. Pingback: News and Events June 22 – Adventure and Business·

  4. Pingback: It’s a coincidence, right? | Rationalising The Universe·

  5. Pingback: It’s a coincidence, right?·

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s