We know from astrophysics that the cosmos expands, i.e. that all galaxies recede from each other. This fact is confirmed by observation. It can also be obtained as a solution of the Einstein equations.

Popular science literature often says that the expansion is due to the Big Bang explosion.

I consider such statements a simile but not a scientific statement. Because Big Bang is a limit point of the theory, and the theory finally breaks down when going backwards to the first split second. Hence Big Bang is a proper singularity of the scientific theory.

  • Do science or natural philosophy make any proposal concerning the driving force of the expansion?
  • Or shall we flag the question as being open and currently out of scope?
  • Or is the question ill-posed?

Note: Postulating the rebounce of a former universe is no explanation. It only shifts the problem.

Added: @Conifold pointed to the paper of Alan Guth Inflation and the New Era of High-Precision Cosmology. I learn from this paper that the theory of inflation makes a proposal for the cosmic expansion as being triggered by the short inflation phase. The latter is explained by the negative pressure of a hypothetical energy named "dark energy".

Hence inflation theory shifts the border of our present knowledge about cosmic expansion nearer to the limit point of Big Bang. Presently, inflation theory still has to leave open the question of dark energy and also of some primordial matter at the start of the inflation phase.

  • 1
    "Popular science literature often says that the expansion is due to the Big Bang explosion" - popular science literature (at least of the reputable kind) wouldn't call the Big Bang an "explosion". The Big Bang is in itself the expansion (someone has once said "Big Bang" is a terrible name for it, and "everywhere stretch" would be a more descriptive name).
    – NotThatGuy
    Oct 13 at 15:14
  • @NotThatGuy Equating Big Bang with the expansion itself, does it help to answer one of my questions?
    – Jo Wehler
    Oct 13 at 15:23
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    The "driving force" of the expansion now is not the Big Bang but dark energy. Dense plasma was driving it initially, during the inflation stage, and the theory does not break down there, it is well-understood and in agreement with observations. That the current theory breaks down at the initial singularity means that it cannot tell us what the Big Bang really was, but it does not mean that it cannot tell us that the dense plasma came from that, whatever it was. So saying "due to" or calling the Big Bang its "cause" is scientific enough, for pop-sci anyway.
    – Conifold
    Oct 13 at 17:53
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    @Conifold Dark energy seems to be not a valid explanation but an attempt to explain obscurum per obscurius. - Is the mechanism how dense plasma drives the inflation phase explained? Do you recommend a specific reference to understand how inflation theory works? – As long as the origin of the dense plasma and its energy is not understood, the origin of the spacetime expansion remains an open question. – Why not admit “ignoramus” also in pop-sci?
    – Jo Wehler
    Oct 14 at 18:44
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    Here is a pop-sci article from one of the fathers of the inflationary model Guth, Inflation and the New Era of High-Precision Cosmology, he also has a book The Inflationary Universe.
    – Conifold
    Oct 14 at 19:57

5 Answers 5


Some points to remember here:

The way we walk back through time to eventually get to the instant when the so-called Big Bang began is by mathematically raising the density, pressure and temperature of matter in the universe incrementally and seeing what happens. As we do this, matter melts into gas, then the gas molecules dissolve into atoms, then the atoms dissolve into subatomic particles, then those things dissolve into radiation, and so on. The rules governing that process are well-known until we get to a time slice of about 10^-40 of a second, and that's where we run out of predictive rules.

At present we have no knowledge of the physics involved at temperatures, pressures and densities higher than that, so the question is indeed out of scope. Lower than that, the driving force for the expansion is the energy contained in the pressurized stuff and the result is written in the laws of thermodynamics.

An excellent exposition of this, specifically including the break point where we run out of laws, is contained in Steven Weinberg's book The First Three Minutes.

  • +1 for the clear answer "out of scope"
    – Jo Wehler
    Oct 13 at 16:23
  • I'm waiting for the sequel: "The First Three Femtoseconds".
    – Scott Rowe
    Oct 20 at 15:20
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    @ScottRowe coming to a theater near you in a few attoseconds. Oct 20 at 17:44
  • Old joke: A man asks God, is it true that to You, a million dollars is like a penny, and a million years is like a second? YES. Can I have a penny? IN A SECOND.
    – Scott Rowe
    Oct 20 at 22:38
  • OMG scott, do you do stand-up? Oct 21 at 4:01

The scientific explanation for the expansion, such as it is, is split between (A) the theory of the unified inflaton field, which progressively decoupled from an electrogravitational to an electronuclear + gravitational to electromagnetic + weak nuclear + strong nuclear + gravitational state, and (B) the so-far-placeholder dark-energy thesis of today, according to which a not-well-understood amalgam of other energy types and/or at least a fifth energy/force (sometimes called by names such as "quintessence" or "phantom energy") is driving the accelerated expansion that began approximately five billion years ago.

Philosophically/metaphysically, we need to distinguish between passive- and active-time theories. In a passive/static time theory, time is like a container in which events are situated; according to an active theory, time has a positive impetus to it, which acts upon objects in space and fundamentally drives them "forward" in time, but which given spacetime unity then comes out to spatial motion also. Per Kant, if we can't resolutely attribute such an active power to time per se, we need to at least imagine a spatial concretization of time's geometric presence, like "particles of time." Hypothetically, these could even turn out to be what inflatons were, but as a novice physicist I wouldn't want to push that hypothesis too simply-and-strongly at this time(!). At any rate, if we think that the "size" of the necessity-of-the-past is a "real phenomenon" (so to speak), it is perhaps intuitive to correlate the expansion of the necessary past (a growing-block view) with an expansion of space, too.

But beware of novice physicists who claim to deduce obscure functions in such a manner ;)

Clarification: what does it take to "explain" a phenomenon scientifically? Let us suppose that a necessary (but hardly sufficient) condition is the identification of a function of which the phenomenon is an output on relevant inputs. With respect to spacetime unity, then, let us say that there is some function of time, to state-of-space outputs, f(t) = s. So at t = 0, the value of s, which corresponds to the extent of the expansion, would have been 0, or perhaps some other infinitesimal value, or 1/2, or the square root of 2, or whatever other value that the other equations would have fall out of themselves and their computation. Then at t = 1, we assume that s > f(0), and so on. Then the expansion of space is a function of the expansion of time, "but we are not done," of course.

  • 2
    I like your final caveat :-)
    – Jo Wehler
    Oct 14 at 17:27
  • @JoWehler is there any way to improve the relevance of my answer to your concerns? Should I format the links as a "Works Cited" list at the end or something? I don't know what I would respond with besides this information; I don't think almost any physicists pretend to know entirely how the initial expansion was even "possible," much less how it actually occurred (out of the myriad of theories). I do have a complex model involving negative temporal pressure and time-antitime particles that I've been working on, but I worry it would veer too close to pseudoscience for now... Oct 14 at 18:17
  • Don't worry :-) I think the paper quoted by @Conifold is helpful. At least to learn about the inflationary phase of the expansion.
    – Jo Wehler
    Oct 17 at 5:15
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    +1 for 'placeholder'. That is an excellent word and should be in bold before every use of "dark matter" and "dark energy". 'shrug' would work just as well. Part of knowing things is being transparent about what you don't know, not just pushing doorstops in place to prop up the theory.
    – Scott Rowe
    Oct 20 at 15:06
  • +1 For drawing out the explanatory nature of 'dark energy' particularly in light of the use of the language 'expansion' which isn't literal expansion since there is technically speaking nothing for the universe to expand into as required by the literal sense.
    – J D
    Oct 20 at 15:18

Science very clearly explains the expansion. If you have a huge amount of energy in an unconfined space expansion is inevitable. The physics of what happened shortly after the Big Bang has been worked out in a way that is self-consistent and consistent with other accepted results, so we can be reasonably confident about it. However, if you want to know what triggered the Big Bang, that is an entirely different kettle of aquatic vertebrates. Our trusted theories of physics give us insufficient guidance to allow us to work backwards beyond a certain point just after the Big Bang- we can only speculate about what might have happened before that point, if, indeed, the concept of 'before' makes any sense in that context.

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    Sentence 2 should read in an unconfined space? In a confined space, expansion is prohibited by definition.
    – g s
    Oct 20 at 17:14
  • @gs In the intuitional sense, you are right about 'confined space'. But our intuitions are the transitivity of volumetric containment which is Euclidean. Modern mathematical physics isn't a Euclidean geometry, it's much more complicated and built of combinations of geometrical systems. Consider the tensor can contain an infinite number of Euclidean vector spaces. and therefore one can have an expansion within the tensor but not necessarily of the tensor.
    – J D
    Oct 20 at 18:14
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    @g-s mea culpa! I will fix it, Oct 20 at 19:07

How to explain the cosmic expansion?

I'm going to explicate Conifold's reference a bit because while he provides the theory that claims to explain (which is physics proper), he doesn't address the how or the why of the explanation (which is metaphysics proper). The TLDR of the question of 'how to explain' is using instrumentalist reasoning consistent with the edifice of the contemporary paradigms of mathematical physics. Let's explore the current scientific methodology for generating scientific explanation of this sort.

is the question ill-posed?

Absolutely not, because the heart of science is providing explanation, but explanation like causality is a metaphysically challenging topic. Just as one can reject causality as a linguistic fiction of highly probable correlation (See Judea Pearl's work on Causality for a detailed mathematical treatment of causality), so too it begs the question 'is an explanation real in any sense beyond it can be experienced and if so how and why'.

Do science or natural philosophy make any proposal concerning the driving force of the expansion?

Conifold has directed you to dark energy and dark matter conceptually. But is dark matter explanatory and if so, in what way? Does it fit Hempel's deductive-nomological structure? Are there statistical formulations of it as in causality? Is the primary method to explain 'expansion' by causal claims? This is where the philosophy of science has to earn its paycheck.

It's easy to point to 'dark matter' as an explanation for the dynamics of 'expansion of the universe', but all sorts of philosophical questions arise. But is such an explanation scientific, and if so, how do we know? How can a universe expand if by definition there is nothing beyond the universe to expand into? How can dark matter be matter at all if it can't be detected? And how does something that seems to have no physical existence directly or indirectly observable explain something that linguistically can't happen. Enter in mathematical physics.

Since the quantum revolution, what has become apparent is that the explanatory function of science has taken on two forms, one that is realist and one that is instrumentalist. Therefore since cosmic expansion is a mathematical model of the universe, to explain it is to explain the mathematical concepts that drive the 'expansion'. A blueberry muffin in an oven is but a model to simplify understanding the mathematics of expansion by appeal to intuition.

Newton's law of gravitation is at the heart of explanation of the effects of gravity, and the relative acceleration of the rate of velocity in the expansion of celestial bodies relies on the fact that acceleration is defined in terms of both mass and force. So, if the universe is expanding and doing so with acceleration and gravity, there can only be one cause of this: mass. Yet, that's problematic because no such mass seems to have been observed to cause the acceleration. Therefore, physicists find themselves in a bit of a contradictory situation. On the one hand, only mass can explain the acceleration, and yet there is no observation of this extra mass to do so. Something has to give.

Physicists simply become philosophers and embrace a new ontological commitment. They engage in semantic ascent and perform existential quantification. They declare 'there is extra mass' (which is energy which is matter by the mass-matter relationship and the mass-energy equivalence Einstein put forth) and label it "dark" and unobservable. Then they get busy trying to use the mathematical model of the standard particle model to try figure out what it means mathematically to be dark matter or dark energy. The details of which are physics and not philosophy.

So, you asked:

How to explain the cosmic expansion?

To a philosopher of science, then, what is of interest here is not so much the answer physicists have cooked up, the dark matter and energy (which are arguably empirical only through a convoluted notion of empirical), but the methodology. Thus, how to explain cosmic expansion is to define it mathematically to align with observations, reason about the causes of the acceleration of bodies using Newtonian laws and GR, and then create a new entity de novo, an alternative to classical notions of matter and energy. This is the actual how of scientific explanation in contemporary mathematical physics that astrophysicists use, and therefore can be shown to be consistent with the various scientific methodologies and methodological naturalism philosophically.

  • I like the well-structured form of your detailed answer. From the viewpoint of natural philosophy, you offer plenty of criteria and comments on the current state-of-the-art how astrophysics deals with the question of cosmic expansion. Concerning several points from your answer I am a bit sceptical. - But the amount of space admitted to a comment is not enough to deal with all points. If you are also interested in the subject, what about breaking up your comment into several separate questions? Then we could discuss each point in more length. (1/2)
    – Jo Wehler
    Oct 20 at 18:40
  • Let me just mention one point: dark energy is a hypothetical energy which generates a negative pressure(!). From a relativistic point of view, it is not enough to argue with energy or mass in separation. One has to combine energy, momentum and pressure into the physical quantity named energy-momentum tensor. Then a repelling negative pressure can counteract the attracting positive gravitational mass. The net-effect can be an expansion. (2/2)
    – Jo Wehler
    Oct 20 at 18:42
  • @JoWehler As I'm am always striving to ferret out irrationality in my position, and that I would love to find consensus between our positions where you are skeptical, it seems to me that the best method to close our metaphysical differences, indeed, would be a series of questions where you have concerns.
    – J D
    Oct 20 at 18:42
  • On the details of expansion, I would suggest that my answer is an oversimplification that pays short shrift to the intricacies of the actual technical requirements of the argument. :D I'll read the paper Conifold cited if you have a particular bone to pick deriving from claims I've made here and address any perceived problems after coming to grips with the author's language.
    – J D
    Oct 20 at 18:45
  • @J D A good entry points seems to be in Guth's paper at p. 33 the section "The Inflationary Universe (Pressure of the False Vacuum)". He explains: "The negative pressure of the false vacuum, therefore, creates a repulsive gravitational field, which is the driving force behind inflation."
    – Jo Wehler
    Oct 20 at 18:54

D1 = (90/360) * 2 * pi * 1 = 0.5pi

D2 = (180/360) * 2 * pi * 1 = pi

D3 = (90/360) * 2 * pi * 2 = pi

D4 = (180/360) * 2 * pi * 2 = 2pi

D2 is twice D1 and D4 is twice D3 i.e. D2/D1 = D4/D3 = 2. In other words if the distance between two points (A and B) on a circle is n times the distance between two other points (C and D) on the circle, the new distance, if this circular 1D space is expanding/inflating (increasing radius), A'B' is n times C'D'. These points are galaxies and further the galaxies are, the faster they recede from each other.

In my rudimentary mathematical experience, this is the only mathematical object I could find that models cosmic expansion/inflation.

Two points A and B are n units apart.

Two other points C and D are mn units apart.

The universe expands ...

The new distance C'D' = m(A'B').

CD/AB = C'D'/A'B' = m

It's a dilation transformation, I think. We could be in a spherical universe 😁😁

  • Let's run away from each other and see if we eventually meet up again :-)
    – Scott Rowe
    Oct 20 at 15:17
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    @ScottRowe, let's 😀 Oct 21 at 3:30

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