Five hundred years ago, Nicolaus Copernicus proposed that the Earth might be one of several planets orbiting the Sun, rather than the centre of the universe. He compared the geocentric model to a monstrous form assembled from parts of different bodies, like the Creature Mary Shelley brought to life three centuries later in Frankenstein — each part appearing human on its own, but as a whole a grotesque patchwork.
The geocentric model was built to directly match the sky: where a planet paused against the background stars and looped into retrograde, a dial was added so the planet would pause in its orbit around the Earth and loop backwards a while before resuming its normal course. In contrast, Copernicus recognised that the outer planets — Mars, Jupiter, and Saturn were known at the time — might enter retrograde loops due to parallax, their apparent positions shifting relative to the background stars as our orbit brings us near and then we pass them on our way around the Sun.
Copernicus had no idea of the physics that Isaac Newton or Albert Einstein would eventually use to explain planetary motion. Nor did he imagine this motion resulted from the same phenomenon that causes apples to fall from trees, or paths of light to bend around the Sun. His model ended up with as many knobs and dials as the geocentric system due to his use of circles rather than ellipses to describe orbits.
Even so, Copernicus recognised that a Sun-centred theory afforded the possibility that it might eventually explain why phenomena like retrograde motion should appear as they do to us, despite the planets’ motion being continuously in one direction only. And in doing so, he paved the way for others like Newton and Einstein, who later fleshed out both the underlying concepts and formal mathematical descriptions of a solar system in which planetary motion is expected to appear with all the complexity we observe.
In hindsight, the discovery Copernicus’s proposal prompted was that broken symmetries — our off-centre perspective from a planet orbiting the Sun, and the non-uniform motions of all planets including ours — would complicate appearances within an ontological framework that is nonetheless simpler.
In a similar sense, it may be argued that the standard cosmological model today — which gives an accurate description of phenomena but is nevertheless an amalgam of ad hoc patches, each inserted to unnaturally force the evolution of a universe that is otherwise expected to be different from the way it appears — bears a closer resemblance to Frankenstein’s monster than it does the simple explanations of planetary motion given by Newton and Einstein. For despite all the dials and knobs that have been added to ensure the standard model does directly resemble appearances, after a century of development it still affords no explanation of why our universe should be expected to expand, as it appears to do.
Why should our universe expand?
In the Copernican tradition, we ought to ask why our universe should expand. The standard cosmological model affords no such explanation. It is based on a principle, famously promoted by Einstein together with his colleague Willem de Sitter, that characterises the universe as expanding in spite of a tendency to decelerate because it is filled with everything we see. This is important: according to the basic Einstein-de Sitter framework for describing cosmic expansion, all the galaxies and light we see across the universe are thought to work against the universe’s expansion, slowing it down; and anything driving expansion is an ad hoc dial we’ve added so that base model fits appearances better than it naturally should.
In fact, this tendency for light and matter to slow cosmic expansion mathematically blows up to an infinite amount at the Big Bang. Therefore, the model’s only “explanation” for why our universe even could be expanding today is that it began with such a tremendous rate that momentum carried it against its natural tendency towards the opposite. For this reason, a century ago British astronomer Arthur Stanley Eddington complained of the Einstein-de Sitter model that would dominate twentieth century cosmology, “One cannot deny the possibility, but it is difficult to see what mental satisfaction such a theory is supposed to afford.”
Much like its Ptolemaic predecessor, this model has since been augmented with various features allowing it to fit the data with impressive accuracy. First, there is an inflationary epoch, thought to have occurred a moment after the Big Bang, which would drive a fleeting period of exponential expansion and erase several tensions the Einstein-de Sitter model otherwise leaves unresolved — though leaving the initial expansion problem untouched. Then for a long while the universe is thought to have decelerated, its slowing rate driven primarily by radiation in the early universe followed later by matter, in good alignment with Einstein-de Sitter. Finally, after several billion years a component we’ve come to call dark energy, which does tend to drive expansion, is thought to have become significant enough that the expansion rate eventually began to accelerate.
In comparison with the Ptolemaic model, both inflation and dark energy are similar to the eccentric and equant: later patches, added to a universe filled with the stuff we observe directly, that enables us to describe the universe we see in spite of the fact that without these patches the more basic physics suggests the universe should not evolve as it appears to do.
A bare Einstein-de Sitter universe should not appear the same in different regions of the sky that could not have interacted before the times we now see, due to the finite speed of light. And such a universe should not appear spatially flat, as ours appears to be. Inflation is the dial we use to fix both of these problems.
An Einstein-de Sitter universe also should never come to expand at an accelerating rate as we’ve observed — let alone expand to start with. Dark energy fixes the former issue, but its effect is null at the Big Bang and only gradually becomes significant over billions of years, so it cannot explain why the universe should ever have expanded in the beginning. And inflation can only happen within an already existing, expanding universe — so invoking it as the primary cause would be tautology.
More recently, two separate cracks have opened in the dark energy patch. There is a persistent and growing tension between the expansion rate measured from the early universe and the rate measured from the late universe, which a cosmological constant does not reconcile. And independently, large surveys of galaxy clustering and supernovae have been read as favouring a dark energy that weakens over time rather than holding steady. So astronomers have proposed evolving dark energy models, adding an evolution dial to a source of repulsion that was never explained in the first place.
When an ad hoc patch needs its own ad hoc patch before a model that fundamentally abhors the phenomenon it is intended to describe can be brought in line, that should be a strong sign that the base model is wrong.
Symmetry breaking and physics
In light of the problems the standard cosmological model has with reconciling the evidence and providing an explanation for the world we seem to live in — the growing number of knobs and dials to recover a phenomenologically accurate description of a universe that is nonetheless fundamentally expected to be different — we ought to take a page from Copernicus and ask what symmetries we may be assuming are fundamental, which our reality may in fact essentially break. We should ask what appearances we see that may not directly represent the world that is, but which may instead only appear as such because our place in the universe is not central, so our perspective is owed in part to a broken symmetry.
This is not idle speculation. In essence, physics is an exercise in recognising the various forms in which symmetries are broken in nature. By this, I mean generally any phenomenon that removes a degree of symmetry within the natural world.
For example, because the Sun spins, it is wider around its equator. The Sun breaks one dimension of symmetry by spinning around an axis, and causes an equatorial bulge we can measure. And by measuring the Sun’s rotational rate and the size of its equatorial bulge, we can estimate other physical properties that are more difficult to measure, like its density profile.
Or imagine that the Earth was at the centre of everything, and we were orbited only by the Sun which moved in a perfect circle around us, and that the sky was perfectly uniform with no randomly scattered stars across it. In this case, the only broken symmetry we could reference in our sky would be the Sun itself. We would still have day and night. The sky would still be brighter as we look closer to the Sun. In this case, we could build a model to describe the Sun as orbiting the Earth once a day, at a fixed distance from Earth.
But with no other symmetry breaking to worry about, we could equivalently describe the Earth as spinning around once a day while the Sun remains fixed in place. In fact, if all else were the same but it was really the Earth orbiting a fixed Sun, still in a perfect circle, we could not tell the difference from the moving Sun picture. Due to unbroken symmetry, either description could be used regardless of what is really going on.
But now consider our reality. Since the Earth follows an elliptical orbit rather than a circular one, careful measurements show that the Sun grows and shrinks in the course of a year. The model that describes the Sun as orbiting around the Earth once a day has no mechanism for the apparent growing and shrinking of the Sun annually, so we would have to add another dial that makes it move outward for six months, then in, as well as orbiting once a day. In contrast, an elliptical orbit of a spinning Earth has the same effect. Each model here has two dials to represent two broken symmetries.
But then, because the sky is filled with recognisable patterns, the Sun not only appears to grow and shrink, but also appears to follow a circular path against the background stars as it grows and shrinks. Now, if we want to use the geocentric model we need a third dial to spin the stars around at a rate that matches the Sun’s daily rotation almost exactly, but which is mismatched by about a degree per day so that in 365.25 days (per year) the Sun appears to follow a 360-degree circular path against the background stars.
In contrast, the Sun-centred model with fixed stars and Earth both spinning daily and orbiting the Sun on an elliptical path needs no extra dial to capture the Sun’s apparent annual orbit, as measured from Earth, with respect to those background stars. It’s already baked in, so the Sun-centred model achieves the same with two dials as the Earth-centred model achieves with three.
Adding in the planets with their retrograde loops, we find more of the same and the disparity between extra dials with the geocentric model grows and grows, while the broken symmetry of our own off-centre position in the Sun-centred model relative to our Earth-centred observing platform continues to do the work of reconciling the apparent phenomena with a minimal set of dials.
And Copernicus’s great contribution, as noted above, was in recognising that the Sun-centred model had the capacity to achieve with fewer dials what the geocentric model required in abundance. He did not figure out the actual dials and the physical framework needed to do the work: all of that was found over the next century, by people like Thomas Digges, Johannes Kepler, and Galileo Galilei, who recognised Copernicus’ push for logical parsimony as a mark in favour of his proposal. And the physical context and minimal set of dials they developed was eventually explained by Newton, who formulated a single law (of universal gravitation) that accounted for all of it, as well as the tides and the fact that apples fall from trees.
It is no exaggeration to say that if we did not live in a solar system with several other planets as well as our own, all following elliptical paths around the Sun, we would not have worked out what gravitation is. It was the hard problem of working out the minimal set of broken symmetries that cause apparent planetary retrograde loops to occur, which took thousands of years and significant wrong turns and ingenuity along the way, that produced Newtonian physics.
Therefore, it was by taking the problem of explanation seriously — by caring enough to sort out the actual cause of the phenomena and the minimal set of dials (i.e. spinning planets following elliptical orbits around the Sun) and associated broken symmetries that would explain the world we observe — that Copernicus spearheaded the Scientific Revolution.
Cosmological symmetry-breaking
In 2009, I decided to work on the problem that the standard cosmological model fails to explain why the universe should expand for my PhD. New evidence for dark energy in the form of a cosmological constant had been discovered just a decade earlier, and I was bothered by the same failure to fundamentally explain cosmic expansion that had perturbed Eddington: while the model does provide an accurate description, I find no mental satisfaction due to its failure to explain why the universe should ever have expanded at all. I think this lack of explanation is the most significant failing in physics, as well as the most underappreciated problem of the past century. Therefore, after a year of beating my head against a problem I found increasingly uninteresting, I decided if I was going to continue studying physics this was where I wanted to put my effort.
I took as my starting point the fact that the standard model, in addition to a few seemingly reasonable and empirically motivated assumptions, contains a significant assumption that the universe’s clock is the same one carried by an average galaxy. You see: according to Einstein’s theories of relativity, everything in the universe has its own personal clock, and times are measured differently when objects move relative to one another. The assumption that galaxies should on average carry the same personal clock as the universe is equivalent to assuming the matter in our universe is, on average, not moving.
We call this frame of reference comoving in cosmology, and use it to describe the bulk motion of galaxies which all have some motion relative to it due to local gravitational interactions with their neighbours. And we take the bundle of worldlines that describe the passage of time measured on comoving clocks to be at rest, and therefore in a relativistic sense to essentially define what space at any given cosmic moment is.
This definition is a somewhat thinly disguised version of the geocentric principle that put the Earth at the centre of motion within our solar system and described the Sun as orbiting around us. Only in cosmology we assume it’s matter-on-the-whole that sets what it means for matter to be at-rest.
This isn’t a terrible assumption to make; but still, it is an assumption, and it could be instead that matter has some nontrivial bulk inertia through the universe. In fact, it could even be that such inertia is what gives matter its mass. These were some early speculations I had that I think turn out to have been rather on-the-nose.
It is no accident that this assumption about matter being on average essentially at rest is deeply embedded in standard cosmology. When Einstein developed general relativity, he was strongly influenced by the writings of Austrian physicist and philosopher Ernst Mach, and on Mach’s principle he believed that inertia itself should be determined by the matter distribution of the universe as a whole. A body’s resistance to acceleration shouldn’t be a brute fact about space, he thought; it should be something the rest of the matter in the universe confers on it. So when Einstein wrote down the first relativistic cosmology in 1917, he built it around a universal “world-matter” — a smooth distribution filling the universe, at rest with respect to itself, which would supply the standard every motion is measured against.
And the thing is that this is an assumed symmetry that could just as well be broken in reality, for all we know. De Sitter had objected to exactly this in 1917, noting that Einstein’s construction makes time “practically absolute” and that the assumption anyway “serves no other purpose than to enable us to suppose it not to exist.” Fifteen years later, he put his name to the Einstein–de Sitter model, built squarely on it. That is how deeply the assumption was already embedded — even its first public critic stopped resisting — and standard formulations of cosmology have taken the same starting point ever since.
In contrast, for my PhD I took as a starting point a universe that is essentially uniform in every direction, as our universe appears to be, and I asked what it would be like if all the matter in the universe moved along lines we typically assign to photons of light, while light gets assigned to the at-rest comoving bundle of worldlines.
The result of this reassignment of worldlines is a cosmological model that has the same form as a black hole, but one in which the universe must grow over time and become larger than its initial size, rather than shrinking towards an end-point. Given my focus of wanting to figure out why the universe should naturally expand as it’s observed to do, this seemed like good progress since such a universe must necessarily expand.
And in physics terms, it poses something rather intriguing: the relativistic spacetime that’s generated is not uniform because it’s all based around this bundle of worldlines that are all moving uniformly in a specific direction; however, since the model universe is uniform by definition, and since matter is all forever moving uniformly through it, at any particular moment in cosmic time a snapshot of the universe at all earlier times must still appear uniform.
You can picture this by imagining every person on Earth as running along our lines of latitude at exactly the rate the Earth spins: none of us would ever move relative to each other, and any snapshot of the Earth taken at any moment would show a constant distribution of people. If instead we described our positions relative to the surface of the Earth, we’d all be moving quickly around it at rates that depend on our distance from the poles.
The model I constructed worked just like this. And then I made a really surprising and I think remarkably intriguing discovery: by forcing the spacetime geometry to be general relativistic (meaning that it’s required to be a solution of Einstein’s field equations), and then by working out the rate that matter (i.e. galaxies) would measure the universe to expand at, I found that the specific rate was forced by the geometry to be a simple trigonometric rate that turns out to equal the flat ΛCDM rate of the standard model — the exact rate that the cosmological data have constrained the standard model to.
This was in the spring of 2010; taking stock:
- I went looking for an explanation of why the universe should necessarily expand, since the standard model doesn’t supply such a reason, and in fact suggests it should not expand, and can only do so if initially supplied an infinite rate at an indescribable moment when all physics blows up, where it also begins with infinite deceleration that balances the infinite rate so that at any moment thereafter both the rate and the deceleration are both finite;
- the move I made was to break a core assumption of standard cosmology that has been deeply baked into our theories from the beginning, while being only justified on a philosophical preference of Einstein’s, and which is not forced by empirical data;
- and I found that this model universe must necessarily expand — and specifically that it must appear to do so at exactly the same rate our universe appears to us to be expanding.
I was very excited about the discovery, and I hastily and excitedly wrote up what I’d found. I sent it to my supervisor to read and went to his office the following morning to discuss and… he screamed at me.
“This is bullshit!” he let out the most blood-curdling yell he could muster, slamming the paper down on his desk as I walked into his office, pure anger and hatred contorting his usually very pleasant face and voice.
This is bullshit
I’ve recently realised that I don’t think I ever got over that moment. All I could think to do was to ask to work through it all more carefully, which he granted though I don’t think he ever was willing to take me seriously after that. He allowed me to work through and defend my thesis, but I don’t know that he ever properly read it, and when I tried to discuss it with him he would make comments like “In physics, description is explanation” (it’s not; we don’t get to redefine words like that just because we don’t care about the one) or “Who is Weyl?” (he knows perfectly well who that is).
I ended up finding postdoc work in hydrology, which was fun for a while but my heart was with physics and astronomy, so I ended up back in my home department where I was able to take on contract teaching roles till a permanent teaching position opened up that I was hired into. I poured my effort into teaching for several years, but I eventually found that my teaching efforts too would never be appreciated. I run the astronomy programme, and while denying the teaching assistants I’d need to get through a term where I was assigned to teach three classes and had an honours student to supervise, my department head told me “This is a department of physics and engineering physics, not an astronomy department. Don’t get that confused.” And after another eight months or so of failing to find any support in spite of all efforts I made, I burned out and curled into a ball for several months, trying to rebuild myself.
It was around November 2024 when I brought up the feeling I had of living in the Twilight Zone to my counsellor. It wasn’t just the lack of support from the university for a programme I’d taken from a few hundred students per year to a couple thousand, or the fact I could see a route to explaining what I still consider the most significant and the most significantly unacknowledged problem in physics. It’s things like the fact that most physicists and physics communicators seem to see no problem at all with describing spacetime as a thing that exists, mistaking the map for the territory.
It’s the fact that when I try to bring up Einstein’s collapse of clock synchrony and ontological simultaneity as a pure symmetry of our world, in spite of the fact that standard cosmology routinely breaks that symmetry but only in the most contrived way possible, people tend to call that “just philosophy.”
It’s the fact that the standard arguments people have used to ground black hole physics for sixty years are logically invalid and no one is willing to acknowledge my reasoning and argue against it, since I’m too easy to ignore.
But slowly, over the past couple of years, with the help of a lot of really good people I think that I have pulled through. A year ago, I managed to publish some articles with my thoughts about spacetime and black holes that were really widely read. And the feedback I’ve received gave me comfort after nearly two decades that I’m probably not insane or stupid or a shitty writer — or any of the other things you worry about when things that seem so obviously wrong are repeatedly met only with apathy, indifference, or ignorance.
And finally this spring I came to a point of understanding and clarity about black holes that pointed the way towards a consistent picture of gravitational collapse and cosmogenesis. I spent the summer working through the mathematical details, fleshing out a framework that augments general relativity by fixing a cosmological symmetry-breaking, and which provides an answer to the rhyme I’d noted in my thesis, in the apparent connection between black hole geometry and this particular cosmology. The many well-known problems of the standard cosmological model are not so much resolved as dissolved within this framework; they simply never arise, and all they really cost is to break that symmetry Einstein preferred.
So, to answer the question I posed as the title of this piece — the one that’s been the main driver of my intellectual journey so far — I’m now reasonably assured it is this: the universe expands because collapsed matter must continue as an expanding cosmology, the expansion is the collapse read from the other side, and the rate is fixed by the cosmological constant alone.
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