The Shadow Universe (part 2)

(Part 1 of this post can be found here)

Some say the world will end in fire,
Some say in ice.

If you toss a ball up into the air it will fly skywards initially, but at some point it will reverse its upward trajectory and plummet back to Earth. What goes up must come down… usually. The harder you throw it, the farther into the air it will rise and the longer it will remain in flight. Throw it hard enough and the point at which gravity curtails its upward path will become so distant that the ball will never return – gravity’s inexorable pull will have been overcome. The escape velocity required to leave Earth’s pull is about 25,000mph, somewhat faster than I could hurl anything (but then I do throw like an eight-year-old girl.) On the moon, which has only 1/6 the mass of the earth and consequently much weaker gravity, the escape velocity is smaller – just over 5,000mph.

The expansion of the universe is governed by almost identical principles. The universe burst into existence 13.75 billion years ago; initially an infinitely dense fireball, it expanded and cooled, allowing atoms to form and then stars, galaxies and planets of the sort that kindly accommodate you and me. Those galaxies continue to stream away from each other, but they do so under the rein of gravity, which lightly but insistently drags them back. The eventual fate of the universe depends on both its current density and the speed with which things are flying apart, in a manner that is completely analogous to the example of the ball tossed up into the air. If there is insufficient mass in the universe, or the galaxies are moving apart too quickly, then their speed of separation will never be slowed to a standstill – the cosmos will expand forever. The galaxies will shrink from view and await a slow mortuary freeze. If, on the other hand, the density of the universe exceeds the “critical density”, at some point it will all come crashing back together: “The Big Crunch” will be the world’s firey end. This criterion also determines the gravitational warping of space demanded by general relativity (GR). Only at the critical density is the universe “flat”; above that density we say the universe is positively curved or closed (parallel beams of light converge, like lines on the surface of a sphere) and below it is negatively curved or open (light rays diverge).



The Big Rip? 

Whichever universe we find ourselves in, open or closed, one thing should be clear; gravity only pulls, it doesn’t push, so the galaxies should definitely be slowing down overall.

They are not. In 1998, two astronomical teams announced a result which set physicists’ hearts aflutter around the world: the expansion of the universe was getting faster (an observation of such importance it earned them last year’s Nobel Prize for Physics). The universe may have started its life obeying conventional gravitational behaviour, but acceleration rather than deceleration has been the norm for longer than the Earth has been in existence. If it continues in this vein, the fate of the universe will be one in which all matter is pulled further apart, with ever-quickening pace.

Gravity is pretty straightforward in this regard. Despite the fantasies of science fiction writes, there is no scope within general relativity (the modern theory of gravity) for repulsion between ordinary matter; unlike electric or magnetic forces, it is always attractive. We do not know what is causing this unusual behaviour, but that’s no barrier to giving it a name. Behold, Dark Energy! – the defining feature of which is that it is whatever is behind the accelerating expansion of the cosmos. Little else can be said about the real nature of Dark Energy, which is partly why it presents such a puzzle. An explanation for it is not hard to find, however…

The Cost of Free Space 

When Einstein produced his general theory of relativity in 1915, there soon emerged a troubling prediction. In common with many of his scientific contemporaries and antecedents, Einstein believed that the universe was static, which posed an awkward question: what stopped everything from collapsing in on itself? This was a problem for GR as much as it was for Newtonian gravity, but Einstein had a trick up his sleeve: his equation for the behaviour of gravitational fields allowed one to introduce an extra term, called a cosmological constant, corresponding roughly to a constant energy field pervading space. A constant and positive energy field has the unusual property that it exerts negative pressure, which overwhelms the attractive pull of its energy content and ends up pushing things apart. Thus the cosmological constant was just the thing needed to still the forces of implosion that gravity demanded and preserve a static universe – or so Einstein thought. In reality, it could only perform this duty through a delicate balancing act, which would collapse with the slightest disturbance. Once Edwin Hubble destroyed the paradigm of a static cosmos with his 1929 observation of an expanding universe, the game was up. Einstein clapped his hand to his forehead, decried the cosmological constant as his “biggest blunder” and the constant was quietly dropped, an unwelcome guest at the increasingly successful party that was the Cosmological Standard Model.

When the cosmic expansion was discovered to be accelerating, the constant rushed straight back into vogue. Although there was no clue from GR as to how large the constant should be, it was nevertheless a near-perfect marriage of theory and experiment: an observation that could be readily explained by a prediction left in limbo for seventy years. Except…

A Noisy Quantum World


Quantum mechanics stirs some pepper into the pot, telling us something completely unexpected about the nature of space. When Ernest Rutherford had his assistants Geiger and Marsden fire alpha particles at a sheet of gold foil in 1909, he found something remarkable: the overwhelming majority of an atom’s mass was concentrated in a minute fraction of the total space the whole atom occupied, while electrons explored the wilderness in orbit around their central focus. What goes for atoms goes for all matter that we normally consider dense, solid or liquid: the appearance of compact impenetrability is naught but an illusion; we are in reality 99.9999999999999% empty space. Introduce a little quantum field theory into the mix, however, and a new story emerges.

It is a basic property of most physical systems, classical or quantum, that they vibrate and oscillate – but in quantum systems, there is a twist: those oscillations can never fully die away. Like a spinning top in someone else’s dream (spoiler!?!), there’s always a bit of life left in any vibrating system that will never die away. Removed of all energy it is possible to take, there is a discrete and indestructible quantum of vibrational energy that prevails in spite of all else. This is ultimately rooted in the famous Heisenberg Uncertainty Principle, which limits simultaneous precision on position and momentum. This principle extends to the vacuum itself; the electron and electromagnetic waves I described in this article cannot be completely purged, so they flicker and fizzle, popping particle/antiparticle pairs in and out of existence.

This fundamentally fidgety nature of the universe has an interesting consequence. There is a constant amount of energy that permeates the universe – a “vacuum energy” – that, to all intents and purposes, mimics a cosmological constant (part of the vacuum energy can also turn up as residual energy from things like the Higgs field, whose base level of energy we can usually ignore, but not when gravity pokes its nose in). Quantum field theory therefore gives us a way to calculate the constant. There is just one slight snag; the prediction is too large. Far, far too large. The “prediction” is in theory infinite (because we must include all possible energies of virtual particle pairs), but we can do better than that. We may reasonably assume that quantum theory resolves into something new around the energy scale at which quantum gravity kicks in, but even if we limit contributions to vacuum energy to below this threshold, we still find a predicted energy density that is too large by 120 orders of magnitude. That means it is a quadrillion quadrillion quadrillion quadrillion quadrillion quadrillion quadrillion quadrillion times too large. It is not the finest prediction physics has ever known.

The vacuum energy problem was something of an embarrassment for years before the discovery of Dark Energy, but it was always possible to imagine some unappreciated principle existed to exactly cancel it out (this sort of thing does happen in quantum physics, and shouldn’t just be viewed as praying for a miracle). The discovery of Dark Energy threw a spanner in the works. Now it appears that there is some kind of vacuum energy, but it is far smaller than any sensible prediction we can make for it. This currently represents one of the most pressing unresolved questions of theoretical physics and symbolises better than anything the fascinating draw of modern physics: the same theoretical framework that makes better predictions than any other theory has ever done also makes the worst.

There is more chin-scratching to be found in the anomalously small value for Dark Energy. Currently, the universe is dominated by this entity; 68% of the cosmic energy budget is Dark Energy, while only 4.9% comes from the stars and planets (the rest turning up as the mysterious Dark Matter). In part 1 of this blog post, I noted how insignificant we were compared to the principle type of matter in the universe, Dark Matter. The discovery of Dark Energy pushes our Copernican humiliation further: we now represent less than one twentieth of the all that’s important to the greater cosmos. What’s puzzling, though, is that our small slice of reality is actually much larger than we might predict. If Dark Energy is explained by a cosmological constant, it will never change, while the density of normal matter will ever shrink as the universe expands. In a never-ending universe, why should we find ourselves at a time when the respective densities are so close in value (or to be more precise, why does Dark Energy appear fine-tuned to give a universe that allows the formation of galactic structure)? There is a world of anthropic reasoning to be explored here, but it’s not one I propose to tackle now.

Another puzzle: the amount of matter around is rather small, and would give rise to an open universe in the absence of Dark Energy (where “open” refers to the warping of space I described earlier; the connection with the fate of the universe is lost once DE turns up). With this new component, the spatial curvature appears to be precisely nil – as far as we can tell, space is completely flat (indeed, observing this fact forms one of the principal pieces of evidence for Dark Energy). Why this should be the case? Providing an answer takes us back all the way to the very beginning of time (and played an important part of my PhD research), and it’s a topic for another blog post.

Before I go:

A cosmological constant/vacuum energy is not the only game in town when it comes to explaining Dark Energy. Other possibilities emerge if you are prepared to give up certain cherished principles of cosmology. Alternatively, it is possible that Dark Energy is not in fact constant. In this case it would represent a scalar field, akin to the Higgs field discussed here. The particularly disturbing consequences of that possibility will be the next subject of discussion…



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