Putting the Heat in the Hot Big Bang

By Mark Trodden | November 24, 2008 6:37 am

Attend enough talks about the future evolution of the universe, and you’re sure to hear a speaker quote the Robert Frost poem, Fire and Ice, uttering the words

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

This is typically a reference to the question of whether the universe will recollapse, forcing all its contents into smaller and smaller volumes, increasing the pressure and the temperature, or whether it will expand forever, gradually cooling to ever lower extremes of temperature. What is less often discussed however, is a related question concerning the very early cosmos – was the universe born in fire or in ice?

If you’re reading Cosmic Variance, chances are you’re aware of and comfortable with the idea of the big bang. Physicists arrive at this concept by first making observations of the universe today and understanding how these are described by well-established theories of gravity and particle physics. We then extrapolate back in time to infer what the early universe must have been like, and then test the theory by working out what new predictions result and checking whether they agree with observations. This methodology works remarkably well and has provided us with an extremely well tested, self-consistent and coherent understanding of the universe.

The central result that arises from this work is that the universe is expanding – all distant galaxies are moving away from us and the further away they are, the faster they are moving. Of course, this means that in the past all galaxies were closer together. When you get far enough back in time, what inevitably results is that one has a very high density of matter and, as your intuition from compressing everyday gases will tell you, one expects that in this early phase the universe should have been extremely hot – a birth in fire, in Frost’s language. In fact, this heat is what we see, diluted and reddened by cosmic expansion, as the cosmic microwave background radiation today.

The prediction and observation of this leftover radiation constitutes compelling evidence for big bang cosmology. However, it doesn’t answer the question of how all that hot matter came into being in the first place. Now, we do know that if we extrapolate far enough back in time one is eventually no longer able to use gravity (describing the physics of space and time and understood by Einstein’s General Relativity) and quantum mechanics (describing the physics of the very small) separately, but is forced to take into account their mutual effects. Thus, it is entirely possible that the origin of matter can only have its explanation in a theoretical framework that allows us to answer questions about gravity and particle physics working together in this way, such as string theory. However, we think we have an explanation that may be well-described within the theory of inflation, seemingly needed to solve the problems of homogeneity and flatness in the early universe, and thought to be responsible for the fluctuations in matter and spacetime that ultimately lead to large scale structure in the universe. Indeed, if inflation is correct, then its diluting power means that any preexisting mechanism for producing regular matter is rendered moot, and a new, post-inflationary mechanism is mandated. In Frost’s language, the universe may have been born in ice, and inflation may explain why, and how fire was breathed into this barren spacetime.

Inflation requires a large vacuum energy, due to the potential energy of a slowly-rolling scalar field, in order to cause the early universe to expand exponentially quickly. While this addresses the problems mentioned above, this accelerated expansion is also extremely efficient at diluting the universe of all other matter, leaving only the vacuum energy behind. Thus, within inflation, the question of the origin of the hot big bang becomes the question of how our huge universe, bereft of matter save for the potential energy of the inflaton and fleeting quantum fluctuations, is ultimately populated with the hot plasma of quantum fields that eventually cools to make galaxies, stars, planets, and you.

To get a handle on how this large vacuum energy can be converted into regular matter fields when inflation ends, it is useful to look at a caricature of an inflaton potential.


As one can see, this consists of a remarkably flat portion, along which the inflaton slowly rolls, leading to inflation, followed by a piece where the field can pick up speed and cease to behave as a cosmological constant. It is this piece in which we will be interested. As the inflaton starts to oscillate rapidly around its minimum, there are two possible damping terms through which it can dissipate energy. One is natural redshifting due to the expansion of the universe. But the second is through decays to other particles. This can be quite an efficient process, and the energy density in the inflaton can be smoothly converted into that of a thermal bath of particles to which it couples. This process is known as reheating, and provides one possible way in which inflation can answer our question.

There is, however, a subtlety that can arise in this picture. The way I described it above, one pictures the decay of the inflaton as rather like a pendulum swinging in air, gradually transferring its energy to the air molecules through friction, and gradually coming to a halt. Indeed, this is a possibility, but it is not the only one. In fact, now that we’ve mentioned swinging, you might be able to imagine what else can happen. Anyone who has sat on a swing knows that if you are given a big push, and just sit on the swing, you will swing back and forth, and gradually come to a halt, as I described for the pendulum. However, one doesn’t have to be so passive, and every child knows that by kicking ones feet at just the right times, one can actually get the amplitude of the swing to grow larger and larger. This is a phenomenon that physicists call resonance.

How might this apply to the inflaton? Obviously, the inflaton doesn’t get to kick its feet – it has a natural frequency governed by the curvature of the potential, and roughly speaking that’s all there is to it. However, if one thinks in Fourier space, one can see that the equation governing how the inflaton decays into other matter fields depends on the wavelength (and therefore frequency) of those fields, or modes (it is, for you experts, a Mathieu equation). For a given inflaton potential, the natural frequency of the inflaton’s oscillations has no particular relationship to the frequency of a randomly chosen mode. However, there are certain ranges of mode frequencies for which the oscillations of the inflaton are just right to excite those modes resonantly, pumping lots of energy into them, just like the child on the swing. This is called parametric resonance, and for the case of the inflaton’s decay into matter, the whole process is referred to as preheating.

Although preheating is an out of equilibrium phenomenon, eventually almost all the energy produced equilibrates, and produces a plasma at a given equilibrium temperature. One might therefore wonder how there could be any observational consequences of this hypothesized early cosmic phase (and hence whether such considerations are scientific at all). But it turns out that some of the energy may never equilibrate, and that there are therefore a number of possible fascinating consequences of preheating. Some of these tightly constrain particle physics and inflationary models, others provide novel ways of approaching some unresolved cosmological conundrums. Next time I’ll tell you about them.

  • http://riofriospacetime.blogspot.com Louise

    The controversy over inflation is very interesting! I would like to hear you discuss inflation vs. the alternatives, like varying the speed of light or the GM=tc^3 theory. Non-gaussianity in the CMB would be a subject that CV could well explain to the readers.

  • td

    Interesting, I could be making an incorrect assumption but you seem to be implying at the end that dark energy could be a non-equilibrium mode of the inflaton potential?? Is there a paper on this anywhere ? It sounds quite neat.

  • Lawrence Crowell

    It is fun to take the FLRW spacetime and a Higgs-like field, couple the spacetime to this field and then numerically run them on a computer. It takes a little study of the literature to set this up. With a bit of programming and running the model the outcome of the inflation is not dependent (or heavily so) on the initial conditions you set up in the numerical simulation. One can show this even if you put some Legendre series of inhomegeneities in the metric. The flatness problem appears to be largely solved this way. Inflation irons out most nonuniformities, which we might assign to initial or early data.

    It seems to me that the heating which occurs with inflation corrsponds in some way to the existence of a cosmological horizon. That horizon is likely some region which decoheres fields, just as black holes emit thermalized radiation. This all points to physics or cosmology concerning the origin of thermodynamics.

    Lawrence B. Crowell

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  • Steve

    I have a question about gravity. Do you think London dispersion forces have anything to do with gravity? Could gravity be accounted for by vast numbers of molecules attracting other molecules with slight polarity? I only ask because we are learning about the intermolecular forces now and the London dispersion force seems similar to gravity in a few key areas like they both are weak, the more massive the stronger the pull, and everything contains both gravity and London dispersion. Thanks for any thought on the matter.

  • http://OccamsRazor,Freenet Sven

    Re Steve:

    I have written a paper on exactly this topic just recently (and believe it to be the working mechanism behind gravity; but “london dispersion force”, who comes up with these names?), however to play Devil’s Advocate:

    If you research electron orbitals you will find constant assertions that electrons don’t orbit the nucleus like planets orbit a star, but rather that they ‘hover’ (for lack of a better word) in a probability field surrounding the nucleus depending on the number of electrons and degree of atomic excitation. Needless to say, given this orthodox theory of electron clouds, how would one justify “london dispersion force”?

    If you want a copy of my paper, drop me a line @ sven.gelbhaar@gmail.com

  • The Pale Scot

    May I be allowed to ask a dumb question that I have never been able to find a specific answer to? This seems a good forum for it.

    When you say “the universe is expanding” does it mean that galaxies are traveling thru the fabric of space-time away from each other? Or is the space-time fabric itself expanding and carrying matter along with it?

    Thank you, I find this stuff fascinating, and a answer to this would setttle some ideas rattling around in my mind.

  • http://blogs.discovermagazine.com/cosmicvariance/sean/ Sean

    It’s better to think of it as the latter: space itself is expanding. But it’s not completely unambiguous; see here:


  • The Pale Scot


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About Mark Trodden

Mark Trodden holds the Fay R. and Eugene L. Langberg Endowed Chair in Physics and is co-director of the Center for Particle Cosmology at the University of Pennsylvania. He is a theoretical physicist working on particle physics and gravity— in particular on the roles they play in the evolution and structure of the universe. When asked for a short phrase to describe his research area, he says he is a particle cosmologist.


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