The Results of Resonance

By Mark Trodden | December 22, 2008 1:31 pm

As I discussed a couple of weeks back, if inflation is the correct description of the very early universe, then reheating is the mechanism by which the universe is populated with matter, and the origin of the “hot” part of the hot big bang. In that post, I described how, in a range of models, depending on the couplings between the inflaton field and other matter fields, reheating can occur in an extremely non-equilibrium fashion, through parametric resonance, known as preheating.

As I said, 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). However, as it turns out, some of the energy may never equilibrate, and there are therefore a number of possible fascinating consequences of preheating. Here’s a whistle-stop tour of some of these.

One motivation for inflation is that the quasi-exponential expansion will dilute away any unwanted relics of the early universe. Examples of this are magnetic monopoles and other superheavy weakly-interacting particles that may be produced during phase transitions at early times. Monopoles, to take a specific example, will generically form if the universe undergoes a grand-unified phase transition, expected at temperatures of around 1016 GeV. If inflation is to rid us of them, then it better be that the reheating temperature after inflation is lower than this temperature, otherwise the universe will go through the phase transition after inflation, and form the offending monopoles after all. Thus, without considering preheating, this means that we are safe from GUT relics if the universe reheats to a temperature below the GUT scale. But preheating can create a problem here. Parametric resonance means that, depending on the model, the energy of the inflaton can be preferentially transferred into certain wavelengths (modes) and this can lead to the formation of particles with masses higher than the typical temperature associated with the original energy density of the inflaton. Thus, although the ultimate reheat temperature is less than the GUT scale (for example), there can nevertheless be a background of relics of much higher masses.

Generally speaking, this is a bad thing, since the overproduction of such heavy particles can lead to them dominating the universe, and a cosmic evolution dramatically different from the one we know. Thus, if the correct model of inflation permits preheating into dangerous relics, then one is forced to consider that inflation must have taken place at considerably lower energies than one might naively have thought. In other words, one needs to have sufficiently low scale inflation that even parametric resonance cannot be powerful enough to resurrect monopoles and their kin. Such considerations can provide strong constraints on models, sometimes pushing reheat temperatures down to troublesomely low ranges (more about this soon).

Another interesting outcome of preheating might be in explaining dark matter. A popular candidate for dark matter is a weakly interacting massive particle (WIMP), the ultimate abundance of which is set by a competition between the particle’s tendency to acquire its equilibrium density and its difficulty of self-interacting in an expanding universe. These competing effects identify the weak scale as a natural place to expect a dark matter WIMP. However, these considerations arise from equilibrium considerations and, as we’ve already seen, these may not apply during preheating.

Indeed, it is possible for GUT scale particles, which would not ordinarily naturally establish the abundance necessary to be dark matter, to be produced during preheating at a density such that they are candidates to be superheavy dark matter or WIMPzillas.

When people usually speak of the gravitational wave signature of inflation, they are referring to the gravity part of the quantum fluctuations of the inflaton (the scalar counterparts of which give rise to structure formation). But with preheating, it is also possible to produce gravitational waves from parametric resonance through the coupling to the graviton. The result is, as one might expect, somewhat model-dependent. Nevertheless, a successful observation might give us a direct window into the earliest times.

Above, I mentioned that constraints from not overproducing dangerous relics during preheating can lead to the allowed reheat temperature being rather low. So what? Well, one problem with this is that we need to have a way of generating the baryon asymmetry of the universe, and many of our known options operate at or above the electroweak scale. What if we never get that hot? Preheating got us into this corner and, fortunately, it provides a couple of options to get out of it. One that I (and others) have worked on is related to the idea of electroweak baryogenesis. As I discussed in my post on this, the usual way people think about electroweak baryogenesis is that baryon number violating processes (occurring through nonperturbative field configurations known as sphalerons) take place during the electroweak phase transition. If the reheat temperature after inflation is below the electroweak scale then this phase transition doesn’t occur. However, if preheating takes place, then it is possible (although tricky, and highly model dependent in practice) for sphalerons to be generated through parametric resonance, and for their decays to generate a baryon asymmetry. Not the prettiest way to produce an excess of matter over antimatter, but a fascinating possibility.

This isn’t an exhaustive list, of course (I didn’t even mention magnetic fields), and I deliberately haven’t provided references (since I don’t need the emails that may generate). But hopefully it gives a flavor of how rich inflationary physics may be, how it is constrained, and one way in which it may be both testable and the answer to some of our cosmological conundrums.

  • spyder

    When somebody like myself (a non-physicist, non-scientist humanities academic), is an avid reader of this blog (and its predecessors), one actually begins to understand these sorts of discussion. This is due to three factors: the clearly stated to-the-layperson style and tone; the general joy of the physicists in communicating their life’s work to others; and the on-going commentary and discussions of the material. All of you rock, and for this i am grateful and appreciative all the year round, not just during holidaze season.

    I was fascinated by this idea while reading Neal Stephenson’s ANATHEM recently (and its associated materials). The book is filled with math and physics, all of which is reframed in new semitocities, yet retaining much of the same structures and constructs one finds in this blogsphere. Without the efforts of all of you, i would not have been able to sort through the material and discover that i had learned so much about cosmology, cosmogony, particle and quantum theory, etc.. Thanks for that alone.

  • John

    I second most of that, but what–speaking of clarity in speaking to us laypeople–are semitocities?

  • Jonathan Vos Post

    The problem seems overconstrained. Don’t we first have to, as Abhay Ashtekar points out, have to get from smooth to quantized (Planck-length) space-time, perhaps with superinflation from t = 10^-45 seconds, then inflate to smooth out inhomogenieties of the electroweak phase transition at ten picoseconds?

    As my Physics professor wife Dr. Christine Carmichael points out in [unpublished stories and novel manuscript] the inhomogenieties may not be merely random, with a distribution to be sought in CMB, but the remnants of intelligent civilization of subatomic beings who were trying to build something lasting (i.e. Tower of Babel) but saw it all swept away in a tragedy at the beginning of time. There’s a lovely science fiction poem that reinvented the same notion, by Tom Digby, and though neither of these two authors knew it, an earlkier and quite lovely science fiction short story by Benjamin Franklin:

    The Ephemera: An Emblem of Human Life

  • Mark

    What problem seems overconstrained? There should be no need to inflate to smooth out inhomogeneities due to the electroweak phase transition – not quite sure where that comes from.

  • spyder

    Sorry John, i didn’t quite spell that right, no wonder you are confused, as am i. That word should have been semioticities, the signs and symbols we use to construct semantical concepts such as words and meanings of them. Stephenson has created a new vocabulary, new words, new phrases–while trying his best to maintain continuity between the material most often discussed here in this blog, with his alternate universe.

  • Neil B

    I’ve heard about a “maximum temperature” (maybe dep. on details) such that trying to raise the energy just causes particles to create more particles by collision energy, as in p + p = 4p and maybe some stray gamma etc. (so kinetic energy is about the mass-energy of nucleons, whatever temperature that is.) Yet that MT doesn’t seem to figure in what I hear about “temperature” like in the early universe, which seems to go to unlimited values. What’s up with that?

    Also, monopoles: seem to be nice for symmetry reasons, but: if you take the vector potential “A” field seriously (whatever that means), monopoles can’t handle that in a tidy way – they need icky tails of A field trailing along, quite contrived. People tried to sort that out but it really isn’t very natural looking is it? And if E field really is determined by Del phi – dA/dt, then the nice circular lines of E around moving monopoles wouldn’t really be the deal, wouldn’t that A-field rope or “seam” have to mess things up somewhere?

    Merry Christmas/ Happy Holidays.

  • Neil B

    Oh that’s p + p —> 3p + p bar.

  • Dmitry

    Hi Mark

    I think we came to pretty similar conclusions while studying dynamics of the effective equation of state during preheating.

    Typically, what you get is prethermalization similar to the one seen in HIC – IR part of the dustribution n_k or k^3 n_k is nearly thermal (n_k resembles Rayleigh-Jeans) with some “effective temperature” which can be quite high immediately after the end of preheating (higher than 10^15 GeV). This “effective temperature” decreases with time much faster than according to the law Tsim 1/a one would naively expect, but there is still a chance to create heavy relics immediately after the end of preheating.

    As for dark matter – one way to generate large amount of it is to remove trilinear coupling terms between inflaton and matter scalar chi from the Lagrangian. Then, the inflaton condensate has a rather large energy density after the end of parametric resonance regime (condensate cannot decay completely without trilinear terms). This energy density is so large typically, that the universe gets overclosed unless you introduce quite a bit of fine tuning into the model.



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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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