A rough history of the temperature of the universe: Figure 6 from Lineweaver (2003)

Turning The Universe Up A Notch

Reheating: What is it and why should you care?

I n the community of people who study cosmology — the science of the origin, evolution and structure of the universe — our Genesis story begins with ???? (we have no idea; we’re not even in widespread agreement about whether this is a scientific question or a theological question) and then what we call the inflationary era. Unlike economic inflation, this is the good kind because it makes everything that follows, including us, possible. Without cosmic inflation or something like it, the rest of the cosmological timeline is difficult to explain: all of the data we have is consistent with inflation and hard to explain without it.*

Pretty much every physicist and astronomer, no matter their field, knows this basic fact about inflation. What isn’t widely discussed is what happens after the end of the inflationary era — at about 10^-35 seconds after ???? What we do know is that inflation should significantly cool the universe down. We also know, this time from actual experimental/observational data, is that in order for the rest of structure formation — galaxies, stars, us — to occur, the universe needs to reheat.

This question has been one of two dominant drivers behind my research in the last two years: how do you reheat a phenomenal cosmic banquet after inflation has flash frozen it — without going too far? This is a question of general interest to cosmologists, as well as people working on technical issues in quantum field theory in curved spacetimes (particle physics at the interface with gravity). I happen to fall into both categories, so this is fun for me.

A general schematic for the expected early universe timeline is given in the figure above. On the horizontal axis we have time increasing in units of seconds from left to right. On the left vertical axis we have the temperature of the universe, increasing from the bottom to the top. On the right we measure the quantity of temperature in units of energy because these are essentially the same thing. I’ll be totally honest and say that I am more comfortable thinking in terms of the right axis than the left one because that’s what becoming a theoretical particle physicist does to your brain.

There’s a dotted line on the plot that’s labeled reheating. It’s a very nice line. But it’s just a placeholder because we don’t actually know what it’s describing or what its shape should really be. This is also the case for the inflation line, which makes the reheating problem even harder. All we know is that at the end of inflation, the particle(s) (inflatons) that drive inflation should continue to give off energy and transfer that energy to other types of matter, thereby reheating the universe, ideally so that the dotted line meets up with the solid line at a point that we should be able to predict mathematically (this is called the thermalization temperature).

So, that’s what reheating is: turning the universe up a notch by energy transfer from the primordial inflaton to the matter that together will come to be known as the Standard Model of particle physics. Now I have to tell you about preheating. At the very beginning of the reheating era, we expect that this energy transfer will happen efficiently through a phenomenon called parametric resonance. Anyone who has ever been on a swing actually has experience with this. Remember pumping your legs at just the right point to make the swing go higher? You were transferring energy from your body to the swing at the perfect moment to maximize the energy transfer — this is parametric resonance. Here’s a really fun video about parametric resonance from one of Alan Guth’s former undergrads, Juana Becerra, who is now a PhD student in History of Science at Harvard:

Preheating is what happens when the matter that will eventually evolve into everything we see swings higher and higher as the inflaton pumps its legs at just the right point.

This leads me to a paper that posted to the arXiv today with by Professor David Kaiser of M.I.T., Dr. Evangelos Sfakianakis of the University of Illinois at Urbana-Champaign, M.I.T. undergraduates Matthew DeCross and Anirudh Prabhu and yes, me, C. Prescod-Weinstein:

Preheating after Multifield Inflation with Nonminimal Couplings, I: Covariant Formalism and Attractor Behavior

Epic sounding title, right? In this paper we consider the aftermath of a model where there is more than one particle driving inflation (that’s the “multi-field inflation”) and those particles have a deeper relationship with spacetime than just living inside of it (that’s the “non-minimal coupling”). What we show in the paper is a. how to work out the mathematical structure of such a system, b. what the strength of the relationship between the particle and the spacetime can be in order for parametric resonance to occur and be most efficient, and c. how such a model gives unique results that are distinctly interesting compared to other, simpler models.

In practice, the paper contains a lot of calculus that was worked out by hand and checked and rechecked repeatedly as well as the results of significant Mathematica coding which allowed us to compare the hand work with a computer’s calculations and see some results that only a computer could get. Here is a sample of our handiwork, an equation that tells us how little changes in the fields grow with time:

see the text around equations 52–53 for context.

In sum: the paper concludes that in (what we consider to be) a realistic model of post-inflationary preheating, the strength of the relationship between the particles and the spacetime determines the outcome of the process.

Straight up though: we don’t say anything about the end of reheating or the thermalization temperature. Nor does our model take into account the existence of most of the standard model. That will have to come later!

Anyway, I suggested in the title that I would explain why you should care. Frankly, I actually think that non-experts will intuitively grok why this is cool. It’s an incredible thing that we are even in a position to consider these questions much less actually fill in the cosmological timeline with potentially realistic answers. Typically, the naysayers are other scientists. Observers and experimentalists may scoff and say, “there are no testable parameters in your paper!” And yes, that is true. But first of all not everyone cares about testable things — although I do. But second of all, seeing whether preheating can occur efficiently in an inflationary model is actually a helpful check on inflation. Third of all, we don’t know what’s around the next scientific corner. Today’s untestable work on preheating may produce tomorrow’s incredibly interesting and highly testable idea.

In other words, this is an ongoing thriller, unfolding before your very eyes. I think we are on a very interesting path, and I hope you’ll stay tuned for paper number 2!

*There is significant debate in the community about what constitutes a direct vs. indirect detection and therefore whether we have a direct detection of inflation, a topic I’ll make the subject of future writing.


Me at age 4, 29 years before contributing to this paper. It’s amazing what people can grow up to do when they are given the resources and opportunities necessary to develop their minds and their passions.