Another young scientist joins the ranks of credentialed scholars. Congratulations to Vikram Duvvuri, who just defended his Ph.D. thesis on “Modified Gravity as an Alternative to Dark Energy”!
This was not an easy one, through no fault of Vikram’s — a certain member of his thesis defense committee got stuck on the East Coast, and had to phone in, after numerous delays. But Vikram kept his cool throughout all of the tense drama, and made it through the defense itself unscathed.
The thesis was based on two papers on which I was a collaborator: Is Cosmic Speed-Up Due to New Gravitational Physics? with Mark Trodden and Michael Turner, and The Cosmology of Generalized Modified Gravity Models with the same authors plus Antonio De Felice and Damien Easson. The idea is to explain the observed acceleration of the universe by modifying gravity rather than introducing dark energy. That is to say, we look out into the universe and see that distant galaxies are accelerating away from us. In the context of Einstein’s general relativity, that can’t happen in a universe consisting of ordinary matter and radiation — we need some form of energy density that persists, rather than dissipating away, as the universe expands. So we fit the data by imagining that about 70% of the universe is some exotic dark energy, perhaps a cosmological constant, that is smoothly distributed through space and nearly-constant in time.
But the other possibility is that Einstein was wrong, and we need to modify general relativity on cosmological scales. There are various ways to do this; one that seems potentially viable is a brane-world construction by Dvali, Gabadadze, and Porrati. Our approach was to ask for the simplest possible modified-gravity model that would make the universe accelerate. So we stuck with four dimensions, no new fields, and just played with the dynamics of the spacetime metric.
Einstein’s equation for general relativity can be derived by minimizing an action, where the action is simply the integral over spacetime of the curvature scalar R. We wanted a new action that looked like Einstein’s when R was large, but looked different when R was small, as in the late universe. So we did the obvious thing: replaced R with R+1/R in the action. Vikram’s thesis was an examination of this model and some more complicated variations on the same theme.
Sadly the original model doesn’t quite work; as noted by Chiba, it is ruled out by tests of gravity in the Solar System. That’s basically because our theory introduces a new degree of freedom. In the weak-field limit, general relativity is a theory of a massless spin-2 particle, the graviton. Our modified action turns on a new degree of freedom, which is a massive (tachyonic) spin-0 particle. This turns out to be fairly generic; if you mess with Einstein’s theory by adding new terms to the action, it almost always happens. Thus, a lesson is learned: general relativity is hard to mess with without running into conflict with experiment. But such messing can nevertheless lead to useful outcomes, like a new doctorate!