Research
Broadly speaking, I am interested in the three major unknown players on the cosmic scene: the inflaton, the dark matter, and the dark energy. Each of these three substances control the dynamics of the Universe during one stage of its evolution, but despite their importance, their nature is still mysterious. |
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- In the first moments after the Big Bang, a period of extremely rapid expansion called inflation smoothed the Universe while simultaneously seeding the inhomogeneities that would eventually become galaxies. The engine driving that expansion, dubbed the inflaton, is unknown.
- About fifteen percent of the matter in the Universe is made of known particles. The composition of the remaining "dark matter" is a mystery.
- Currently, most of the Universe's energy is "dark energy." This energy is unlike any other energy that we know of because it is causing the Universe's expansion to accelerate, even though gravity should be slowing the expansion down.
On a more personal note, my Ph.D. thesis will have three main sections: asymmetric inflation, solar system tests of modified gravity, and supermassive black hole mergers. These topics are connected, albeit loosely, by an underlying question: what happens when we alter fundamental cosmological theories?
Here are brief descriptions of these research projects. For those in search of more information, my publication list will direct you to the articles that contain all the details about these projects along with some other projects that I have worked on. I have also given presentations on these topics, and slides are available here. |
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Asymmetric Inflation
Collaborators: Sean Carroll and Marc KamionkowskiNew Scientist Article: 10 June 2008
Sean's blog posts: part 1 part 2
The cosmic microwave background (CMB) has an intriguing and unexpected feature: the average fluctuation amplitude in one half of the sky is about 10% larger than the average amplitude on the other half of the sky. This fluctuation power asymmetry was first found by Eriksen et al., and it is significant at the 99% confidence level.
We proposed that this power asymmetry could be produced by a very large-amplitude and long-wavelength perturbation in the energy density of the Universe during inflation. Such a perturbation would effectively make the mean energy density on one side of the Universe larger than the mean energy density on the other side. Since the mean energy density determines the amplitude of the energy fluctuations, the long wavelength mode would create a power asymmetry just like the asymmetry observed in the CMB.
This picture illustrates our mechanism for generating a power asymmetry during inflation. The blue sphere represents the CMB sky around us, while the pink curves represent the energy density during inflation.
| The long-wavelength mode changes the background value, making it asymmetrical. The short-wavelength fluctuations, also shown in pink, have different amplitudes on different sides of the sky because they are fluctuations in different backgrounds. |
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Unfortunately, our mechanism for generating the power asymmetry has an unwelcome side effect. The long-wavelength fluctuation will change the mean temperature of the CMB in addition to changing the amplitude of the small-wavelength fluctuations. We calculated how such long-wavelength fluctuations create temperature fluctuations in the CMB, and we found that the near-uniformity of the CMB temperature limits how much the mean energy density may vary from one side of the sky to the other. These limits rule out our original model, which assumed that the inflaton was the only type of energy present during inflation. Instead, we were forced to postulate that there was a second type of energy during inflation and that inhomogeneities in this secondary energy source led to the power asymmetry observed in the CMB sky.
Solar System Tests of f(R) Gravity
Collaborators: Tristan Smith, Takeshi Chiba, and Marc KamionkowskiGiven the strangeness of dark energy, it is reasonable to wonder if the cosmic acceleration may be a sign that our understanding of gravity is flawed. While Einstein's theory of general relativity has passed every test we have given it, all of those tests are necessarily confined to the borders of the Solar System. It is possible that galaxies are accelerating away from each other because gravity behaves differently between galaxies than it does between the planets and the Sun.
How can we modify gravity so that galaxies accelerate apart? One possibility is to replace the Lagrangian of general relativity, which is simply the Ricci curvature scalar R, with some function of the Ricci curvature scalar f(R). This modification is called f(R) gravity, and there are several types of f(R) gravity that will drive cosmic acceleration.
The problem with f(R) gravity is that it is very difficult to change how gravity behaves between galaxies without changing how it behaves in the Solar System. Moreover, while there is only one spherically symmetric vacuum solution to the gravitational equations in general relativity, there are many such solutions in f(R) gravity. To determine how f(R) gravity will behave locally, you have to find the particular solution that corresponds to our Solar System, and this subtlety generated some confusion regarding whether or not f(R) gravity was consistent with tests of general relativity.
We showed that one form of f(R) gravity, known as 1/R gravity, is incompatible with Solar System gravitational tests and is therefore ruled out. We then generalized our calculation to other forms of f(R) gravity. We found that all forms of f(R) gravity that satisfy a few simple conditions are incompatible with Solar System tests and are not viable alternatives to dark energy. One of these conditions demands that the value of the Ricci scalar does not deviate much from its vacuum value. Forms of f(R) gravity that do not satisfy this condition can mimic general relativity inside the Solar System and are currently under investigation as possible alternatives to dark energy.
Solar System Tests of Chern-Simons Gravity
Collaborators: Tristan Smith, Robert Caldwell, and Marc KamionkowskiChern-Simons gravity is a modification of general relativity that adds a new term to the gravitational action. The new term is higher-order in the curvature and violates parity, which means that Chern-Simons gravity behaves differently when viewed in a mirror.
Chern-Simons gravity is interesting for two reasons. First, it is a simple example of a gravitational theory that is parity-violating. Since other fundamental forces are known to violate parity, it is interesting to test whether or not gravity is parity-violating. Studying Chern-Simons gravity tells us where to look for parity-violating gravitational effects. Second, the new term that is added to the general relativity action in Chern-Simons gravity is a common feature of low-energy effective gravitational theories derived from string theory.
Chern-Simons gravity is very difficult to distinguish from general relativity because the differences between the two theories only emerge in systems that are not spherically symmetric. Consequently, there were no constraints on Chern-Simons gravity prior to our work. We derived the Chern-Simons gravitational effects due to the Earth's rotation, and we showed that these effects would slightly alter the orbits of satellites. We were able to use the orbits of the LAGEOS satellites to place the first constraints on the parameters of Chern-Simons gravity, and we noted that these constraints will be significantly improved by Gravity Probe B.
SMBH Mergers and Halo Merger Theory
Collaborators: Marc Kamionkowski and Andrew BensonThe merger of two supermassive black holes (SMBHs) is expected to produce a gravitational-wave signal detectable by the satellite LISA. The rate of SMBH mergers is intimately connected to the galaxy merger rate, and the extended Press-Schechter formalism is often employed when calculating the rate at which these events will be observed. This merger theory is flawed and provides two rates for the merging of the same pair of galactic haloes.
An alternate merger rate proposed by Andrew Benson, Marc Kamionkowski, and Steven Hassani (BKH) may be obtained directly from the Press-Schechter halo mass function. We calculated the SMBH merger event rate using both versions of the extended Press-Schechter formalism and a preliminary version of the BKH merger rate.
We found that the SMBH merger event rate is dominated by mergers of galaxies with nearly equal masses; consequently, the two versions of the extended Press-Schechter merger rate give nearly equal SMBH merger rates. However, the preliminary BKH merger rate leads to a SMBH merger event rate that is thirty percent lower than the event rate derived from the extended Press-Schechter formalism.