Other work:
My previous work in cosmology was about the big bounce scenario in which the universe went through a contraction phase followed by a bounce into the current expansion phase. In this scenario, quantum fluctuations of the spacetime during the contraction phase gave rise to small inhomogeneities in the universe, which passed through the bounce and generated primordial density fluctuations in the early expansion phase. (Those density fluctuations eventually led to the formation of galactic structures in today's universe.) This contrasts with the commonly studied big bang scenario, in which the inhomogeneities were generated during an inflation (i.e., rapid expansion) phase right after the big bang. The big bounce scenario was proposed as an alternative theory of the cosmic history, which is free from several issues with the big bang theory (see this article). My work focused on the process of bouncing from contraction to expansion, addressing the stability of the bounce and the propagation of inhomogeneities through the bounce.
- Cosmological perturbations during a nonsingular bounce
The big bounce can be either singular or nonsingular. A singular bounce is one in which the universe contracts to an infinitesimal volume and then expands. Such models must involve quantum gravity effects, which are not well understood yet. Alternatively, we may consider a nonsingular bounce, in which the universe stops contraction and reverses to expansion at a finite size, well described by classical general relativity and effective field theory. Using models of a nonsingular bounce, we may study if the inhomogeneities generated in the contraction phase could pass through the bounce. With my PhD advisor Paul Steinhardt, I developed theoretical methods for calculating the behavior of small perturbations to the spacetime metric during the bounce. It was found that spatial curvature and anisotropy tend to grow and become unstable near the bounce (see this paper). Avoiding those problems puts theoretical constraints on bouncing models.
- Numerical simulation of a nonsingular bounce
Since small perturbations may be greatly amplified during the bounce, it is important to study the bounce using nonperturbative methods. In a collaboration with Frans Pretorius and David Garfinkle, we designed a nonsingular bouncing model that is free from the instability mentioned above, and used methods from numerical relativity to simulate the bouncing process. Our approach led to results that could not be obtained using perturbation theory. We found that not all parts of the universe could make it through the bounce --- regions where inhomogeneity and anisotropy happen to be large compared to the background energy density would end up in a gravitational collapse, whereas regions that are relatively homogeneous and isotropic would bounce into the expansion phase. For sufficiently small inhomogeneities, their power spectrum would remain unchanged throughout the bounce, which provides a theoretically consistent source for the observed primordial density fluctuations in the early expansion phase (see this paper). Our results thus establish the plausibility of the big bounce theory.
- Regularization of the big bang singularity
My latest work in bouncing cosmology took on a new perspective. I studied a singular bounce model using a dynamical systems approach, first suggested by my collaborator Edward Belbruno. In such a model, the solution to the classical equations that govern the dynamics of cosmic contraction and expansion has a singularity at the point where the universe contracts to an infinitesimal volume. As a result, the evolution of the universe could not be followed continuously through this point within the theory of classical gravity. Using methods from dynamical systems theory, we analyzed whether the solution could be ``regularized'' by constructing a unique extension through the singularity. This was shown to be possible for a special set of values for the parameter controlling the equation of state of the universe near the bounce (see this paper). We have further generalized our result to include random perturbations that are meant to represent classical inhomogeneities or quantum fluctuations. Our results seem to imply that singular bounce models have to be extremely fine-tuned, at least classically.