Cosmology

Standard inflationary theory predicts that primordial fluctuations in the universe were nearly Gaussian random. Therefore, searches for, and limits on, primordial nongaussianity are some of the most fundamental tests of inflation and the early universe in general. I first briefly review the history of its measurements from the cosmic microwave background anisotropies and large-scale structure in the universe. I then present results from recent work where effects of primordial nongaussianity on the distribution of largest virialized objects was studied numerically and analytically. We found that the bias of dark matter halos takes strong scale dependence in nongaussian cosmological models. Therefore, measurements of scale dependence of the bias, using various tracers of large-scale structure, can - and do - constrain primordial nongaussianity more than an order of magnitude better than previously thought.

Scalar field models of early universe inflation are effective field theories, typically valid only up to some UV energy scale, and receive corrections through higher dimensional operators due to the UV physics. Corrections to the tree level inflationary potential by these operators can ruin an otherwise suitable model of inflation. In this talk, I will consider higher dimensional kinetic operators, and the corrections that they give to the dynamics of the inflaton field. In particular, I will show how inflationary solutions exist even when the higher dimensional operators are important and not tuned to be negligible. I will then show that these solutions, which include the usual slow roll inflationary solutions, are attractors in phase space. I will end by speculating on the role of the corrections from these higher dimensional operators in alleviating the homogeneous initial conditions problem for inflation.

Most often, the dark matter puzzle is analyzed along a single perspective, thus trying to answer a single question. Either "what is the dark matter?", focusing on its microscopic nature, or "how is dark matter distributed in the universe?" focusing on the large scale structure of the universe, or still "how does it affect what we observe in the sky?". Both my scientific interests and some random fluctuations at the beginning of my career have conspired so that I would take on projects in all these fields. Leaving aside the ambition -- and the impossible task -- to be comprehensive, I will review some interesting aspects of these fields and some of my contributions, ranging from using astrophysical cross-correlations to put constraints on the neutrino masses, to the interplay between Higgs searches at colliders and dark matter experiments, to using gamma ray observations to detect and measure properties of extra dimensions.

The basic structure of quantum mechanics was delineated in the early days of the theory and has not been modified since. Still it is interesting to ask whether that basic structure can be altered or generalized. In the last decade Bender et al have shown that one of the fundamental assumptions of quantum mechanics, that operators are represented by Hermitian matrices, can to an extent be relaxed. In this theory, the parity (P) and time-reversal (T) operators play a role analogous to the Hermitian conjugate. Recently we have extended the realm of `PT quantum mechanics' to include systems that are odd under time-reversal (T^2 = - 1), in the interest of constructing the PT-analogue of the Dirac equation. We find that the fundamental representation of the Dirac equation, which describes relativistic fermions, remains unchanged in the generalization to the non-Hermitian theory. Higher dimensional representations, which ordinarily decouple into pairs of Dirac fermions in Hermitian quantum mechanics, here describe new types of particles with extremely compelling properties. Most notably we have constructed a toy model representing two generations of massless neutrinos that nonetheless undergo flavor oscillations; furthermore this model is Lorentz invariant and unitary in time. The Standard Model requires that the neutrino be massive in order to accomodate the observed flavor oscillations, thus this toy model represents a significant departure from Standard Model physics.