Cosmology and Gravitation

The possibility that rotational invariance ins broken during the inflationary era is discussed. The implications of this for the microwave background asymmetry are derived using a model independent approach. A particular inflationary model that realizes these ideas is studied.

We consider a six-dimensional space-time, in which two of the dimensions are compactified by a flux. Matter can be localized on a codimension one brane coupled to the bulk gauge field and wrapped around an axis of symmetry of the internal space. By studying the linear perturbations around this background, we show that the gravitational interaction between sources on the brane is described by Einstein 4d gravity at large distances. Our model provides a consistent setup for the study of gravity in a football compactification, without having to deal with the complications of a delta–like, codimension two brane. Moreover, it allows us to identify the origin of the problems that emerge when one takes the limit of a codimension-two brane.

The general relativity has been tested from mm scales to solar system scales. The discovery of cosmic acceleration motivates the study of infrared modification of gravity at horizon scales. The cosmic expansion can be accelerated by dark energy without any correction to GR, but alternatively it can be explained by the modified gravity at large scales without introducing the unknown exotic energy. We introduce the linear structure formation theory of DGP and f(R) gravity, and present what it the strategy to test general relativity at cosmological scales.

Current measurements from WMAP and other cosmological probes are consistent with a simple inflationary model. Such models predict a background of gravitational waves which may soon be observable in the polarized component of the Cosmic Microwave Background. However, WMAP has observed significant levels of polarized radiation from our galaxy, due to both synchrotron radiation and thermal dust emission. A better understanding of this radiation will be vital if we are to correctly remove it and confidently detect an inflationary signal. As well as discussing the observational case for inflation, I will review the physical origins of the polarized galactic emission, present a simple model for the galactic magnetic field, and discuss current and future directions for improving upon our galactic models.

I first summarize how the recent avalanche of precision measurements involving the cosmic microwave background, galaxy clustering, the Lyman alpha forest, gravitational lensing, supernovae Ia and other tools probes has transformed our understanding of our universe. I then discuss key open problems such as the nature of dark matter, dark energy and the early universe.

Cosmology ultimately aims to explain the initial conditions at the beginning of time and the entire subsequent evolution of the universe. The "beginning of time" can be understood in the Wheeler-DeWitt approach to quantum gravity, where homogeneous universes are described by a Schroedinger equation with a potential barrier. Quantum tunneling through the barrier is interpreted as a spontaneous creation of a small (Planck-size) closed universe, which then enters the regime of cosmological inflation and reaches an extremely large size. After sufficient growth, the universe can be adequately described as a classical spacetime with quantum matter. The initial quantum state of matter in the created universe can be determined by solving the Schroedinger equation with appropriate boundary conditions. I show that the most likely initial state is close to the vacuum state. This is the initial condition for inflation favored both by observational data and theoretical considerations.

We consider N=2 supersymmetric quantum electrodynamics (SQED) with 2 flavors, the Fayet--Iliopoulos parameter, and a mass term $beta$ which breaks the extended supersymmetry down to N=1. The bulk theory has two vacua; at $beta=0$ the BPS-saturated domain wall interpolating between them has a moduli space parameterized by a U(1) phase $sigma$ which can be promoted to a scalar field in the effective low-energy theory on the wall world-volume. At small nonvanishing $beta$ this field gets a sine-Gordon potential. As a result, only two discrete degenerate BPS domain walls survive. We find an explicit solitonic solution for domain lines -- string-like objects living on the surface of the domain wall which separate wall I from wall II. The domain line is seen as a BPS kink in the world-volume effective theory. The domain line carries the magnetic flux which is exactly 1/2 of the flux carried by the flux tube living in the bulk on each side of the wall. Thus, the domain lines on the wall confine charges living on the wall, resembling Polyakov's three-dimensional confinement.

I begin with a brief description of the black strings in backgrounds with compact circle, the Gregory-Laflamme instability and the resulting phase transition, and the critical dimensions.Then I describe a Landau-Ginzburg thermodynamic perspective on the instability and on the order of the phase transition. Next, the approach is generalized from a circle compactification to an arbitrary torus compactification. It is shown that the transition order depends only on the number of extended dimensions. I end up with outlining several open questions and puzzles related to the outcome of the Gregory-Laflamme instability.

We discuss the properties of matter in the low temperature regime at density that may exist in the core of compact stars. Assuming that in these conditions quarks are deconfined the attractive color interaction determines the formation of Cooper pairs of quarks and the resulting quark matter has properties analogous to standard superconductors. We show that under reasonable conditions a state were Cooper pairs have non-zero total momentum is energetically favored and the resulting non-homogeneous condensate is characterized by a crystal symmetry. Studying the elastic properties of such a state we find that it behaves like a solid crystal with a very large shear modulus. Our results raise the possibility that (some) pulsar glitches may originate within the Crystalline Color Superconductor core of Neutron stars.

During multi-field Inflation, the curvature perturbation can evovlve on superhorizon scales and will develop non-gaussianity due to non-linear interactions. In this talk I will discuss the calculation of this effect for models of inflation with two scalar fields.