This series consists of talks in the areas of Cosmology, Gravitation and Particle Physics.
I introduce a general method for constraining the shape of the inflationary potential from Cosmic Microwave Background (CMB) temperature and polarization power spectra. This approach relates the CMB observables to the shape of the inflaton potential via a single source function that is responsible for the observable features in the initial curvature power spectrum.
The entropy outside of an event horizon can never decrease if one includes a term proportional to the horizon area. For a long time, this astonishing result had only been shown for quantum fields that are in an approximately steady state. I will describe a new proof of the generalized second law for arbitrary slices of semiclassical, rapidly-changing horizons. I will start with the simplest case, Rindler horizons, and then describe how the proof can be adapted to other cases (black holes, de Sitter, etc.) by restricting the field algebra to the horizon.
If dark matter consists of a multiplet with small mass splittings, it is possible to simultaneously account for DAMA/CoGeNT hints of direct detection and the INTEGRAL 511 keV gamma ray excess from the galactic center; such dark matter must be in the 4-12 GeV mass range. I present scenarios where the DM transforms under a hidden SU(2) that can account for these observations. These models can be tested in low-energy beam dump experiments, like APEX. To explain PAMELA/Fermi excess electrons from dark matter annihilations, heavier TeV scale DM is required.
The quantum spin Hall effect relates seemingly unrelated degrees of freedom, i.e., charge and spin degrees of freedom. We will discuss such "duality" can be extended to much wider class of quantum numbers, and the corresponding order parameters. In particular, two valleys in graphene can be viewed as an SU(2) pseudo spin degree of freedom, which turns out to be "dual" to the charge degree of freedom, pretty much in the same way as spin in the quantum spin Hall effect is closely tied with charge. I.e., graphene can host "the quantum valley Hall effect" (QVHE).
Using a formulation of the post-Newtonian expansion in terms of Feynman graphs, we discuss how various tests of General Relativity (GR) can be translated into measurement of the three- and four-graviton vertices. The timing of the Hulse-Taylor binary pulsar provides a bound on the deviation of the three-graviton vertex from the GR prediction at the 0.1% level.
Constraints on the formation of primordial black holes - especially the ones which are small enough to evaporate - provide a unique probe of the early universe, high energy physics and extra dimensions. For evaporating black holes, the dominant constraints are associated with big bang nucleosynthesis and the extragalactic photon background, but there are also other limits associated with the cosmic microwave background, cosmic rays and various types of relic particles.
I consider some of the issues we face in trying to understand dark energy. Huge fluctuations in the unknown dark energy equation of state can be hidden in distance data, so I argue that model-independent tests which signal if the cosmological constant is wrong are valuable. These can be constructed to remove degeneracies with the cosmological parameters. Gravitational effects can play an important role. Even small inhomogeneity clouds our ability to say something definite about dark energy.
Although inflation is, by far, the best known mechanism to explain the observed properties of our Universe, there is still some room for alternative models, most of which implying a contracting phase preceding the current expanding one. Both phases are connected by a bounce at which the expansion rate must vanish. General relativity can only produce such a phase provided the spatial curvature is positive, in contradiction with the current observations.