Cosmology

There has been a long-running discussion as to whether free gravitons on dS have a dS-invariant state. On the one hand, de Sitter invariant states are clearly singular in gauges favored by cosmologists; e.g. transverse traceless synchronous gauge associated with the k=0 slicing of dS. However, Higuchi has constructed a dS-invariant state using a different gauge. We resolve this tension by showing that the above “cosmologists gauge” is in fact singular on global de Sitter space. This observation may prove useful in understanding the physics of calculations indicating large IR effects involving gravity in dS.

The definition of correlation functions relies on measuring distances on some late surface of equal energy density. If invariant distances are used, the curvature correlation functions of single-field inflation are free of any IR sensitivity. By contrast, conventional correlation functions, defined using the coordinate distance between pairs of points, receive large IR corrections if measured in a "large box" and if inflation lastet for a sufficiently long period. The underlying large logarithms are associated with long-wavelength fluctuations of both the scalar and the graviton background. This effect is partially captured by the familiar delta-N-formalism. Conventional, IR-sensitive correlation functions are related to their IR-safe counterparts by simple and very general formulae. In particular, the coefficient of the leading logarithmic correction to any n-point function is controlled by the first and second logarithmic derivatives of this function with respect to the overall momentum scale. This allows for a simple evaluation of corrections to leading and higher-order non-Gaussianity parameters.

We discuss the definition of the Feynman propagator in de Sitter space. We show that the ambiguities in the propagator zero-mode can be used to make sense of the behavior of low-momentum modes in an inflating space-time. We use this tool to calculate loop corrections to non-Gaussian correlation functions, and show that there are limits where the loop terms dominate. These models can be probed with the Planck satellite.

Much work on quantum gravity has focussed on short-distance problems such as non-renormalizability and singularities. However, quantization of gravity raises important long-distance issues, which may be more important guides to the conceptual advances required. These include the problems of black hole information and gauge invariant observables, and those of inflationary cosmology. An overview of aspects of these problems, and apparent connections, will be given.

I will argue that the dynamical renormalization group can be used to resum late time divergences appearing in loop computations in de Sitter. In the case of a scalar field with quartic interactions, the resummed propagator is the massive one. Standard mean field theory techniques can then be used to estimate the mass. This is analogous to the thermal field theory story but with some notable differences. We discuss whether a critical point can exist in dS where mean field methods fail.

We clarify the origin of IR divergence in single-field models of inflation and provide the correct way to calculate the observable fluctuations. First, we show the presence of gauge degrees of freedom in the frequently used gauges such as the comoving gauge and the flat gauge. These gauge degrees of freedom are responsible for the IR divergences that appear in loop corrections of primordial perturbations. We propose, in this talk, one simple but explicit example of gauge-invariant quantities. Then, we explicitly calculate such a quantity to find that the IR divergence is absent in the slow-roll approximation. In this formalism, we revisit the consistency relation that connects the three-point function in the squeezed limit with the spectral index.

General Relativity receives quantum corrections relevant at macroscopic distance scales and near event horizons. These arise from the conformal scalar degrees of freedom in the extended effective field theory of gravity generated by the trace anomaly of massless quantum fields in curved space. Linearized perturbations of the Bunch-Davies state in de Sitter space show that these new scalar degrees of freedom are associated with macroscopic changes of state on the cosmological horizon scale, with potentially large stress tensors that can lead to substantial backreaction effects in cosmology. In the extended effective theory the cosmological ``constant" is a state dependent condensate whose value is scale dependent and which possesses an infrared stable conformal fixed point at zero. These considerations suggest that the observed dark energy of our universe may be a macroscopic finite size effect whose value depends not upon Planck scale physics but upon extreme infrared physics on the cosmological horizon scale.

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 source function is, to an excellent approximation, simply related to the slope and curvature of the inflaton potential, even in the presence of large or rapidly changing deviations from scale-free initial conditions. Oscillatory features in the WMAP temperature power spectrum have led to interest in exploring models with features in the inflationary potential, but such cases are typically studied on a case-by-case basis. This formalism generalizes previous studies by exploring the complete parameter space of inflationary models in a single analysis. I will present results from a Markov Chain Monte Carlo likelihood analysis of WMAP 7-year and other data sets that probe the inflationary potential both at large and small scales, and I will discuss constraints from upcoming high-sensitivity experiments.

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. The generalized second law holds because the horizon is invariant under a larger symmetry group than the rest of the spacetime.

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. I will present new more stringent constraints from Fermi gamma ray data that tend to rule out such models. However we find a loophole: DM annihilations in a nearby DM subhalo, between us and the galactic center, could provide the excess leptons while respecting gamma ray constraints.

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). We will show that one of the best venues to observe the QVHE in graphene is actually superconductivity that can be induced in graphene by proximity effect, say, where passing supercurrent in one direction induces accumulation of pseudo spin ("valley spin") at the boundary of graphene sample. We will also discuss the "inverse QVHE" as a possible scenario to explain the highly resistive state found in N=0 Landau level in graphene in a high magnetic field.