Cosmology and Gravitation

I present a simple exactly solveable model of eternal inflation.  The correlation functions have a discrete analogue of conformal symmetry, which can be compactly expressed using the machinery of p-adic numbers.  I comment on the implications for actual cosmology, and in particular for holographic descriptions of eternal inflation.

Supersymmetry plays a fundamental role in the radiative stability of many inflationary models.  I will explain how supersymmetry and naturalness require additional scalar degrees of freedom with masses on the order of the inflationary Hubble scale.  These fields lead to distinctive non-gaussian signatures that may be observable in both the CMB and large scale structure.

Hawking's discovery of black holes radiance along with Bekenstein's conjecture of the generalized second law of thermodynamics inspired a conceptually pleasing connection between gravity, thermodynamics and quantum theory. However, the discovery that the spectrum of the radiation is in fact thermal, together with the no-hair theorem, has brought along with it some undesirable consequences, most notably the information loss paradox. There have been many proposals to the resolution of this paradox, with the most natural resolution being that during the time of collapse the radiation given off is not completely thermal and can carry small amounts of information with it. In this talk, we will revisit the so-called pre-Hawking radiation given off during the scenario of gravitational collapse by utilizing the so-called functional Schroedinger equation (FSE) and quantum kinetic equation (QKE). Here we find that the spectrum never becomes thermal and discuss the reasons for this. Finally we will discuss the implications of this result, as well as previous results, toward the resolution of the information paradox.

The advent of large spectroscopic surveys of galaxies in the early 1980s has shown us that galaxies assemble in large scale structures. Recently, cosmic voids have received more attention through the availability wide and deep galaxy surveys. Voids have a simple phase space structure and thus are easier to model than cluster of galaxies. I will present two important applications of the precise analysis of voids in the context of constraining the equation of state of dark energy. First I will discuss how they could be used to have a much better determination of the expansion factor than using traditional methods, like Baryonic Acoustic Oscillations. Second, I will show that voids is maybe the only large-scale structure for which the dynamics can be finely modelled, notably through the use of the Monge-Ampere-Kantorovitch orbit reconstruction method. For the two above cases, I will present how we can mathematically define cosmic voids, the methods that have been developed to find them and some results based on N-body simulations for constraining the Dark Energy equation of state.

The study of the anisotropies in the cosmic microwave background radiation over the past two decades has provided us with important information about the early universe. In particular, there is strong evidence that these anisotropies were generated long before the cosmic microwave radiation was emitted. The most commonly studied idea is that they originated as quantum fluctuations during a period of inflation. In addition to a spectrum of scalar perturbations consistent with the one that has been observed, inflation also predicts the presence of gravitational waves. These might be observable in the polarization of the cosmic microwave background. An observation of this signal would indicate that the inflaton must have traversed a super-Planckian distance. Realizing this in string theory has been challenging. I will describe the basic ingredients for a string theoretic setup in which the inflaton can move over a super-Planckian distance, leading to an observable gravitational wave signal within string theory. In addition to an observable tensor signal, the model may also lead to other interesting signatures which I will discuss such as modulations in the power spectrum of scalar perturbations, interesting shapes of non-Gaussianities, and possibly the formation of oscillons at the end of inflation.

General relativity is a covariant theory of two transverse, traceless graviton degrees of freedom. According to a theorem of Hojman, Kuchar, and Teitelboim, modifications of general relativity must either introduce new degrees of freedom or violate the principle of general covariance. In my talk, I will discuss modifications of general relativity that retain the same number of gravitational degrees of freedom, and therefore explicitly break general covariance. Motivated by cosmology, the modifications of interest maintain spatial covariance. Demanding consistency of the theory forces the physical Hamiltonian density to obey an analogue of the renormalization group equation, which encodes the invariance of the theory under flow through the space of conformally equivalent spatial metrics.

Problematic growths of curvature and anisotropy are found in nonsingular bouncing cosmologies that include both an ekpyrotic phase and a bouncing phase. Classically, initial curvature and anisotropy that are suppressed during the ekpyrotic phase will grow back exponentially during the nonsingular bouncing phase. Besides, curvature and shear perturbations are generated by quantum fluctuations during the ekpyrotic phase. In the bouncing phase, an adiabatic curvature perturbation grows to dominate and gives rise to a blue spectrum that spoils the scale-invariance. Meanwhile, a scalar shear perturbation grows nonlinear and creates an overwhelming anisotropy that disrupts the nonsingular bounce altogether. We examine the common origin of these problems and discuss possible ways to avoid them.

The talk consists of two parts: (1) Quasi-single inflation, where the isocurvature direction has mass of order Hubble parameter. This part is based on 0911.3380 and new results about higher mass, and a sharp turn in trajectory. (2) Multi-stream inflation, where the inflationary trajectory bifurcates. This part is based on 0903.2123, 1006.5021 and a on-going project on calculating the bifurcation probability in a complicated landscape.

Cosmic strings are a generic prediction of Grand Unified Theories that can leave a sufficient imprint in the Cosmic Microwave Background anisotropies to open an observational window into an otherwise unreachable high energy domain. Being formed as topological defects of a Higgs field, they are also naturally coupled to various other fields, that can lead to superconducting-like currents, hence radically changing their structure and properties. After having summarized the standard string network behaviour and its cosmological effects, I will concentrate on the current-carrying properties and show how those can modify drastically the overall picture. In particular, I will exhibit the many current case, including the special non abelian situation that requires more care to be fully understood.

Several mechanisms can lead to production of particles during inflation. I discuss how this phenomenon can induce a contribution to the primordial spectrum of gravitational waves with unusual properties: the tensors produced this way can violate parity; can have a large three-point function; can have a relatively large tensor-to-scalar ratio even if inflation occurs at low energies; finally, their spectrum can display a feature that can be directly detected by second-generation gravitational interferometers such as advanced LIGO.

The time variation of physical constants has been much discussed in the literature, motivated by claims of fine structure constant variations together with several theoretical ideas. Although it is well understood (by most, but not all!) cosmologists that one must consider only dimensionless constants, most discussions of the strength of gravity involve "G", which is of course dimensional. I discuss some applications of variations of "G" on cosmological observables, stressing the need to stay dimensionless. "Constants" might also vary in space. An idea which is perhaps less crazy is that cosmological parameters might vary across the observable Universe. I show how this leads to dipole modulation, which corresponds to a correlation between neighbouring multipoles in maps of the cosmic microwave sky. Searches for such signals could lead to constraints on the variation of the cosmological model on the largest accessible scales.

A recently discovered class of active galactic nuclei, TeV luminous blazars, constitute a small fraction of the power output of black holes. Nevertheless, there are suggestions that unlike the UV and X-ray luminosity of quasars, the very-high energy gamma-ray emission from the TeV blazars can be thermalized on cosmological scales with order unity efficiency, resulting in a potentially dramatic heating of the low-density intergalactic medium. The way in which this occurs, however, imparts a variety of peculiar properties to this novel heating source, resulting in a number of robust cosmological consequences. I will discuss the process by which TeV blazars heat the Universe, the strange properties that this heating has, and the variety of signatures that it has left behind, many of which have already been observed!