Cosmology and Gravitation

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!

I will introduce the gravitational microlensing, its application to the compact dark matter detection and the extra-solar planet observations. EROS has been performed the microlensing observation in four directions of the Galactic plane, away from the Galactic center. I will report the observational results and the interpret the data within the Standard Galactic model. As a result we extract the best fit to the dust contribution in the Galactic disk, orientation of the Galactic bar and the abundance of the red giants compare to local stellar distribution.

I'll discuss how to systematically construct a (d+2)-dimensional solution of the vacuum Einstein equations that is dual to a (d+1)-dimensional fluid satisfying the incompressible Navier-Stokes equations with specific higher-derivative corrections. The solution takes the form of a non-relativistic gradient expansion that is in direct correspondence with the hydrodynamic expansion of the dual fluid. The dual fluid has nevertheless an underlying description in terms of relativistic hydrodynamics, with the unusual property of having a vanishing equilibrium energy density. Using the gravitational results, as well as an interesting and exact constraint on its stress tensor, we identify the transport coefficients of the dual fluid. A simple Lagrangian model is sufficient to realise its key properties.

Cosmic strings are predicted to arise in both inflationary and non-inflationary cosmological models. The signatures of such strings will stand out particularly well at higher redshifts. I will discuss how to look for these signatures in CMB redshift and polarization maps and in 21cm redshift surveys.

String theory should give a well-defined answer to the following question: What is the state of matter in the limit of infinite energy density? We use results obtained from the understanding of black hole entropy to conjecture this equation of state, noting that the maximum entropy state in string theory has vastly more entropy than the states used in traditional approaches to early Universe Cosmology. The evolution of the Universe with this equation of state can be obtained in closed form.