Cosmology and Gravitation

We study the general class of gravitational field theories constructed on the basis of scale invariance (and therefore absence of any mass parameters) and invariance under transverse diffeomorphisms (TDiff), which are the 4-volume conserving coordinate transformations. We show that these theories are equivalent to a specific type of scalar-tensor theories of gravity (invariant under all diffeomorphisms) with a number of properties, making them phenomenologically interesting. In particular, they lead to the evolution of the universe supported by present observations: inflation in the past, followed by the radiation and matter dominated stages and accelerated expansion at present. All mass scales in this type of theories come from one and the same source. The massless particle spectrum of these theories contains the graviton and a new particle -- dilaton, which has only derivative couplings and thus escapes the fifth force constraints.

In this talk, I am going to test the concordance cosmology in three different cosmic scales. (1) On the super-horizon scale, “Copi etal. (2009)” have been arguing that the lack of large angular correlations of the CMB temperature field provides strong evidence against the standard, statistically isotropic, LCDM cosmology. I am going to argue that the “ad-hoc” discrepancy is due to the sub-optimal estimator of the low-l multipoles, and a posteriori statistics, which exaggerates the statistical significance. (2) LCDM model also predict the existence of primordial gravitational wave, for which B-mode polarization will be a powerful tool to distinguish different models of the early Universe; (3) On Galactic scales, “Watkins et al. (2008)” shows that the very large bulk flow prefers a very large density fluctuation, which seems to contradict to the LCDM model. We provide a physical explanation for this big bulk flow, based on the assumption that CMB frame does not coincide with matter rest frame, resulting in the tilted Universe. We show that the ‘tilted Universe’ could well explain the bulk flow phenomena and more importantly, the constraints for this tilted Universe can lead to the constraint on the number of e-folds of inflation; (4) In addition, cosmic Mach Number from peculiar velocity catalog may provide a powerful test of the growth of the structure.

I will discuss some work on the collider phenomenology and cosmology of light gravitino dark matter, and will touch on some related issues concerning infrared divergences in charged-particle decay at finite temperature.
Light gravitinos, with mass in the eV to MeV range, are well-motivated in particle physics, but their status as dark-matter candidates is muddled by early-Universe uncertainties.

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.