Cosmology and Gravitation

I will show the calculation of the probability distribution for the volume of the Universe after slow-roll inflation both in the eternal and the non-eternal regime. Far from the eternal regime the probability distribution for the number of e-foldings, defined as one third of the logarithm of the volume, is sharply peaked around the number of e-foldings of the classical inflaton trajectory. At the transition to the eternal regime this probability is still peaked (with the width of order one e-foldings) around the average, which however gets twice larger at the transition point. As one enters the eternal regime the probability for the volume to be finite rapidly becomes exponentially small. In addition to developing techniques to study eternal inflation, these results allow us to establish the quantum generalization of the recently proposed bound on the number of e-foldings in non-eternal regime: the probability for slow-roll inflation to produce a finite volume larger than Exp[S_dS/2], where S_dS is the de Sitter entropy at the end of the inflationary stage, is smaller than the uncertainty due to non-perturbative quantum gravity effects. The existence of such a bound provides a consistency check for the idea of de Sitter complementarity.

I will review recent progress in testing with cosmological data the inflationary hypothesis for describing the very early universe. I will present snapshots of different aspects of confronting the theory with data, including a \'bottom-up\' approach: the latest results from a systematic reconstruction of the inflationary dynamics; and a \'top- down\' approach: testing specific string theoretic constructions that attempt to implement inflation, while predicting distinctive observables not found in simple field-theory models. I will discuss the ambiguities inherent in attempting to quantify generic predictions of the inflationary \'paradigm\' (as opposed to the predictions of specific models). Finally, I will discuss (in a manner accessible to theoreticians) the astrophysical complexities underlying an observational program to look for primordial tensor modes that will discriminate between inflation and alternative theories.

It has long been thought that theories based on equations of motion possessing derivatives of order higher than second are not unitary. Specifically, they are thought to possess unphysical ghost states with negative norm. However, it turns out that the appropriate Hilbert space for such theories had not been correctly constructed, and when the theory is formulated properly [Bender and Mannheim, PRL 100, 110402 (2008). (arXiv:0706.0207 [hep-th]] there are no ghost states at all and time evolution is fully unitary. Unitarity can be established for theories based on both second and fourth order derivatives, and for theories based on fourth order derivatives alone. In this latter case the Hamiltonian is a non-diagonalizable, Jordan-block operator which possesses fewer eigenstates than eigenvalues. Despite the lack of completeness of the energy eigenstates, a consistent, unitary quantum mechanics for the theory can still be formulated [Bender and Mannheim, PRD 78, 025022 (2008). (arXiv:0807.2607 [hep-th]).] The implications of these results for the construction of a consistent theory of quantum gravity in four spacetime dimensions will be briefly discussed.

Gravitomagnetism is a subtle concept. Adding Lorentz invariance to Newtonian gravity leads to magnetism, but Einsteinian gravitomagnetism differs from Maxwell\'s electromagnetism. The differences lead to confusion when Lense-Thirring precession is wrongly ascribed to gyroscopes, and when authors disagree about whether lunar laser ranging has measured gravitomagnetism. To clarify these issues, we analyze electric and magnetic effects in local Lorentz frames using the tetrad formalism.

It is argued that space-time is discretized on the basis of the gravitational interactions among the degrees of freedom of quantum fields.Configurations of fields fall into 2 classes,propagating (cisplanckian in length scale) and those that are transplanckian, sequestered in the space-time that is localized in discrete elements.Only the former determine the hubble expansion parameter and are therefore used to construct the inflaton.The model used for discretization is Sorkin\'s causet construction.From this the covariant massy Klein Gordon equation can be rationalized.The mass is encoded as an exchange matrix element between the sequestered (bound) degrees of freedom and those that propagate,presumably by tunneling thereby exlaining why m<<1.

I will illustrate the case of interacting dark Energy, that is to say cosmologies in which the dark energy scalar field interacts with other things in the universe (gravity, cold dark matter or neutrinos). After briefly presenting the status of our work for the first two classes of models, regarding both linear perturbations and Nbody simulations, I will in particular focus on the case of \'growing neutrinos\': in these models, neutrinos with a mass increasing with time might be driven to cluster at very large scales, due to a new interaction stronger than gravity and mediated by the dark energy scalar field.

The Lee-Wick model has recently been put forwards as an alternative to supersymmetry for solving the hierarchy problem of particle physics. I will show that, modulo important consistency questions, coupling the Lee-Wick model to cosmology leads to a bouncing universe cosmology with a scale-invariant spectrum of cosmological fluctuations emerging from quantum vacuum fluctuations in the contracting phase.

The Cosmic Microwave Background Radiation is our most important source of information about the early universe. Many of its features are in good agreement with the predictions of the so-called standard model of cosmology -- the Lambda Cold Dark Matter Inflationary Big Bang. However, the large-angle correlations in the microwave background exhibit several statistically significant anomalies compared to the predictions of the standard model. On the one hand, the lowest multipoles seem to be correlated not just with each other but with the geometry of the solar system. On the other hand, when we look at the part of the sky that we most trust -- the part outside the galactic plane, there is a dramatic lack of large angle correlations. So much so that no choice of angular powerspectrum can explain it if the alms are Gaussian random statistically isotropic variables of zero mean.

The Dark Energy might constitute an observable fraction of the total energy density of our Universe as far back as the time of matter radiation equality or even big bang nucleosynthesis. In this talk, I will review the cosmological implications of such an \'Early Dark Energy\' component, and discuss how it might - or might not - be detected by observations. In particular, I will show how assuming the early dark energy to be negligible will bias the interpretation of cosmological data.

One of the most challenging problems in theoretical physics today is the so called cosmological constant problem. While current observational constraints are consistent with the predictions of GR with a tiny cosmological constant, often referred to as the dark energy, it remains possible that it\'s the deviation of the law of gravity at large distance from Einstein\'s theory that resolves the puzzle. In this talk, I will briefly review some of the theoretical attempts made along this line, including the simple massive gravity, large extra dimensions, Unimodular gravity, classically constrained gravity, as well as their difficulties. I will then focus on some most recent study on the theory of massive graviton in de Sitter space, which may be more closely related to the reality both today and during the inflationary epoch. In particular, I would describe a model, in which one is able to open up the forbidden mass range of the graviton on a de Sitter background discovered by Higuchi.