Cosmology and Gravitation

We have two strong reasons to argue that Einstein\'s theory of general relativity may be incomplete. First, given that it cannot be expressed within a consistent quantum field theory there is reason to expect higher energy corrections. Second, the observation that we are undergoing a current epoch of accelerated expansion might indicate that our understanding of gravity breaks down at the largest scales. A generic result of modified gravity is the creation of a new degree of freedom within the gravitational sector. This new degree of freedom then generically connects local physics to cosmological dynamics. I will present the results of studying two modified theories of gravity emphasizing how they bridge the gap between local and cosmological physics. First I will discuss work I have done on f(R) modified gravity theories, delineating under what conditions these theories deviate strongly from general relativity. Using these results I will talk about some recent work on attempting to detect a characteristic signature of these theories from gravitational lensing. Second I will discuss recent results on ways we may test Chern-Simons gravity (a result of the low energy effective string action) in the Solar System. Chern-Simons gravity has been identified as a candidate for leptogenesis as well as a source for circularly polarized gravitational-waves from inflation. As I will discuss, constraints to Chern-Simons gravity may improve in the near future with further observations of double pulsar systems.

I will discuss a new method of inflaton potential reconstruction that combines the flow formalism, which is a stochastic method of inflationary model generation, with an exact numerical calculation of the mode equations of quantum fluctuations. This technique allows one to explore regions of the inflationary parameter space yielding spectra that are not well parameterized as power-laws. We use this method to generate an ensemble of generalized spectral shapes that provide equally good fits to current CMB and LSS as data as do simpler power-law spectra. Within this ensemble are spectra that exhibit a strong running on large angular scales (where cosmic variance is large) that turns off on small scales. Such strongly running spectra are accompanied by large tensor components that lie outside the 1 and 2 sigma limits of current WMAP3 and SDSS data. This demonstrates that the generalization of the spectral shape adversely impacts our ability to constrain key inflationary observables. The inflationary models giving rise to such spectra are characterized by an initially fast rolling inflaton, in marked contrast to the dominant paradigm of slow roll inflation.

The detection of primordial non-Gaussianity could provide a powerful means to rule out various inflationary scenarios. Although scale-invariant non-Gaussianity is currently best constrained by the Cosmic Microwave Background, single-field inflation models with changing sound speed can have strongly scale dependent non-Gaussianity. I will discuss the theoretical motivation for such models and present work on the likely ability of current and future large scale structure measurements to constrain them.

f(R) theories are an alternative approach at the phenomenon of cosmic acceleration, in which the Einstein-Hilbert action for gravity is modified by adding a function of the Ricci scalar, f(R). While at the background level viable f(R) models must closely mimic LCDM, the difference in their prediction for the growth of large scale structures can be sufficiently large to leave detectable signatures in future surveys. In this talk, after reviewing the conditions for the background viability of f(R) theories, I will focus on scalar perturbations. I will present in some details the dynamics of linear perturbations, showing what are the characteristic imprints of f(R) models in the growth of structures and consider possible observational tests

The non-Gaussianity of the primordial cosmological perturbations will be strongly constrained by future observations like Planck. It will provide us with important information about the early universe and will be used to discriminate among models. I will review how different models of the early universe can generate different amount and shapes of non-Gaussianity.

The Origin of the Large Scale Structure is one of the key issue in Cosmology. A plausible assumption is that structures grow via gravitational amplification and collapse of density fluctuations that are small at early times. The growth history of cosmological fluctuations is a fundamental observable which helps in hunting for evidences of new physics, currently missing from our picture of the universe, but potentially crucial to explain its past, present and future history. I'll show how we investigated if the gradual growth of structures observed over a period of nearly 9 billion years can be used to discriminate between different gravitational models. I'll also discuss how the measurement of the cosmic growth rate provides an alternative independent probe to understand the origin of the accelerated expansion of the universe.

We introduce a framework that allows to calculate cosmological perturbations in a gauge invariant manner to any order. The two main features of this framework are to take physical observables as basic objects and to treat the variables describing the background geometry as fully dynamical. Backreaction effects can therefore naturally adressed. At the end I will mention applications to Loop Quantum Cosmology.

Dark matter and dark energy can be explained without resorting to exotic fields if one accepts that the geometry of spacetime is governed by suitable generalized gravitational theories based on Lagrangians that are non-linear in the curvature of a metric and/or a torsionless linear connection, i.e. in second order and first order formalisms. A convenient choice of nonquadratic Lagrangians can fit well most of the astrophysical, cosmological and solar system requirements imposed by experimental results, without drastic modifications of Einstein field equations and with FRW Cosmologies preserved as a good approximation of Nature at a global scale.

We show that the current accelerated expansion of the Universe can be explained without resorting to dark energy. Models of generalized modified gravity, with inverse powers of the curvature can have late time accelerating attractors without conflicting with solar system experiments. We have solved the Friedman equations for the full dynamical range of the evolution of the Universe. This allows us to perform a detailed analysis of Supernovae data in the context of such models that results in an excellent fit. Hence, inverse curvature gravity models represent an example of phenomenologically viable models in which the current acceleration of the Universe is driven by curvature instead of dark energy. If we further include constraints on the current expansion rate of the Universe from the Hubble Space Telescope and on the age of the Universe from globular clusters, we obtain that the matter content of the Universe is 0.07 <= omega_m <= 0.21 (95% Confidence). Hence the inverse curvature gravity models considered can not explain the dynamics of the Universe just with a baryonic matter component.