Cosmology

Among the possible explanations for the observed acceleration of the universe, perhaps the boldest is the idea that new gravitational physics might be the culprit. In this colloquium I will discuss some of the challenges of constructing a sensible phenomenological extension of General Relativity, give examples of some candidate models of modified gravity and survey existing observational constraints on this approach. I will conclude by discussing how we might hope to distinguish between modifications of General Relativity and dark energy as competing hypotheses to explain cosmic acceleration.

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.

In the future it may be possible to observe the CMB radiation at very low frequencies. I review the origin of the signal from 21cm absorption by dark-age gas and explain the huge potential for observational cosmology. I summarise recent work on theoretical expectations for the observable power spectrum, including discussion of Hubble-scale perturbations, the effects of perturbed recombination and non-linear evolution.

Anthropic arguments based on selection effects for observers have been claimed to succesfully explain the measured value of the cosmological constant.In this talk I review the fundations of such claims in the context of probability theory and show that different (and equally legitimate) ways of assigning probabilities to candidate universes lead to totally different anthropic predictions. As an explicit example, I discuss a weighting scheme based on the total number of possible observations that observers can carry out over the entire lifetime of the Universe. I show that this leads to an extremely small probability for observing a value of the cosmological constant equal to or greater than what we now measure, in marked contrast with the usual result. I also discuss principles of consistent probabilistic reasoning, showing that the anthropic principle as applied in most of the literature is logically inconsistent. I conclude that current implementations of the anthropic principle display a worrysome lack of predictivity, and cannot be used to explain the value of the cosmological constant, nor, likely, any other physical parameters.

The possibility that rotational invariance ins broken during the inflationary era is discussed. The implications of this for the microwave background asymmetry are derived using a model independent approach. A particular inflationary model that realizes these ideas is studied.

We consider a six-dimensional space-time, in which two of the dimensions are compactified by a flux. Matter can be localized on a codimension one brane coupled to the bulk gauge field and wrapped around an axis of symmetry of the internal space. By studying the linear perturbations around this background, we show that the gravitational interaction between sources on the brane is described by Einstein 4d gravity at large distances. Our model provides a consistent setup for the study of gravity in a football compactification, without having to deal with the complications of a delta–like, codimension two brane. Moreover, it allows us to identify the origin of the problems that emerge when one takes the limit of a codimension-two brane.

The general relativity has been tested from mm scales to solar system scales. The discovery of cosmic acceleration motivates the study of infrared modification of gravity at horizon scales. The cosmic expansion can be accelerated by dark energy without any correction to GR, but alternatively it can be explained by the modified gravity at large scales without introducing the unknown exotic energy. We introduce the linear structure formation theory of DGP and f(R) gravity, and present what it the strategy to test general relativity at cosmological scales.