Modified Gravity and Cosmology

Over the past decade, f(R) theories have been extensively studied as one of the simplest modifications to General Relativity. In this article we review various applications of f(R) theories to cosmology and gravity - such as inflation, dark energy, local gravity constraints, cosmological perturbations, and spherically symmetric solutions in weak and strong gravitational backgrounds. We present a number of ways to distinguish those theories from General Relativity observationally and experimentally. We also discuss the extension to other modified gravity theories such as Brans-Dicke theory and Gauss-Bonnet gravity, and address models that can satisfy both cosmological and local gravity constraints.

f(R) theories

http://inspirehep.net/record/1084324/files/arXiv:1201.2434.pdf

Observational probes of cosmic acceleration

Euclid is a European Space Agency medium-class mission selected for launch in 2020 within the cosmic vision 2015–2025 program. The main goal of Euclid is to understand the origin of the accelerated expansion of the universe. Euclid will explore the expansion history of the universe and the evolution of cosmic structures by measuring shapes and red-shifts of galaxies as well as the distribution of clusters of galaxies over a large fraction of the sky. Although the main driver for Euclid is the nature of dark energy, Euclid science covers a vast range of topics, from cosmology to galaxy evolution to planetary research. In this review we focus on cosmology and fundamental physics, with a strong emphasis on science beyond the current standard models. We discuss five broad topics: dark energy and modified gravity, dark matter, initial conditions, basic assumptions and questions of methodology in the data analysis. This review has been planned and carried out within Euclid’s Theory Working Group and is meant to provide a guide to the scientific themes that will underlie the activity of the group during the preparation of the Euclid mission.

/pdf/cosmology-and-fundamental-physics-with-the-euclid-satellite-1pi37a138r.pdf

Cosmology and Fundamental Physics with the Euclid Satellite

Massive gravity has seen a resurgence of interest due to recent progress which has overcome its traditional problems, yielding an avenue for addressing important open questions such as the cosmological constant naturalness problem. The possibility of a massive graviton has been studied on and off for the past 70 years. During this time, curiosities such as the van Dam, Veltman, and Zakharov (vDVZ) discontinuity and the Boulware-Deser ghost were uncovered. These results are rederived in a pedagogical manner and the St\"uckelberg formalism to discuss them from the modern effective field theory viewpoint is developed. Recent progress of the last decade is reviewed, including the dissolution of the vDVZ discontinuity via the Vainshtein screening mechanism, the existence of a consistent effective field theory with a stable hierarchy between the graviton mass and the cutoff, and the existence of particular interactions which raise the maximal effective field theory cutoff and remove the ghosts. In addition, some peculiarities of massive gravitons on curved space, novel theories in three dimensions, and examples of the emergence of a massive graviton from extra dimensions and brane worlds are reviewed.

Theoretical Aspects of Massive Gravity

The nature of the fuel that drives today’s cosmic acceleration is an open and tantalizing mystery. The braneworld theory of Dvali, Gabadadze, and Porrati (DGP) provides a context where late-time acceleration is driven not by some energy-momentum component (dark energy), but rather is the manifestation of the excruciatingly slow leakage of gravity off our four-dimensional world into an extra dimension. At the same time, DGP gravity alters the gravitational force law in a specific and dramatic way at cosmologically accessible scales. We derive the DGP gravitational force law in a cosmological setting for spherical perturbations at subhorizon scales and compute the growth of large-scale structure. We find that a residual repulsive force at large distances gives rise to a suppression of the growth of density and velocity perturbations. Explaining the cosmic acceleration in this framework leads to a present day fluctuation power spectrum normalization �8 ≤ 0.8 at about the two-sigma level, in contrast with observations. We discuss further theoretical work necessary to go beyond our approximations to confirm these results.

/pdf/probing-newton-s-constant-on-vast-scales-dvali-gabadadze-1vx7gmf1ba.pdf

Probing Newton's constant on vast scales: Dvali-Gabadadze-Porrati gravity, cosmic acceleration, and large scale structure

The phenomenology of Dvali–Gabadadze–Porrati cosmologies

The braneworld model of Dvali-Gabadadze-Porrati (DGP) is a theory where gravity is modified at large distances by the arrested leakage of gravitons off our four-dimensional universe. Cosmology in this model has been shown to support both "conventional" and exotic explanations of the dark energy responsible for today's cosmic acceleration. We present new results for the gravitational field of a clustered matter source on the background of an accelerating universe in DGP braneworld gravity, and articulate how these results differ from those of general relativity. In particular, we show that orbits nearby a mass source suffer a universal anomalous precession as large as 5 microarcseconds/year, dependent only on the graviton's effective linewidth and the global geometry of the full, five-dimensional universe. Thus, this theory offers a local gravity correction sensitive to factors that dictate cosmological history.

Gravitational leakage into extra dimensions: Probing dark energy using local gravity

We examine two semianalytical methods for estimating the baryon asymmetry of the Universe (BAU) generated in scenarios of ``local'' electroweak baryogenesis (in which the requisite baryon number violation and $\mathrm{CP}$ violation occur together in space and time). We work with the standard electroweak theory augmented by the addition of a $\mathrm{CP}$-violating dimension-six operator. We work in the context of a first order phase transition, but the processes we describe can also occur during the evolution of a network of topological defects. Both the approaches we explore deal with circumstances where the bubble walls which convert the high temperature phase to the low temperature phase are thin and rapidly moving. We first consider the dynamics of localized configurations with winding number one which remain in the broken phase immediately after the bubble wall has passed. Their subsequent decay can anomalously produce fermions. In a prelude to our analysis of this effect, we demonstrate how to define the $C$ and $\mathrm{CP}$ symmetries in the bosonic sector of the electroweak theory when configurations with nonzero winding are taken into account. Second, we consider the effect of the passage of the wall itself on configurations which happen to be near the crest of the ridge between vacua as the wall arrives. We find that neither of the simple approaches followed here can be pushed far enough to obtain a convincing estimate of the BAU which is produced. A large scale numerical treatment seems necessary.

Semianalytical approaches to local electroweak baryogenesis

Cosmologists today are confronted with the perplexing reality that the universe is currently accelerating in its expansion. Nevertheless, the nature of the fuel that drives today's cosmic acceleration is an open and tantalizing mystery. There exists the intriguing possibility that the acceleration is not the manifestation of yet another mysterious ingredient in the cosmic gas tank (dark energy), but rather our first real lack of understanding of gravity itself, and even possibly a signal that there might exist dimensions beyond that which we can currently observe. The braneworld model of Dvali, Gabadadze and Porrati (DGP) is a theory where gravity is altered at immense distances by the excruciatingly slow leakage of gravity off our three-dimensional Universe and, as a modified-gravity theory, has pioneered this line of investigation. I review the underlying structure of DGP gravity and those phenomenological developments relevant to cosmologists interested in a pedagogical treatment of this intriguing model.

Arthur Lue

Papers

Probing Newton's constant on vast scales: Dvali-Gabadadze-Porrati gravity, cosmic acceleration, and large scale structure

The phenomenology of Dvali–Gabadadze–Porrati cosmologies

Gravitational leakage into extra dimensions: Probing dark energy using local gravity

Semianalytical approaches to local electroweak baryogenesis

The Phenomenology of Dvali-Gabadadze-Porrati Cosmologies