Constantinos Skordis

Modified Gravity and Cosmology

Abstract In this review we present a thoroughly comprehensive survey of recent work on modified theories of gravity and their cosmological consequences. Amongst other things, we cover General Relativity, scalar–tensor, Einstein–aether, and Bimetric theories, as well as TeVeS, f ( R ) , general higher-order theories, Hořava–Lifschitz gravity, Galileons, Ghost Condensates, and models of extra dimensions including Kaluza–Klein, Randall–Sundrum, DGP, and higher co-dimension braneworlds. We also review attempts to construct a Parameterised Post-Friedmannian formalism, that can be used to constrain deviations from General Relativity in cosmology, and that is suitable for comparison with data on the largest scales. These subjects have been intensively studied over the past decade, largely motivated by rapid progress in the field of observational cosmology that now allows, for the first time, precision tests of fundamental physics on the scale of the observable Universe. The purpose of this review is to provide a reference tool for researchers and students in cosmology and gravitational physics, as well as a self-contained, comprehensive and up-to-date introduction to the subject as a whole.

The tensor-vector-scalar theory and its cosmology

Over the last few decades, astronomers and cosmologists have accumulated vast amounts of data clearly demonstrating that our current theories of fundamental particles and of gravity are inadequate to explain the observed discrepancy between the dynamics and the distribution of the visible matter in the universe. The modified Newtonian dynamics (MOND) proposal aims at solving the problem by postulating that Newtons second law of motion is modified for accelerations smaller than ~10−10 m s−2. This simple amendment, has had tremendous success in explaining galactic rotation curves. However, being non-relativistic, it cannot make firm predictions for cosmology. A relativistic theory called tensor-vector-scalar (TeVeS) has been proposed by Bekenstein building on earlier work of Sanders which has a MOND limit for non-relativistic systems. In this review I give a short introduction to TeVeS theory and focus on its predictions for cosmology as well as some non-cosmological studies.

Generalizing tensor-vector-scalar cosmology

I consider an extented version of Bekenstein’s Tensor-Vector-Scalar theory where the action of the vector field is of a general Einstein-Ether form. This work presents the cosmological equations of this theory, both at the background and perturbed level, for scalar, vector and tensor perturbation modes. By solving the background equations in the radiation era analytically, to an excellent approximation, I construct the primordial adiabatic perturbation for a general family of scalar field kinetic functions.

Models of dark matter coupled to dark energy

We present three distinct types of models of dark energy in the form of a scalar field which is explicitly coupled to dark matter. Our construction draws from the pull-back formalism for fluids and generalises the fluid action to involve couplings to the scalar field. We investigate the cosmology of each class of model both at the background and linearly perturbed level. We choose a potential for the scalar field and a specific coupling function for each class of models and we compute the Cosmic Microwave Background and matter power spectra.

Eddington-Born-Infeld gravity and the large scale structure of the Universe

It has been argued that a Universe governed by Eddington-Bom-Infeld gravity can be compatible with current cosmological constraints. The extra fields introduced in this theory can behave as both dark matter and dark energy, unifying the dark sector in one coherent framework. We show the various roles the extra fields can play in the expansion of the Universe and study the evolution of linear perturbations in the various regimes. We find that, as a unified theory of the dark sector, Eddington-Born-Infeld gravity will lead to excessive fluctuations in the cosmic microwave background on large scales. In the presence of a cosmological constant, however, the extra fields can behave as a form of nonparticulate dark matter and can lead to a cosmology which is entirely compatible with current observations of large scale structure. We discuss the interpretation of this form of dark matter and how it can differ from standard, particulate dark matter.

Ambiguous tests of general relativity on cosmological scales

There are a number of approaches to testing General Relativity (GR) on linear scales using parameterized frameworks for modifying cosmological perturbation theory. It is sometimes assumed that the details of any given parameterization are unimportant if one uses it as a diagnostic for deviations from GR. In this brief report we argue that this is not necessarily so. First we show that adopting alternative combinations of modifications to the field equations significantly changes the constraints that one obtains. In addition, we show that using a parameterization with insufficient freedom significantly tightens the apparent theoretical constraints. Fundamentally we argue that it is almost never appropriate to consider modifications to the perturbed Einstein equations as being constraints on the effective gravitational constant, for example, in the same sense that solar system constraints are. The only consistent modifications are either those that grant near-total freedom, as in decomposition methods, or ones which map directly to a particular part of theory space.

Linking Tests of Gravity On All Scales: from the Strong-Field Regime to Cosmology

The current eort to test General Relativity employs multiple disparate formalisms for dierent observables, obscuring the relations between laboratory, astrophysical and cosmological constraints. To remedy this situation, we develop a parameter space for comparing tests of gravity on all scales in the universe. In particular, we present new methods for linking cosmological large-scale structure, the Cosmic Microwave Background and gravitational waves with classic PPN tests of gravity. Diagrams of this gravitational parameter space reveal a noticeable untested regime. The untested window, which separates small-scale systems from the troubled cosmological regime, could potentially hide the onset of corrections to General Relativity. Subject headings: gravitation { dark energy

Note on bigravity and dark matter

We show that a class of bigravity theories contain solutions describing dark matter. A particular member of this class is also shown to be equivalent to the Eddington-Born-Infeld gravity, recently proposed as a candidate for dark matter. Bigravity theories also have cosmological de Sitter backgrounds and we find solutions interpolating between matter and acceleration eras.

Linear growth rate of structure in parametrized post-Friedmannian universes

A possible solution to the dark energy problem is that Einsteins theory of general relativity is modified. A suite of models have been proposed that, in general, are unable to predict the correct amount of large scale structure in the distribution of galaxies or anisotropies in the cosmic microwave background. It has been argued, however, that it should be possible to constrain a general class of theories of modified gravity by focusing on properties such as the growing mode, gravitational slip, and the effective, time-varying Newtons constant. We show that assuming certain physical requirements such as stability, metricity, and gauge invariance, it is possible to come up with consistency conditions between these various parameters. In this paper we focus on theories which have, at most, second derivatives in the metric variables and find restrictions that shed light on current and future experimental constraints without having to resort to a (as yet unknown) complete theory of modified gravity. We claim that future measurements of the growth of structure on small scales (i.e. from

Cosmological behavior of Bekenstein's modified theory of gravity

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