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Modified Newtonian dynamics is an empirical modification to Poisson's equation which has had success in accounting for the "gravitational field" φ in a variety of astrophysical systems. The field φ may be interpreted in terms of the weak-field limit of a variety of spacetime geometries. Here we consider three of these geometries in a more comprehensive manner and look at the effect on timelike and null geodesies. In particular we consider the aquadratic Lagrangian (AQUAL) theory, tensor-vector-scalar (TeVeS) theory and generalized Einstein-aether theory. We uncover a number of novel features, some of which are specific to the theory considered while others are generic. In the case of AQUAL and TeVeS theories, the spacetime exhibits an excess (AQUAL) or deficit TeVeS solid angle akin to the case of a Barrióla-Vilenkin global monopole. In the case of generalized Einstein-aether, a disformal symmetry of the action emerges in the limit of … φ → 0. Finally, in all theories studied, massive particles can never reach spatial infinity while photons can do so only after experiencing infinite redshift. [ABSTRACT FROM AUTHOR]

General Relativity (GR) is a phenomenologically successful theory that rests on firm foundations, but has not been tested on cosmological scales. The deep mystery of dark energy (and possibly even the requirement of cold dark matter), has increased the need for testing modifications to GR, as the inference of such otherwise undetected fluids, depends crucially on the theory of gravity. Here I discuss a general scheme for constructing consistent and covariant modifications to the Einstein equations. This framework is such that there is a clear connection between the modification and the underlying field content that produces it. I argue that this is mandatory for distinguishing modifications of gravity from conventional fluids. I give a non-trivial example, a simple metric based modification of the fluctuation equations for which the background is exact ΛCDM but differs from it in the perturbations. [Copyright &y& Elsevier]

I consider a unified description of the phenomena of dark matter and dark energy which is given by a simple modification of gravity. Gravity is modified with new degrees of freedom which come from a second connection, different from the usual Levi-Civita connection. A candidate action, the Eddington-Born-Infeld action (EBI) for these degrees of freedom was proposed by Bañados and is shown to be dual to a theory with two metrics called bi-gravity. This modification directly gives solutions to the field equations which mimic dark matter for spherically symmetric systems while for cosmological spacetimes it gives, in addition, the effect of dark energy. I shall further show that the effect of dark matter is present even at the linearized cosmological level and that this makes it in harmony with all known large scale cosmological observations. [Copyright &y& Elsevier]

A number of theories of gravity have been proposed as proxies for dark matter in the regime of galaxies and cosmology. The recent observations of gravitational waves (GW170817) from the merger of two neutron stars, followed by an electromagnetic counterpart (GRB170817a) have placed stringent constraints on the difference between the speeds of gravity and light, severely restricting the phenomenological viability of such theories. We revisit the impact of these observations on the tensor-vector-scalar paradigm of relativistic modified Newtonian dynamics (MOND) and demonstrate the existence of a previously unknown class of this paradigm where the speed of gravity always equals the speed of light. We show that this holds without altering the usual (bimetric) MOND phenomenology in galaxies. [ABSTRACT FROM AUTHOR]

Recently, an extension to the parametrized post-Newtonian (PPN) formalism has been proposed. This formalism, the parametrized post-Newtonian-Vainshteinian (PPNV) formalism, is well suited to theories which exhibit Vainshtein screening of scalar fields. In this paper we apply the PPNV formalism to the quartic and quintic Galileon theories for the first time. As simple generalizations of standard scalar-tensor field theories they are important guides for the generalization of parametrized approaches to the effects of gravity beyond general relativity. In the quartic case, we find new PPNV potentials for both screened and unscreened regions of spacetime, showing that in principle these theories can be tested. In the quintic case we show that Vainshtein screening does not occur to Newtonian order, meaning that the theory behaves as Brans-Dicke to this order, and we discuss possible higher order effects. [ABSTRACT FROM AUTHOR]

The cold dark matter (CDM) model, wherein the dark matter is treated as a pressureless perfect fluid, provides a good fit to galactic and cosmological data. With the advent of precision cosmology, it should be asked whether this simplest model needs to be extended, and whether doing so could improve our understanding of the properties of dark matter. One established parametrization for generalizing the CDM fluid is the generalized dark matter (GDM) model, in which dark matter is an imperfect fluid with pressure and shear viscosity that fulfill certain postulated closure equations. We investigate these closure equations and the three new parametric functions they contain: the background equation of state w, the speed of sound cs² and the viscosity cvis². Taking these functions to be constant parameters, we analyze an exact solution of the perturbed Einstein equations in a flat GDM-dominated universe and discuss the main effects of the three parameters on the cosmic microwave background (CMB). Our analysis suggests that the CMB alone is not able to distinguish between the GDM sound speed and viscosity parameters, but that other observables, such as the matter power spectrum, are required to break this degeneracy. In order to elucidate further the meaning of the GDM closure equations, we also consider other descriptions of imperfect fluids that have a nonperturbative definition and relate these to the GDM model. In particular, we consider scalar fields, an effective field theory (EFT) of fluids, an EFT of large-scale structure, nonequilibrium thermodynamics and tightly coupled fluids. These descriptions could be used to extend the GDM model into the nonlinear regime of structure formation, which is necessary if the wealth of data available on those scales is to be employed in constraining the model. We also derive the initial conditions for adiabatic and isocurvature perturbations in the presence of GDM and standard cosmological fluids and provide the result in a form ready for implementation in Einstein-Boltzmann solvers. [ABSTRACT FROM AUTHOR]

The growth rate of the large-scale structure of the Universe has been advocated as the observable par excellence for testing gravity on cosmological scales. By considering linear-order deviations from general relativity, we show that corrections to the growth rate, f, can be expressed as an integral over a "source" term, weighted by a theory-independent "response kernel." This leads to an efficient and accurate "plug-and-play" expression for generating growth rates in alternative gravity theories, bypassing lengthy theory-specific computations. We use this approach to explicitly show that f is sensitive to a degenerate combination of modified expansion and modified clustering effects. Hence the growth rate, when used in isolation, is not a straightforward diagnostic of modified gravity. [ABSTRACT FROM AUTHOR]

A unified framework for theories of modified gravity will be an essential tool for interpreting the forthcoming deluge of cosmological data. We present such a formalism, the parameterized post- Friedmann framework (PPF), which parameterizes the cosmological perturbation theory of a wide variety of modified gravity models. PPF is able to handle spin-U degrees of freedom from new scalar, vector, and tensor fields, meaning that it is not restricted to simple models based solely on cosmological scalar fields. A direct correspondence is maintained between the parameterization and the underlying space of theories, which allows us to build up a "dictionary" of modified gravity theories and their PPF correspondences. In this paper we describe the construction of the parameterization and demonstrate its use through a number of worked examples relevant to the current literature. We indicate how the formalism will be implemented numerically, so that the dictionary of modified gravity can be pitted against forthcoming observations. [ABSTRACT FROM AUTHOR]

There is a distinct possibility that current and future cosmological data can be used to constrain Einstein's theory of gravity on the very largest scales. To be able to do this in a model-independent way, it makes sense to work with a general parameterization of modified gravity. Such an approach would be analogous to the Parameterized Post-Newtonian (PPN) approach which is used on the scale of the Solar System. A few such parameterizations have been proposed and preliminary constraints have been obtained. We show that the majority of such parameterizations are only exactly applicable in the quasistatic regime. On larger scales they fail to encapsulate the full behavior of typical models currently under consideration. We suggest that it may be possible to capture the additions to the 'Parameterized Post-Friedmann' (PPF) formalism by treating them akin to fluid perturbations. [ABSTRACT FROM AUTHOR]

We perform the first test of dark matter (DM) stress-energy evolution through cosmic history, using cosmic microwave background measurements supplemented with baryon acoustic oscillation data and the Hubble Space Telescope key project data. We constrain the DM equation of state (EoS) in 8 redshift bins, and its sound speed and (shear) viscosity in 9 redshift bins, finding no convincing evidence for non-ΛCDM values in any of the redshift bins. Despite this enlarged parameter space, the sound speed and viscosity are constrained relatively well at late times (due to the inclusion of CMB lensing), whereas the EoS is most strongly constrained around recombination. These results constrain for the first time the level of "coldness" required of DM across various cosmological epochs at both the background and perturbative levels. We show that simultaneously allowing time dependence for both the EoS and sound speed parameters shifts the posterior of the DM abundance before recombination to a higher value, while keeping the present day DM abundance similar to the ΛCDM value. This shifts the posterior for the present day Hubble constant compared to ΛCDM, suggesting that DM with time-dependent parameters is well-suited to explore possible solutions to persistent tensions within the ΛCDM model. We perform a detailed comparison with our previous study involving a vanishing sound speed and viscosity using the same datasets in order to explain the physical mechanism behind these shifts. [ABSTRACT FROM AUTHOR]

We demonstrate that the Vlasov equation describing collisionless self-gravitating matter may be solved with the so-called Schrödinger method (ScM). With the ScM, one solves the Schrödinger-Poisson system of equations for a complex wave function in d dimensions, rather than the Vlasov equation for a 2d-dimensional phase space density. The ScM also allows calculating the d-dimensional cumulants directly through quasilocal manipulations of the wave function, avoiding the complexity of 2d-dimensional phase space. We perform for the first time a quantitative comparison of the ScM and a conventional Vlasov solver in d=2 dimensions. Our numerical tests were carried out using two types of cold cosmological initial conditions: the classic collapse of a sine wave and those of a Gaussian random field as commonly used in cosmological cold dark matter N-body simulations. We compare the first three cumulants, that is, the density, velocity and velocity dispersion, to those obtained by solving the Vlasov equation using the publicly available code ColDICE. We find excellent qualitative and quantitative agreement between these codes, demonstrating the feasibility and advantages of the ScM as an alternative to N-body simulations. We discuss, the emergence of effective vorticity in the ScM through the winding number around the points where the wave function vanishes. As an application we evaluate the background pressure induced by the non-linearity of large scale structure formation, thereby estimating the magnitude of cosmological backreaction. We find that it is negligibly small and has time dependence and magnitude compatible with expectations from the effective field theory of large scale structure. [ABSTRACT FROM AUTHOR]

We offer a pedagogical introduction to isocurvature cosmological perturbations and their detection or constraint using recent cosmic microwave background anisotropy and large-scale structure data. The status of the constraints imposed by the first year WMAP data is presented. [Copyright &y& Elsevier]