One century after its formulation, Einsteinʼs general relativity (GR) has made remarkable predictions and turned out to be compatible with all experimental tests. Most of these tests probe the theory in the weak-field regime, and there are theoretical and experimental reasons to believe that GR should be modified when Class. Quantum Grav. 32 (2015) 243001Topical Review physical laboratories to probe strong-field gravity are black holes and neutron stars, whether isolated or in binary systems. We review the motivations to consider extensions of GR. We present a (necessarily incomplete) catalog of modified theories of gravity for which strong-field predictions have been computed and contrasted to Einsteinʼs theory, and we summarize our current understanding of the structure and dynamics of compact objects in these theories. We discuss current bounds on modified gravity from binary pulsar and cosmological observations, and we highlight the potential of future gravitational wave measurements to inform us on the behavior of gravity in the strong-field regime.

We present an accurate non-linear matter power spectrum prediction scheme for a variety of extensions to the standard cosmological paradigm, which uses the tuned halo model previously developed in Mead et al.. We consider dark energy models that are both minimally and non-minimally coupled, massive neutrinos and modified gravitational forces with chameleon and Vainshtein screening mechanisms. In all cases we compare halo-model power spectra to measurements from high-resolution simulations. We show that the tuned halo model method can predict the non-linear matter power spectrum measured from simulations of parameterized w(a) dark energy models at the few per cent level for k < 10 hMpc −1 , and we present theoretically motivated extensions to cover non-minimally coupled scalar fields, massive neutrinos and Vainshtein screened modified gravity models that result in few per cent accurate power spectra for k < 10 hMpc −1 . For chameleon screened models we achieve only 10 per cent accuracy for the same range of scales. Finally, we use our halo model to investigate degeneracies between different extensions to the standard cosmological model, finding that the impact of baryonic feedback on the non-linear matter power spectrum can be considered independently of modified gravity or massive neutrino extensions. In contrast, considering the impact of modified gravity and massive neutrinos independently results in biased estimates of power at the level of 5 per cent at scales k > 0.5 hMpc −1 . An updated version of our publicly available HMCODE can be found at https://github.com/alexander-mead/hmcode.

We consider modified gravity models driven by a scalar field whose effects are screened in high density regions due to the presence of non-linearities in its interaction potential and/or its coupling to matter. Our approach covers chameleon, f (R) gravity, dilaton and symmetron models and allows a unified description of all these theories. We find that the dynamics of modified gravity are entirely captured by the time variation of the scalar field mass and its coupling to matter evaluated at the cosmological minimum of its effective potential, where the scalar field sits since an epoch prior to Big Bang Nucleosynthesis. This new parameterisation of modified gravity allows one to reconstruct the potential and coupling to matter and therefore to analyse the full dynamics of the models, from the scale dependent growth of structures at the linear level to non-linear effects requiring N -body simulations. This procedure is illustrated with explicit examples of reconstruction for chameleon, dilaton, f (R) and symmetron models. I. INTRODUCTIONThe discovery of the acceleration of the expansion of the Universe [1] has led to a reappraisal of some of the tenets of modern cosmology. In particular, the possibility of modifying the laws of gravity on short or large scales is taken more and more seriously [2].In view of Weinberg's theorem stating that any Lorentz invariant field theory involving spin-2 fields must reduce to General Relativity (GR) at low energy [3], any attempt to modify GR must involve extra degree(s) of freedom. The majority of known models involve scalar fields and can be separated into two broad classes, the ones involving non-linearities in the kinetic terms and others with non-linear interaction potentials. All these models have a coupling of the scalar field to matter and there could be an environmental dependence which would manifest itself in the screening behaviour of the scalar field in high density regions [4,5]. Examples of such models abound: the dilatonic models [6,7] generalising the Damour-Polyakov mechanism [8] where the coupling to gravity turns off in dense environments, the chameleon models [9,10,[12][13][14] where a thin shell shielding the scalar field in dense bodies is present, the symmetron models [15][16][17][18][19][20][21] where the scalar field has a symmetry breaking potential where the field is decoupled at high density.Some models are essentially spin-offs of the previous ones like the f (R) theories [22][23][24][25][26][27][28][29][30][31][32] (for recent reviews of the f (R) gravity see [33,34]) which are only valid when they behave like chameleon theories with a thin shell mechanism in dense environments [32]. In all these *

Despite its continued observational successes, there is a persistent (and growing) interest in extending cosmology beyond the standard model, ΛCDM. This is motivated by a range of apparently serious theoretical issues, involving such questions as the cosmological constant problem, the particle nature of dark matter, the validity of general relativity on large scales, the existence of anomalies in the CMB and on small scales, and the predictivity and testability of the inflationary paradigm. In this paper, we summarize the current status of ΛCDM as a physical theory, and review investigations into possible alternatives along a number of different lines, with a particular focus on highlighting the most promising directions. While the fundamental problems are proving reluctant to yield, the study of alternative cosmologies has led to considerable progress, with much more to come if hopes about forthcoming high-precision observations and new theoretical ideas are fulfilled.Keywords: cosmology -dark energy -cosmological constant problem -modified gravitydark matter -early universe Cosmology has been both blessed and cursed by the establishment of a standard model: ΛCDM. On the one hand, the model has turned out to be extremely predictive, explanatory, and observationally robust, providing us with a substantial understanding of the formation of large-scale structure, the state of the early Universe, and the cosmic abundance of different types of matter and energy. It has also survived an impressive battery of precision observational tests -anomalies are few and far between, and their significance is contentious where they do arise -and its predictions are continually being vindicated through the discovery of new effects (B-mode polarization [1] and lensing [2,3] of the cosmic microwave background (CMB), and the kinetic Sunyaev-Zel'dovich effect [4] being some recent examples). These are the hallmarks of a good and valuable physical theory.On the other hand, the model suffers from profound theoretical difficulties. The two largest contributions to the energy content at late times -cold dark matter (CDM) and the cosmological constant (Λ) -have entirely mysterious physical origins. CDM has so far evaded direct detection by laboratory experiments, and so the particle field responsible for it -presumably a manifestation of "beyond the standard model" particle physics -is unknown. Curious discrepancies also appear to exist between the predicted clustering properties of CDM on small scales and observations. The cosmological constant is even more puzzling, giving rise to quite simply the biggest problem in all of fundamental physics: the question of why Λ appears to take such an unnatural value [5,6,7]. Inflation, the theory of the very early Universe, has also been criticized for being fine-tuned and under-predictive [8], and appears to leave many problems either unsolved or fundamentally unresolvable. These problems are indicative of a crisis.From January 14th-17th 2015, we held a conference in Oslo, Norway to surve...

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Abstract. We present a general parallelized and easy-to-use code to perform numerical simulations of structure formation using the COLA (COmoving Lagrangian Acceleration) method for cosmological models that exhibit scale-dependent growth at the level of first and second order Lagrangian perturbation theory. For modified gravity theories we also include screening using a fast approximate method that covers all the main examples of screening mechanisms in the literature. We test the code by comparing it to full simulations of two popular modified gravity models, namely f (R) gravity and nDGP, and find good agreement in the modified gravity boost-factors relative to ΛCDM even when using a fairly small number of COLA time steps.

Additional information:Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. ABSTRACT Scalar fields, strongly coupled to matter, can be present in nature and still be invisible to local experiments if they are subject to a screening mechanism. The symmetron is one such mechanism that relies on restoration of a spontaneously broken symmetry in regions of high density to shield the scalar fifth force. We have investigated structure formation in the symmetron model by using N-body simulations and find observable signatures in both the linear and nonlinear matter power spectrum and on the halo mass function. The mechanism for suppressing the scalar fifth force in high-density regions is also found to work very well.

We present a measurement of the anisotropic void-galaxy cross-correlation function in the CMASS galaxy sample of the BOSS DR12 data release. We perform a joint fit to the data for redshift space distortions (RSD) due to galaxy peculiar velocities and anisotropies due to the Alcock-Paczynski (AP) effect, for the first time using a velocity field reconstruction technique to remove the complicating effects of RSD in the void centre positions themselves. Fits to the void-galaxy function give a 1% measurement of the AP parameter combination DA(z)H(z)/c = 0.4367±0.0045 at redshift z = 0.57, where DA is the angular diameter distance and H the Hubble parameter, exceeding the precision obtainable from baryon acoustic oscillations (BAO) by a factor of ∼ 3.5 and free of systematic errors. From voids alone we also obtain a 10% measure of the growth rate, f σ8(z = 0.57) = 0.501 ± 0.051. The parameter degeneracies are orthogonal to those obtained from galaxy clustering. Combining void information with that from BAO and galaxy RSD in the same CMASS sample, we measure DA(0.57)/rs = 9.383 ± 0.077 (at 0.8% precision), H(0.57)rs = (14.05 ± 0.14) 10 3 kms −1 Mpc −1 (1%) and f σ8 = 0.453 ± 0.022 (4.9%), consistent with cosmic microwave background (CMB) measurements from Planck. These represent a factor ∼ 2 improvement in precision over previous results through the inclusion of void information. Fitting a flat cosmological constant ΛCDM model to these results in combination with Planck CMB data, we find up to an 11% reduction in uncertainties on H0 and Ωm compared to use of the corresponding BOSS consensus values. Constraints on extended models with non-flat geometry and a dark energy of state that differs from w = −1 show an even greater improvement.