The acceleration of the universe can be explained either through dark energy or through the modification of gravity on large scales. In this paper we investigate modified gravity models and compare their observable predictions with dark energy models. Modifications of general relativity are expected to be scale-independent on super-horizon scales and scale-dependent on sub-horizon scales. For scale-independent modifications, utilizing the conservation of the curvature scalar and a parameterized post-Newtonian formulation of cosmological perturbations, we derive results for large scale structure growth, weak gravitational lensing, and cosmic microwave background anisotropy. For scale-dependent modifications, inspired by recent f (R) theories we introduce a parameterization for the gravitational coupling G and the post-Newtonian parameter γ. These parameterizations provide a convenient formalism for testing general relativity. However, we find that if dark energy is generalized to include both entropy and shear stress perturbations, and the dynamics of dark energy is unknown a priori, then modified gravity cannot in general be distinguished from dark energy using cosmological linear perturbations.

We investigate the observational consequences of the quintessence field rolling to and oscillating near a minimum in its potential, if it happens close to the present epoch (z 0.2). We show that in a class of models, the oscillations lead to a rapid growth of the field fluctuations and the gravitational potential on subhorizon scales. The growth in the gravitational potential occurs on timescales H −1 . This effect is present even when the quintessence parameters are chosen to reproduce an expansion history consistent with observations. For linearized fluctuations, we find that although the gravitational potential power spectrum is enhanced in a scale-dependent manner, the shape of the dark matter/galaxy power spectrum is not significantly affected. We find that the best constraints on such a transition in the quintessence field is provided via the integrated Sachs-Wolfe effect in the CMB temperature power spectrum. Going beyond the linearized regime, the quintessence field can fragment into large, localized, longlived excitations (oscillons) with sizes comparable to galaxy clusters; this fragmentation could provide additional observational constraints. Two quoted signatures of modified gravity are a scale-dependent growth of the gravitational potential and a difference between the matter power spectrum inferred from measurements of lensing and galaxy clustering. Here, both effects are achieved by a minimally coupled scalar field in general relativity with a canonical kinetic term. In other words we show that, with some tuning of parameters, scale-dependent growth does not necessarily imply a violation of General Relativity. 1 mamin@mit.edu 2 zukin@mit.edu 3 edbert@mit.edu arXiv:1108.1793v2 [astro-ph.CO] 23 Aug 2012 * * When the Floquet exponents are zero, there exist another class of solutions δϕ k (t) ∝ tP 1 (t) and δϕ k (t) ∝ P 2 (t) where P 1,2 (t) are periodic functions.

N-body simulations have revealed a wealth of information about dark matter halos however their results are largely empirical. Using analytic means, we attempt to shed light on simulation results by generalizing the self-similar secondary infall model to include tidal torque. In this first of two papers, we describe our halo formation model and compare our results to empirical mass profiles inspired by N-body simulations. Each halo is determined by four parameters. One parameter sets the mass scale and the other three define how particles within a mass shell are torqued throughout evolution. We choose torque parameters motivated by tidal torque theory and N-body simulations and analytically calculate the structure of the halo in different radial regimes. We find that angular momentum plays an important role in determining the density profile at small radii. For cosmological initial conditions, the density profile on small scales is set by the time rate of change of the angular momentum of particles as well as the halo mass. On intermediate scales, however, ρ ∝ r −2 , while ρ ∝ r −3 close to the virial radius.

We investigate how different cosmological parameters, such as those delivered by the WMAP and Planck missions, affect the nature and evolution of dark matter halo substructure. We use a series of flat Λ cold dark matter (ΛCDM) cosmological N -body simulations of structure formation, each with a different power spectrum but the same initial white noise field. Our fiducial simulation is based on parameters from the WMAP 7th year cosmology. We then systematically vary the spectral index, n s , matter density, Ω M , and normalization of the power spectrum, σ 8 , for 7 unique simulations. Across these, we study variations in the subhalo mass function, mass fraction, maximum circular velocity function, spatial distribution, concentration, formation times, accretion times, and peak mass. We eliminate dependence of subhalo properties on host halo mass and average over many hosts to reduce variance. While the "same" subhalos from identical initial overdensity peaks in higher σ 8 , n s , and Ω m simulations accrete earlier and end up less massive and closer to the halo center at z = 0, the process of continuous subhalo accretion and destruction leads to a steady state distribution of these properties across all subhalos in a given host. This steady state mechanism eliminates cosmological dependence on all properties listed above except subhalo concentration and V max , which remain greater for higher σ 8 , n s and Ω m simulations, and subhalo formation time, which remains earlier. We also find that the numerical technique for computing scale radius and the halo finder used can significantly affect the concentration-mass relationship computed for a simulation.