Fabian Schmidt

Nonlinear evolution of f(R) cosmologies. III. Halo statistics

The statistical properties of dark matter halos, the building blocks of cosmological observables associated with structure in the Universe, offer many opportunities to test models for cosmic acceleration, especially those that seek to modify gravitational forces. We study the abundance, bias, and profiles of halos in cosmological simulations for one such model: the modified action f(R) theory. The effects of f(R) modified gravity can be separated into a large- and small-field limit. In the large-field limit, which is accessible to current observations, enhanced gravitational forces raise the abundance of rare massive halos and decrease their bias but leave their (lensing) mass profiles largely unchanged. This regime is well described by scaling relations based on a modification of spherical collapse calculations. In the small-field limit, the enhancement of the gravitational force is suppressed inside halos and the effects on halo properties are substantially reduced for the most massive halos. Nonetheless, the scaling relations still retain limited applicability for the purpose of establishing conservative upper limits on the modification to gravity.

Cluster Constraints on f(R) Gravity

Modified gravitational forces in models that seek to explain cosmic acceleration without dark energy typically predict deviations in the abundance of massive dark matter halos. We conduct the first, simulation calibrated, cluster abundance constraints on a modified gravity model, specifically the modified action f(R) model. The local cluster abundance, when combined with geometric and high redshift data from the cosmic microwave background, supernovae, H0 and baryon acoustic oscillations, improve previous constraints by nearly 4 orders of magnitude in the field amplitude. These limits correspond to a 2 order of magnitude improvement in the bounds on the range of the force modification from the several Gpc scale to the tens of Mpc scale.

Large-scale clustering of galaxies in general relativity

Several recent studies have shown how to properly calculate the observed clustering of galaxies in a relativistic context, and uncovered corrections to the Newtonian calculation that become significant on scales near the horizon. Here, we retrace these calculations and show that, on scales approaching the horizon, the observed galaxy power spectrum depends strongly on which gauge is assumed to relate the intrinsic fluctuations in galaxy density to matter perturbations through a linear bias relation. Starting from simple physical assumptions, we derive a gauge-invariant expression relating galaxy density perturbations to matter density perturbations on large scales, and show that it reduces to a linear bias relation in a synchronous-comoving gauge, corroborating an assumption made in several recent papers. We evaluate the resulting observed galaxy power spectrum, and show that it leads to corrections similar to an effective non-Gaussian bias corresponding to a local f_(NL,eff)≲0.5. This number can serve as a guideline as to which surveys need to take into account relativistic effects. We also discuss the scale-dependent bias induced by primordial non-Gaussianity in the relativistic context, which again is simplest in a synchronous-comoving gauge.

Dynamical Masses in Modified Gravity

Differences in masses inferred from dynamics, such as velocity dispersions or x rays, and those inferred from lensing are a generic prediction of modified gravity theories. Viable models, however, must include some nonlinear mechanism to restore general relativity (GR) in dense environments, which is necessary to pass Solar System constraints on precisely these deviations. In this paper, we study the dynamics within virialized structures in the context of two modified gravity models, f(R) gravity and Dvali-Gabadadze-Porrati (DGP). The nonlinear mechanisms to restore GR, which f(R) and DGP implement in very different ways, have a strong impact on the dynamics in bound objects; they leave distinctive signatures in the dynamical mass-lensing mass relation as a function of mass and radius. We present measurements from N-body simulations of f(R) and DGP, as well as semianalytical models that match the simulation results to surprising accuracy in both cases. The semianalytical models are useful for making the connection to observations. Our results confirm that the environment and scale dependence of the modified gravity effects have to be taken into account when confronting gravity theories with observations of dynamics in galaxies and clusters.

Self-Consistent Cosmological Simulations of DGP Braneworld Gravity

We perform cosmological N-body simulations of the Dvali-Gabadadze-Porrati (DGP) braneworld model, by solving the full nonlinear equations of motion for the scalar degree of freedom in this model, the brane-bending mode. While coupling universally to matter, the brane-bending mode has self-interactions that become important as soon as the density field becomes nonlinear. These self-interactions lead to a suppression of the field in high-density environments, and restore gravity to general relativity. The code uses a multigrid relaxation scheme to solve the nonlinear field equation in the quasistatic approximation. We perform simulations of a flat self-accelerating DGP model without cosmological constant. However, the type of nonlinear interactions of the brane-bending mode, which are the focus of this study, are generic to a wide class of braneworld cosmologies. The results of the DGP simulations are compared with standard gravity simulations assuming the same expansion history, and with DGP simulations using the linearized equation for the brane-bending mode. This allows us to isolate the effects of the nonlinear self-couplings of the field which are noticeable already on quasilinear scales. We present results on the matter power spectrum and the halo mass function, and discuss the behavior of the brane-bending mode within cosmological structure formation. We find that, independently of cosmic microwave background constraints, the self-accelerating DGP model is strongly constrained by current weak lensing and cluster abundance measurements.

Dark Energy Versus Modified Gravity

Understanding the reason for the observed accelerated expansion of the Universe represents one of the fundamental open questions in physics. In cosmology, a classification has emerged among physical models for the acceleration, distinguishing between Dark Energy and Modified Gravity. In this review, we give a brief overview of models in both categories as well as their phenomenology and characteristic observable signatures in cosmology. We also introduce a rigorous distinction between Dark Energy and Modified Gravity based on the strong and weak equivalence principles.

Cluster Density Profiles as a Test of Modified Gravity

We present a new test of gravitational interactions at the r≃(0.2–20)  Mpc scale, around the virial radius of dark matter halos measured through cluster-galaxy lensing of maxBCG clusters from the Sloan Digital Sky Survey (SDSS). We employ predictions from self-consistent simulations of f(R) gravity to find an upper bound on the background field amplitude of |f_R0|<3.5×10^(-3) at the 1D-marginalized 95% confidence level. As a model-independent assessment of the constraining power of cluster profiles measured through weak gravitational lensing, we also constrain the amplitude F_0 of a phenomenological modification based on the profile enhancement induced by f(R) gravity when not including effects from the increased cluster abundance in f(R). In both scenarios, dark-matter-only simulations of the concordance model corresponding to |fR0|=0 and F0=0 are consistent with the lensing measurements, i.e., at the 68% and 95% confidence level, respectively.

Non-Gaussian Halo Bias Re-examined: Mass-dependent Amplitude from the Peak-Background Split and Thresholding

Recent results of N-body simulations have shown that current theoretical models are not able to correctly predict the amplitude of the scale-dependent halo bias induced by primordial non-Gaussianity, for models going beyond the simplest, local quadratic case. Motivated by these discrepancies, we carefully examine three theoretical approaches based on (1) the statistics of thresholded regions, (2) a peak-background split method based on separation of scales, and (3) a peak-background split method using the conditional mass function. We first demonstrate that the statistics of thresholded regions, which is shown to be equivalent at leading order to a local bias expansion, cannot explain the mass-dependent deviation between theory and N-body simulations. In the two formulations of the peak-background split on the other hand, we identify an important, but previously overlooked, correction to the non-Gaussian bias that strongly depends on halo mass. This new term is in general significant for any primordial non-Gaussianity going beyond the simplest local fNL model. In a separate paper (to be published in PRD rapid communication), the authors compare these new theoretical predictions with N-body simulations, showing good agreement for all simulated types of non-Gaussianity.

Cosmological simulations of normal-branch braneworld gravity

We introduce a cosmological model based on the normal branch of Dvali-Gabadadze-Porrati (DGP) braneworld gravity with a smooth dark energy component on the brane. The expansion history in this model is identical to ΛCDM, thus evading all geometric constraints on the DGP crossover scale r_c. This well-defined model can serve as a first approximation to more general braneworld models whose cosmological solutions have not been obtained yet. We study the formation of large-scale structure in this model in the linear and nonlinear regime using N-body simulations for different values of r_c. The simulations use the code presented in 25 and solve the full nonlinear equation for the brane-bending mode in conjunction with the usual gravitational dynamics. The brane-bending mode is attractive rather than repulsive in the DGP normal branch, hence the sign of the modified gravity effects is reversed compared to those presented in 25. We compare the simulation results with those of ordinary ΛCDM simulations run using the same code and initial conditions. We find that the matter power spectrum in this model shows a characteristic enhancement peaking at k ~ 0.7h/Mpc. We also find that the abundance of massive halos is significantly enhanced. Other results presented here include the density profiles of dark matter halos, and signatures of the brane-bending mode self-interactions (Vainshtein mechanism) in the simulations. Independently of the expansion history, these results can be used to place constraints on the DGP model and future generalizations through their effects on the growth of cosmological structure.

Halo clustering with nonlocal non-Gaussianity

We show how the peak-background split (PBS) can be generalized to predict the effect of nonlocal primordial non-Gaussianity on the clustering of halos. Our approach is applicable to arbitrary primordial bispectra. We show that the scale dependence of halo clustering predicted in the peak-background split agrees with that of the local-biasing model on large scales. On smaller scales, k ≳ 0:01h Mpc^(-1), the predictions diverge, a consequence of the assumption of separation of scales in the peak-background split. Even on large scales, PBS and local biasing do not generally agree on the amplitude of the effect outside of the high-peak limit. The scale dependence of the biasing—the effect that provides strong constraints to the local-model bispectrum—is far weaker for the equilateral and self-ordering-scalar-field models of non-Gaussianity. The bias scale dependence for the orthogonal and folded models is weaker than in the local model (~k^(-1)), but likely still strong enough to be constraining.We show that departures from scale-invariance of the primordial power spectrum may lead to order-unity corrections, relative to predictions made assuming scale-invariance—to the non-Gaussian bias in some of these nonlocal models for non-Gaussianity. An Appendix shows that a nonlocal model can produce the local-model bispectrum, a mathematical curiosity we uncovered in the course of this investigation.