Large-scale velocities and primordial non-Gaussianity

We study the peculiar velocities of density peaks in the presence of primordial non-Gaussianity. Rare, high-density peaks in the initial density field can be identified with tracers such as galaxies and clusters in the evolved matter distribution. The distribution of relative velocities of peaks is derived in the large-scale limit using two different approaches based on a local biasing scheme. Both approaches agree, and show that halos still stream with the dark matter locally as well as statistically, i.e. they do not acquire a velocity bias. Nonetheless, even a moderate degree of (not necessarily local) non-Gaussianity induces a significant skewness (~0.1–0.2) in the relative velocity distribution, making it a potentially interesting probe of non-Gaussianity on intermediate to large scales. We also study two-point correlations in redshift space. The well-known Kaiser formula is still a good approximation on large scales, if the Gaussian halo bias is replaced with its (scale-dependent) non-Gaussian generalization. However, there are additional terms not encompassed by this simple formula which become relevant on smaller scales (k ≳ 0.01h/Mpc). Depending on the allowed level of non-Gaussianity, these could be of relevance for future large spectroscopic surveys

Beyond LIMD bias: a measurement of the complete set of third-order halo bias parameters

We present direct measurements of cubic bias parameters of dark matter halos from the halo-matter-matter-matter trispectrum. We measure this statistic efficiently by cross-correlating the halo field measured in N-body simulations with specific third-order nonlocal transformations of the initial density field in the same simulation. Together with the recent Abidi & Baldauf (2018), these are the first measurements of halo bias using the four-point function that have been reported to date. We also obtain constraints on the quadratic bias parameters. For all individual cubic parameters involving the tidal field $\mathcal{K}_{ij}$, we find broad consistency with the prediction of the Lagrangian local-in-matter-density ansatz, with some indications of a positive Lagrangian coefficient $b_{\rm td}^L$ multiplying the time derivative of $\mathcal{K}_{ij}$. For the quadratic tidal bias ($b_{K^2}$), we obtain a significant detection of a negative Lagrangian tidal bias.Comment: 29 pages, 12 figures; v2: new renormalization procedure, added figure 12, results at higher redshifts on figs 1-5, added appendix B, C and F, clarifications throughout; v3: clarifications throughout, version accepted by JCA

Weak Lensing Probes of Modified Gravity

We study the effect of modifications to General Relativity on large scale weak lensing observables. In particular, we consider three modified gravity scenarios: f(R) gravity, the DGP model, and TeVeS theory. Weak lensing is sensitive to the growth of structure and the relation between matter and gravitational potentials, both of which will in general be affected by modified gravity. Restricting ourselves to linear scales, we compare the predictions for galaxy-shear and shear-shear correlations of each modified gravity cosmology to those of an effective Dark Energy cosmology with the same expansion history. In this way, the effects of modified gravity on the growth of perturbations are separated from the expansion history. We also propose a test which isolates the matter-potential relation from the growth factor and matter power spectrum. For all three modified gravity models, the predictions for galaxy and shear correlations will be discernible from those of Dark Energy with very high significance in future weak lensing surveys. Furthermore, each model predicts a measurably distinct scale dependence and redshift evolution of galaxy and shear correlations, which can be traced back to the physical foundations of each model. We show that the signal-to-noise for detecting signatures of modified gravity is much higher for weak lensing observables as compared to the ISW effect, measured via the galaxy-CMB cross-correlation.Comment: 16 pages, 8 figures; accepted for publication in Phys. Rev. D; v2: references added; v3: clarifications and additions to the text in response to refere

Cosmic Rulers

We derive general covariant expressions for the six independent observable modes of distortion of ideal standard rulers in a perturbed Friedmann-Robertson-Walker spacetime. Our expressions are gauge-invariant and valid on the full sky. These six modes are most naturally classified in terms of their rotational properties on the sphere, yielding two scalars, two vector (spin-1), and two tensor (spin-2) components. One scalar corresponds to the magnification, while the spin-2 components correspond to the shear. The vector components allow for a polar/axial decomposition analogous to the E/B-decomposition for the shear. Scalar modes do not contribute to the axial (B-)vector, opening a new avenue to probing tensor modes. Our results apply, but are not limited to, the distortion of correlation functions (of the CMB, 21cm emission, or galaxies) as well as to weak lensing shear and magnification, all of which can be seen as methods relying on "standard rulers".Comment: 31 pages, 3 figures (v3); v2: minor changes reflecting PRD published version; v3: evolving ruler case relegated to arXiv:1305.1299, added proper time condition for observer, additional test cases for magnificatio

Large-Scale Structure Observables in General Relativity

We review recent studies that rigorously define several key observables of the large-scale structure of the Universe in a general relativistic context. Specifically, we consider i) redshift perturbation of cosmic clock events; ii) distortion of cosmic rulers, including weak lensing shear and magnification; iii) observed number density of tracers of the large-scale structure. We provide covariant and gauge-invariant expressions of these observables. Our expressions are given for a linearly perturbed flat Friedmann-Robertson-Walker metric including scalar, vector, and tensor metric perturbations. While we restrict ourselves to linear order in perturbation theory, the approach can be straightforwardly generalized to higher order.Comment: 24 pages, 3 figures. A review article submitted to CQG focus issue "Relativistic Effects in Cosmology". arXiv admin note: substantial text overlap with arXiv:1204.3625, v2: correct one missing referenc