Tobias Baldauf

Confirmation of general relativity on large scales from weak lensing and galaxy velocities

Although general relativity underlies modern cosmology, its applicability on cosmological length scales has yet to be stringently tested. Such a test has recently been proposed, using a quantity, EG, that combines measures of large-scale gravitational lensing, galaxy clustering and structure growth rate. The combination is insensitive to ‘galaxy bias’ (the difference between the clustering of visible galaxies and invisible dark matter) and is thus robust to the uncertainty in this parameter. Modified theories of gravity generally predict values of EG different from the general relativistic prediction because, in these theories, the ‘gravitational slip’ (the difference between the two potentials that describe perturbations in the gravitational metric) is non-zero, which leads to changes in the growth of structure and the strength of the gravitational lensing effect. Here we report that EG = 0.39 ± 0.06 on length scales of tens of megaparsecs, in agreement with the general relativistic prediction of EG ≈ 0.4. The measured value excludes a model within the tensor–vector–scalar gravity theory, which modifies both Newtonian and Einstein gravity. However, the relatively large uncertainty still permits models within f() theory, which is an extension of general relativity. A fivefold decrease in uncertainty is needed to rule out these models.

Cosmological parameter constraints from galaxy–galaxy lensing and galaxy clustering with the SDSS DR7

Recent studies have shown that the cross-correlation coefficient between galaxies and dark matter is very close to unity on scales outside a few virial radii of galaxy haloes, independent of the details of how galaxies populate dark matter haloes. This finding makes it possible to determine the dark matter clustering from measurements of galaxy–galaxy weak lensing and galaxy clustering. We present new cosmological parameter constraints based on large-scale measurements of spectroscopic galaxy samples from the Sloan Digital Sky Survey (SDSS) data release 7. We generalize the approach of Baldauf et al. to remove small-scale information (below 2 and 4 h^(−1) Mpc for lensing and clustering measurements, respectively), where the cross-correlation coefficient differs from unity. We derive constraints for three galaxy samples covering 7131 deg^2, containing 69 150, 62 150 and 35 088 galaxies with mean redshifts of 0.11, 0.28 and 0.40. We clearly detect scale-dependent galaxy bias for the more luminous galaxy samples, at a level consistent with theoretical expectations. When we vary both σ_8 and Ω_m (and marginalize over non-linear galaxy bias) in a flat Λ cold dark matter model, the best-constrained quantity is σ_8(Ω_m/0.25)^(0.57) = 0.80 ± 0.05 (1σ, stat. + sys.), where statistical and systematic errors (photometric redshift and shear calibration) have comparable contributions, and we have fixed n_s = 0.96 and h = 0.7. These strong constraints on the matter clustering suggest that this method is competitive with cosmic shear in current data, while having very complementary and in some ways less serious systematics. We therefore expect that this method will play a prominent role in future weak lensing surveys. When we combine these data with Wilkinson Microwave Anisotropy Probe 7-year (WMAP7) cosmic microwave background (CMB) data, constraints on σ_8, Ω_m, H_0, w_(de) and ∑m_ν become 30–80 per cent tighter than with CMB data alone, since our data break several parameter degeneracies.

Evidence for quadratic tidal tensor bias from the halo bispectrum

The relation between the clustering properties of luminous matter in the form of galaxies and the underlying dark matter distribution is of fundamental importance for the interpretation of ongoing and upcoming galaxy surveys. The so-called local bias model, where galaxy density is a function of local matter density, is frequently discussed as a means to infer the matter power spectrum or correlation function from the measured galaxy correlation. However, gravitational evolution generates a term quadratic in the tidal tensor and thus nonlocal in the Eulerian density field, even if this term is absent in the initial conditions (Lagrangian space). Because the term is quadratic, it contributes as a loop correction to the power spectrum, so the standard linear bias picture still applies on very large scales; however, it contributes at leading order to the bispectrum for which it is significant on all scales. Such a term could also be present in Lagrangian space if halo formation were influenced by the tidal field. We measure the corresponding coupling strengths from the matter-matter-halo bispectrum in numerical simulations and find a nonvanishing coefficient for the tidal tensor term. We find no scale dependence of the inferred bias parameters up to k∼0.1h  Mpc−1 and that the tidal effect is increasing with halo mass. While the local Lagrangian bias picture is a better description of our results than the local Eulerian bias picture, our results suggest that there might be a tidal tensor bias already in the initial conditions. We also find that the coefficients of the quadratic density term deviate quite strongly from the theoretical predictions based on the spherical collapse model and a universal mass function. Both quadratic density and tidal tensor bias terms must be included in the modeling of galaxy clustering of current and future surveys if one wants to achieve the high precision cosmology promise of these data sets.

Galaxy bias and non-linear structure formation in general relativity

Length scales probed by the large scale structure surveys are becoming closer and closer to the horizon scale. Further, it has been recently understood that non-Gaussianity in the initial conditions could show up in a scale dependence of the bias of galaxies at the largest possible distances. It is therefore important to take General Relativistic effects into account. Here we provide a General Relativistic generalization of the bias that is valid both for Gaussian and for non-Gaussian initial conditions. The collapse of objects happens on very small scales, while long-wavelength modes are always in the quasi linear regime. Around every small collapsing region, it is therefore possible to find a reference frame that is valid for arbitrary times and where the space time is almost flat: the Fermi frame. Here the Newtonian approximation is applicable and the equations of motion are the ones of the standard N-body codes. The effects of long-wavelength modes are encoded in the mapping from the cosmological frame to the local Fermi frame. At the level of the linear bias, the effect of the long-wavelength modes on the dynamics of the short scales is all encoded in the local curvature of the Universe, which allows us to define a General Relativistic generalization of the bias in the standard Newtonian setting. We show that the bias due to this effect goes to zero as the square of the ratio between the physical wavenumber and the Hubble scale for modes longer than the horizon, confirming the intuitive picture that modes longer than the horizon do not have any dynamical effect. On the other hand, the bias due to non-Gaussianities does not need to vanish for modes longer than the Hubble scale, and for non-Gaussianities of the local kind it goes to a constant. As a further application of our setup, we show that it is not necessary to perform large N-body simulations to extract information about long-wavelength modes: N-body simulations can be done on small scales and long-wavelength modes are encoded simply by adding curvature to the simulation, as well as rescaling the time and the scale.

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.

Precision cluster mass determination from weak lensing

Weak gravitational lensing has been used extensively in the past decade to constrain the masses of galaxy clusters, and is the most promising observational technique for providing the mass calibration necessary for precision cosmology with clusters. There are several challenges in estimating cluster masses, particularly (a) the sensitivity to astrophysical effects and observational systematics that modify the signal relative to the theoretical expectations, and (b) biases that can arise due to assumptions in the mass estimation method, such as the assumed radial profile of the cluster. All of these challenges are more problematic in the inner regions of the cluster, suggesting that their influence would ideally be suppressed for the purpose of mass estimation. However, at any given radius the differential surface density measured by lensing is sensitive to all mass within that radius, and the corrupted signal from the inner parts is spread out to all scales. We develop a new statistic ϒ(R;R0) that is ideal for estimation of cluster masses because it completely eliminates mass contributions below a chosen scale (which we suggest should be about 20 per cent of the virial radius), and thus reduces sensitivity to systematic and astrophysical effects. We use simulated and analytical profiles including shape noise to quantify systematic biases on the estimated masses for several standard methods of mass estimation, finding that these can lead to significant mass biases that range from 10 to over 50 per cent. The mass uncertainties when using the new statistic ϒ(R;R0) are reduced by up to a factor of 10 relative to the standard methods, while only moderately increasing the statistical errors. This new method of mass estimation will enable a higher level of precision in future science work with weak lensing mass estimates for galaxy clusters.

Halo stochasticity from exclusion and nonlinear clustering

The clustering of galaxies in ongoing and upcoming galaxy surveys contains a wealth of cosmological information, but extracting this information is a nontrivial task since galaxies and their host haloes are stochastic tracers of the nonlinear matter density field. This stochasticity is usually modeled as the Poisson shot noise, which is constant as a function of wave number with amplitude given by 1=n, where n is the number density of galaxies. Here we use dark matter haloes in N-body simulations to show evidence for deviations from this simple behavior and develop models that explain the behavior of the stochasticity on large scales. First, haloes are extended, nonoverlapping objects, i.e., their correlation function needs to go to -1 on small scales. This leads to a negative correction to the stochasticity relative to the Poisson value at low wave number k, decreasing to zero for wave numbers large compared to the inverse exclusion scale. Second, haloes show a nonlinear enhancement of clustering outside the exclusion scale, leading to a positive stochasticity correction. Both of these effects go to zero for high k, making the stochasticity scale dependent even for k < 0:1h Mpc-1. We show that the corrections in the low-k regime are the same in Eulerian and Lagrangian space, but that the transition scale is pushed to smaller scales for haloes observed at present time (Eulerian space), relative to the initial conditions (Lagrangian space). These corrections vary with halo mass, and we present approximate scalings with halo mass and redshift. We also discuss simple applications of these effects to galaxy samples with nonvanishing satellite fraction, where the stochasticity can again deviate strongly from the fiducial Poisson expectation. Overall, these effects affect the clustering of galaxies at a level of a few percent even on very large scales and need to be modeled properly if we want to extract high precision cosmological information from the upcoming galaxy redshift surveys.

Primordial non-Gaussianity in the bispectrum of the halo density field

The bispectrum vanishes for linear Gaussian fields and is thus a sensitive probe of non-linearities and non-Gaussianities in the cosmic density field. Hence, a detection of the bispectrum in the halo density field would enable tight constraints on non-Gaussian processes in the early Universe and allow inference of the dynamics driving inflation. We present a tree level derivation of the halo bispectrum arising from non-linear clustering, non-linear biasing and primordial non-Gaussianity. A diagrammatic description is developed to provide an intuitive understanding of the contributing terms and their dependence on scale, shape and the non-Gaussianity parameter fNL. We compute the terms based on a multivariate bias expansion and the peak-background split method and show that non-Gaussian modifications to the bias parameters lead to amplifications of the tree level bispectrum that were ignored in previous studies. Our results are in a good agreement with published simulation measurements of the halo bispectrum. Finally, we estimate the expected signal to noise on fNL and show that the constraint obtainable from the bispectrum analysis significantly exceeds the one obtainable from the power spectrum analysis.

Testing Inflation with Large Scale Structure: Connecting Hopes with Reality

The statistics of primordial curvature fluctuations are our window into the period of inflation, where these fluctuations were generated. To date, the cosmic microwave background has been the dominant source of information about these perturbations. Large scale structure is however from where drastic improvements should originate. In this paper, we explain the theoretical motivations for pursuing such measurements and the challenges that lie ahead. In particular, we discuss and identify theoretical targets regarding the measurement of primordial non-Gaussianity. We argue that when quantified in terms of the local (equilateral) template amplitude

Effective field theory of large scale structure at two loops: The apparent scale dependence of the speed of sound

f_{\rm NL}^{\rm loc}