Weak Lensing Convergence Power Spectrum Research Articles

Estimating redshift distributions using hierarchical logistic Gaussian processes

ABSTRACT This work uses hierarchical logistic Gaussian processes to infer true redshift distributions of samples of galaxies, through their cross-correlations with spatially overlapping spectroscopic samples. We demonstrate that this method can accurately estimate these redshift distributions in a fully Bayesian manner jointly with galaxy-dark matter bias models. We forecast how systematic biases in the redshift-dependent galaxy-dark matter bias model affect redshift inference. Using published galaxy-dark matter bias measurements from the Illustris simulation, we compare these systematic biases with the statistical error budget from a forecasted weak gravitational lensing measurement. If the redshift-dependent galaxy-dark matter bias model is mis-specified, redshift inference can be biased. This can propagate into relative biases in the weak lensing convergence power spectrum on the 10–30 per cent level. We, therefore, showcase a methodology to detect these sources of error using Bayesian model selection techniques. Furthermore, we discuss the improvements that can be gained from incorporating prior information from Bayesian template fitting into the model, both in redshift prediction accuracy and in the detection of systematic modelling biases.

Tomographic weak lensing bispectrum: a thorough analysis towards the next generation of galaxy surveys

ABSTRACT We address key points for an efficient implementation of likelihood codes for modern weak lensing large-scale structure surveys. Specifically, we focus on the joint weak lensing convergence power spectrum–bispectrum probe and we tackle the numerical challenges required by a realistic analysis. Under the assumption of (multivariate) Gaussian likelihoods, we have developed a high performance code that allows highly parallelized prediction of the binned tomographic observables and of their joint non-Gaussian covariance matrix accounting for terms up to the six-point correlation function and supersample effects. This performance allows us to qualitatively address several interesting scientific questions. We find that the bispectrum provides an improvement in terms of signal-to-noise ratio (S/N) of about 10 per cent on top of the power spectrum, making it a non-negligible source of information for future surveys. Furthermore, we are capable to test the impact of theoretical uncertainties in the halo model used to build our observables; with presently allowed variations we conclude that the impact is negligible on the S/N. Finally, we consider data compression possibilities to optimize future analyses of the weak lensing bispectrum. We find that, ignoring systematics, five equipopulated redshift bins are enough to recover the information content of a Euclid-like survey, with negligible improvement when increasing to 10 bins. We also explore principal component analysis and dependence on the triangle shapes as ways to reduce the numerical complexity of the problem.

General relativistic corrections to the weak lensing convergence power spectrum

We compute the weak lensing convergence power spectrum, $C^{\kappa\kappa}(\theta)$, in a dust-filled universe using fully non-linear general relativistic simulations. The spectrum is then compared to more standard, approximate calculations by computing the Bardeen (Newtonian) potentials in linearized gravity and utilizing the Born approximation. We find corrections to the angular power spectrum amplitude of order ten percent at very large angular scales, $\ell ~ 2-3$, and percent-level corrections at intermediate angular scales of $\ell ~ 20-30$.

Constraints on the dark matter and dark energy interactions from weak lensing bispectrum tomography

We estimate uncertainties of cosmological parameters for phenomenological interacting dark energy models using weak lensing convergence power spectrum and bispectrum. We focus on the bispectrum tomography and examine how well the weak lensing bispectrum with tomography can constrain the interactions between dark sectors, as well as other cosmological parameters. Employing the Fisher matrix analysis, we forecast parameter uncertainties derived from weak lensing bispectra with a two-bin tomography and place upper bounds on strength of the interactions between the dark sectors. The cosmic shear will be measured from upcoming weak lensing surveys with high sensitivity, thus it enables us to use the higher order correlation functions of weak lensing to constrain the interaction between dark sectors and will potentially provide more stringent results with other observations combined.

Exploring degeneracies in modified gravity with weak lensing

By considering linear-order departures from general relativity, we compute a novel expression for the weak lensing convergence power spectrum under alternative theories of gravity. This comprises an integral over a 'kernel' of general relativistic quantities multiplied by a theory-dependent 'source' term. The clear separation between theory-independent and -dependent terms allows for an explicit understanding of each physical effect introduced by altering the theory of gravity. We take advantage of this to explore the degeneracies between gravitational parameters in weak lensing observations.

Modeling of weak-lensing statistics

We investigate the performance of an analytic model of the 3D matter distribution, which combines perturbation theory with halo models, for weak-lensing statistics. We compare our predictions for the weak-lensing convergence power spectrum and bispectrum with numerical simulations and fitting formulas proposed in previous works. We find that this model provides better agreement with simulations than published fitting formulas. This shows that building on systematic and physically motivated models is a promising approach. Moreover, this makes explicit the link between the weak-lensing statistics and the underlying properties of the 3D matter distribution, as a function of scale $\ell$. Thus, we obtain the contributions to the lensing power spectrum and bispectrum that arise from perturbative terms (complete up to one-loop) and nonperturbative terms (e.g., "1-halo" term). Finally, we show that this approach recovers the dependence on cosmology (for realistic scenarios).

Weak lensing signal in unified dark matter models

Weak gravitational lensing is a powerful tool for studying both the geometry and the dynamics of the Universe. Its power spectrum contains information on the sources emitting photons and on the large-scale structures that these photons cross. We calculate the weak lensing cosmic convergence and shear power spectra, in linear theory and Limber's approximation, for two different classes of cosmological models: the standard Λ cold dark matter (ΛCDM) and unified dark matter (UDM) models. The latter models attempt to solve the problems of the dark matter in the dynamics of galaxies and galaxy clusters and of the late-time acceleration of the Universe expansion by introducing a scalar field that mimics both dark matter and dark energy. A crucial feature of the UDM models is the speed of sound c∞, i.e. the value of the sound speed at late times, on which structure formation depends. In this paper, we provide the predictions of the UDM models for the weak lensing signal, with various values of c∞. We consider both the cosmic microwave background and background galaxies at different redshifts as sources for the weak lensing power spectra. We find that the power spectra in UDM models are more sensitive to the variations of c∞ for sources located at low redshifts. Moreover, we find that for c∞ > 10−3 (in units of the speed of light), the UDM weak lensing convergence power spectrum Cκκ(l) for background galaxies is strongly suppressed with respect to the ΛCDM spectrum, particularly at small angular scales l≳ 100.

Nonlinear growth in modified gravity theories of dark energy

Theoretical differences in the growth of structure offer the possibility that we might distinguish between modified gravity theories of dark energy and $\ensuremath{\Lambda}\mathrm{CDM}$. A significant impediment to applying current and prospective large scale galaxy and weak lensing surveys to this problem is that, while the mildly nonlinear regime is important, there is a lack of numerical simulations of nonlinear growth in modified gravity theories. A major question exists as to whether existing analytical fits, created using simulations of standard gravity, can be confidently applied. In this paper we address this, presenting results of N-body simulations of a variety of models where gravity is altered including the Dvali, Gabadadze, and Porrati model. We consider modifications that alter the Poisson equation and also consider the presence of anisotropic shear stress that alters how particles respond to the gravitational potential gradient. We establish how well analytical fits of the matter power spectrum by Peacock and Dodds and Smith et al. are able to predict the nonlinear growth found in the simulations from $z=50$ up to today, and also consider implications for the weak lensing convergence power spectrum. We find that the analytical fits provide good agreement with the simulations, being within $1\ensuremath{\sigma}$ of the simulation results for cases with and without anisotropic stress and for scale-dependent and independent modifications of the Poisson equation. No strong preference for either analytical fit is found.

Is it possible to tell the difference between fermionic and bosonic hot dark matter?

We study the difference between thermally produced fermionic and bosonic hot darkmatter in detail. In the linear regime of structure formation, their distinct free-streamingbehaviours can lead to pronounced differences in the matter power spectrum. Whilenot detectable with current cosmological data, such differences will be clearlyobservable with upcoming large scale weak lensing surveys for particles as light asmHDM∼0.2 eV. In the nonlinear regime, bosonic hot dark matter is not subject to the same phasespace constraints that severely limit the amount of fermionic hot dark matter infall intocold dark matter halos. Consequently, the overdensities in fermionic and bosonic hot darkmatter of equal particle mass can differ by more than a factor of five in the central part of ahalo. However, this unique manifestation of quantum statistics may prove very difficult todetect unless the mass of the hot dark matter particle and its decoupling temperature fallwithin a very narrow window, and . In this case, hot dark matter infall may have some observable consequences for thenonlinear power spectrum and hence the weak lensing convergence power spectrum at at the per cent level.

Nulling tomography with weak gravitational lensing

We explore several strategies of eliminating (or nulling) the small-scale information in weak lensing convergence power spectrum measurements in order to protect against undesirable effects, for example, the effects of baryonic cooling and pressure forces on the distribution of large-scale structures. We selectively throw out the small-scale information in the convergence power spectrum that is most sensitive to the unwanted bias, while trying to retain most of the sensitivity to cosmological parameters. The strategies are effective in the difficult but realistic situations when we are able to guess the form of the contaminating effect only approximately. However, we also find that the simplest scheme of simply not using information from the largest multipoles works about as well as the proposed techniques in most, although not all, realistic cases. We advocate further exploration of nulling techniques and believe that they will find important applications in the weak lensing data mining.

Weak lensing and dark energy

We study the power of upcoming weak lensing surveys to probe dark energy. Dark energy modifies the distance-redshift relation as well as the matter power spectrum, both of which affect the weak lensing convergence power spectrum. Some dark-energy models predict additional clustering on very large scales, but this probably cannot be detected by weak lensing alone due to cosmic variance. With reasonable prior information on other cosmological parameters, we find that a survey covering 1000 sq deg down to a limiting magnitude of $R=27$ can impose constraints comparable to those expected from upcoming type Ia supernova and number-count surveys. This result, however, is contingent on the control of both observational and theoretical systematics. Concentrating on the latter, we find that the nonlinear power spectrum of matter perturbations and the redshift distribution of source galaxies both need to be determined accurately in order for weak lensing to achieve its full potential. Finally, we discuss the sensitivity of the three-point statistics to dark energy.