Many weak lensing calculations make use of the Born approximation where the light ray is approximated by a straight path. We examine the effect of Born-corrections for lensing of the cosmic microwave background in an analytical approach by taking perturbative corrections to the geodesic into account. The resulting extra power in the lensing potential spectrum is comparable to the power generated by nonlinear structure formation and affects especially the polarisation spectra, leading to relative changes of the order of one per cent for the E-mode spectrum and up to 10 per cent on all scales to the B-mode spectrum. In contrast, there is only little change of spectra involving the CMB temperature. Additionally, the corrections excite one more degree of freedom resulting in a deflection component which can not be described as a gradient of the lensing potential as it is related to image rotation in lens-lens coupling. We estimate the magnitude of this effect on the CMB-spectra and find it to be negligible.

In this paper, we revisit the acquisition of angular momentum of galaxies by tidal shearing and compute the angular momentum variance as well as the angular momentum correlation function CL(r), using tidal torquing in the Zel’dovich approximation as the model for angular momentum build‐up. Under the assumption that haloes form at peaks in the density field we determine the protohalo’s inertia from the peak shape and embed it in a tidal field. Inertia and shear are drawn from a random process and we compute the angular momentum variance and correlation function by sampling from a Gaussian distribution which shows the correct covariances between all relevant quantities. We describe the way in which the correlations in angular momentum result from an interplay of long‐ranged correlations in the tidal shear and short‐ranged correlations in the inertia field. Our description takes care of the relative orientation of the eigensystems of these two symmetric tensors. We propose a new form of the angular momentum correlation function which is able to distinguish between parallel and antiparallel alignment of angular momentum vectors, and comment on implications of intrinsic alignments for weak lensing measurements. We confirm the scaling L/M ∝ M2/3 and find the angular momentum distribution of Milky Way sized haloes to be correlated on scales of ∼1 Mpc h−1. The correlation function can be well fitted by an empirical relation of the form CL(r) ∝ exp(−[r/r0]β).

Future observations of the large-scale structure have the potential to investigate cosmological models with a high degree of complexity, including the properties of gravity on large scales, the presence of a complicated dark energy component, and the addition of neutrinos changing structures on small scales. Here we study Horndeski theories of gravity, the most general minimally coupled scalar-tensor theories of second order. While the cosmological background evolution can be described by an effective equation of state, the perturbations are characterised by four free functions of time. We consider a specific parametrisation of these functions tracing the dark energy component. The likelihood of the full parameter set resulting from combining cosmic microwave background primary anisotropies including their gravitational lensing signal, tomographic angular galaxy clustering and weak cosmic shear, together with all possible non-vanishing cross-correlations is evaluated; both with the Fisher-formalism as well as without the assumption of a specific functional form of the posterior through Monte-Carlo Markov-chains (MCMCs). Our results show that even complex cosmological models can be constrained and could exclude variations of the effective Newtonian gravitational coupling larger than 10% over the age of the Universe. In particular, we confirm strong correlations between parameter groups. Furthermore, we find that the expected contours from MCMC are significantly larger than those from the Fisher analysis even with the vast amount of signal provided by stage IV experiments, illustrating the importance of a proper treatment of non-Gaussian likelihoods and the high level of precision needed for unlocking the sensitivity on gravitational parameters.

Weak gravitational lensing changes the angular power spectra of the cosmic microwave background (CMB) temperature and polarization in a characteristic way containing valuable information for cosmological parameter estimation. So far, analytical expressions for the lensed CMB power spectra assume the probability density function (PDF) of the lensing excursion angle to be Gaussian. However, coherent light deflection by non‐linear structures at low redshifts causes deviations from a pure Gaussian PDF. Working in the flat‐sky limit, we develop a method for computing the lensed CMB power spectra which takes these non‐Gaussian features into account. Our method does not assume any specific PDF but uses instead an expansion of the characteristic function of the lensing excursion angle into its moments. Measuring these in the CMB lensing deflection field obtained from the Millennium Simulation we show that the change in the lensed power spectra is only at the 0.1–0.4 per cent level on very small scales (Δθ≲ 4 arcmin, l≳ 2500) and demonstrate that the assumption of a Gaussian lensing excursion angle PDF is well applicable.

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