Simulations play a vital role in testing and validating H i 21-cm power spectrum estimation techniques. Conventional methods use techniques like N-body simulations to simulate the sky signal which is then passed through a model of the instrument. This makes it necessary to simulate the H i distribution in a large cosmological volume, and incorporate both the light-cone effect and the telescope's chromatic response. The computational requirements may be particularly large if one wishes to simulate many realizations of the signal. In this paper we present an analytical method to simulate the H i visibility signal. This is particularly efficient if one wishes to simulate a large number of realizations of the signal. Our method is based on theoretical predictions of the visibility correlation which incorporate both the light-cone effect and the telescope's chromatic response. We have demonstrated this method by applying it to simulate the H i visibility signal for the upcoming Ooty Wide Field Array Phase I.

We carry out an exploratory weak gravitational lensing analysis on a combined Very Large Array and Multi‐Element Radio‐Linked Interferometer Network radio data set: a deep (3.3 μJy beam−1 rms noise) 1.4 GHz image of the Hubble Deep Field‐North. We measure the shear estimator distribution at this radio sensitivity for the first time, finding a similar distribution to that of optical shear estimators for Hubble Space Telescope Advanced Camera for Surveys data in this field. We examine the residual systematics in shear estimation for the radio data and give cosmological constraints from radio–optical shear cross‐correlation functions. We emphasize the utility of cross‐correlating shear estimators from radio and optical data in order to reduce the impact of systematics. Unexpectedly, we find no evidence of correlation between optical and radio intrinsic ellipticities of matched objects; this result improves the properties of optical–radio lensing cross‐correlations. We explore the ellipticity distribution of the radio counterparts to optical sources statistically, confirming the lack of correlation; as a result, we suggest a connected statistical approach to radio shear measurements.

Relativistic contributions to the dynamics of structure formation come in a variety of forms, and can potentially give corrections to the standard picture on typical scales of 100 Mpc. These corrections cannot be obtained by Newtonian numerical simulations, so it is important to accurately estimate the magnitude of these relativistic effects. Density fluctuations couple to produce a background of gravitational waves, which is larger than any primordial background. A similar interaction produces a much larger spectrum of vector modes which represent the frame-dragging rotation of spacetime. These can change the metric at the percent level in the concordance model at scales below the equality scale. Vector modes modify the lensing of background galaxies by large-scale structure. This gives in principle the exciting possibility of measuring relativistic frame dragging effects on cosmological scales. The effects of the non-linear tensor and vector modes on the cosmic convergence are computed and compared to first-order lensing contributions from density fluctuations, Doppler lensing, and smaller Sachs-Wolfe effects. The lensing from gravitational waves is negligible so we concentrate on the vector modes. We show the relative importance of this for future surveys such as Euclid and SKA. We find that these non-linear effects only marginally affect the overall weak lensing signal so they can safely be neglected in most analyses, though are still much larger than the linear Sachs-Wolfe terms. The second-order vector contribution can dominate the first-order Doppler lensing term at moderate redshifts and are actually more important for survey geometries like the SKA.