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Fast Radio Bursts (FRBs) have emerged as powerful cosmological probes in recent years offering valuable insights into cosmic expansion. These predominantly extragalactic transients encode information on the expansion of the Universe through their dispersion measure, reflecting interactions with the intervening medium along the line of sight. In this study, we introduce a novel method for reconstructing the late-time cosmic expansion rate and estimating the Hubble constant, solely derived from FRBs measurements coupled with their redshift information while employing Artificial Neural Networks. Our approach yields a Hubble constant estimate of $H_0 = 67.3\pm6.6\rm \ km \ s^{-1} \ Mpc^{-1}$. With a dataset comprising 23 localised data points, we demonstrate a precision of $\sim10\%$. However, our forecasts using simulated datasets indicate that in the future it could be possible to achieve precision comparable to the SH0ES collaboration or the Planck satellite. Our findings underscore the potential of FRBs as alternative, independent tools for probing cosmic dynamics.

Cosmic flexion, like cosmic shear, is a correlation function whose signal originates from the large-scale structure of the universe. Building on the observational success of cosmic shear, along with the unprecedented quality of large-scale cosmological datasets, the time is ripe to explore the practical constraints from cosmic flexion. Unlike cosmic shear, which has a broad window function for power, cosmic flexion is only measurable on small scales and therefore can uniquely place constraints on the small-scale matter power spectrum. Here, we present a full theoretical formalism for cosmic flexion, including both flexion-flexion and shear-flexion two-point correlations. We present forecasts for measuring cosmic flexion in the Dark Energy Survey (DES), a Stage III cosmological survey, and comment on the future prospects of measuring these cosmological flexion signals in the upcoming era of Stage IV experiments., Comment: 21 pages, 9 figures; accepted for publication in Phys.Rev.D; revisions to Section IV. A and Appendix A, as well as other minor changes from submitted version

Generative adversarial networks (GANs) have been recently applied as a novel emulation technique for large scale structure simulations. Recent results show that GANs can be used as a fast, efficient and computationally cheap emulator for producing novel weak lensing convergence maps as well as cosmic web data in 2-D and 3-D. However, like any algorithm, the GAN approach comes with a set of limitations, such as an unstable training procedure and the inherent randomness of the produced outputs. In this work we employ a number of techniques commonly used in the machine learning literature to address the mentioned limitations. In particular, we train a GAN to produce both weak lensing convergence maps and dark matter overdensity field data for multiple redshifts, cosmological parameters and modified gravity models. In addition, we train a GAN using the newest Illustris data to emulate dark matter, gas and internal energy distribution data simultaneously. Finally, we apply the technique of latent space interpolation to control which outputs the algorithm produces. Our results indicate a 1-20% difference between the power spectra of the GAN-produced and the training data samples depending on the dataset used and whether Gaussian smoothing was applied. Finally, recent research on generative models suggests that such algorithms can be treated as mappings from a lower-dimensional input (latent) space to a higher dimensional (data) manifold. We explore such a theoretical description as a tool for better understanding the latent space interpolation procedure., Comment: 20 pages, 23 figures, 3 tables

The LOFAR Two-metre Sky Survey (LoTSS) will map the complete Northern sky and provide an excellent opportunity to study the distribution and evolution of the large-scale structure of the Universe. We study the completeness of the LoTSS first data release (DR1) and find a point-source completeness of 99 % above flux densities of 0.8 mJy and define a suite of quality cuts. We determine the count-in-cell statistics and differential source counts statistic and measure the angular two-point correlation function of the LoTSS radio sources. The counts-in-cell statistic reveals that the distribution of radio sources cannot be described by a spatial Poisson process. Instead, a good fit is provided by a compound Poisson distribution. The differential source counts are in good agreement with previous findings in deep fields at low radio frequencies and with simulated catalogues from the SKA design study sky and the Tiered Radio Extragalactic Continuum Simulation. The angular two-point correlation is $<10^{-2}$ at angular scales $> 1$ deg. Restricting the value added source catalogue to low-noise regions and a flux density threshold of 2 mJy provides our most reliable estimate of the angular two-point correlation. For smaller flux density thresholds systematic issues are identified, most likely related to the flux density calibration of the individual pointings. Based on the distribution of photometric redshifts of LoTSS sources and the Planck 2018 best-fit cosmological model, the theoretically predicted angular two-point correlation between 0.1 deg and 6 deg agrees with the measured clustering for a subsample of radio sources with redshift information. We find agreement with the expectation of large-scale statistical isotropy of the radio sky at the per cent level. The angular two-point correlation agrees well with the expectation of the cosmological standard model. (abbreviated), Comment: 30 pages, 35 figures; corrections of affiliations and acknowledgements; version accepted by A&A

We present a detailed overview of the cosmological surveys that will be carried out with Phase 1 of the Square Kilometre Array (SKA1), and the science that they will enable. We highlight three main surveys: a medium-deep continuum weak lensing and low-redshift spectroscopic HI galaxy survey over 5,000 sqdeg; a wide and deep continuum galaxy and HI intensity mapping survey over 20,000 sqdeg from z = 0.35 - 3; and a deep, high-redshift HI intensity mapping survey over 100 sqdeg from z = 3 - 6. Taken together, these surveys will achieve an array of important scientific goals: measuring the equation of state of dark energy out to z ~ 3 with percent-level precision measurements of the cosmic expansion rate; constraining possible deviations from General Relativity on cosmological scales by measuring the growth rate of structure through multiple independent methods; mapping the structure of the Universe on the largest accessible scales, thus constraining fundamental properties such as isotropy, homogeneity, and non-Gaussianity; and measuring the HI density and bias out to z = 6. These surveys will also provide highly complementary clustering and weak lensing measurements that have independent systematic uncertainties to those of optical surveys like LSST and Euclid, leading to a multitude of synergies that can improve constraints significantly beyond what optical or radio surveys can achieve on their own. This document, the 2018 Red Book, provides reference technical specifications, cosmological parameter forecasts, and an overview of relevant systematic effects for the three key surveys, and will be regularly updated by the Cosmology Science Working Group in the run up to start of operations and the Key Science Programme of SKA1., Comment: Red Book 2018 of the Square Kilometre Array Cosmology Science Working Group; 35 pages, 27 figures; To be submitted to PASA

We present a new method to measure the redshift-dependent galaxy bias by combining information from the galaxy density field and the weak lensing field. This method is based on Amara et al. (2012), where they use the galaxy density field to construct a bias-weighted convergence field kg. The main difference between Amara et al. (2012) and our new implementation is that here we present another way to measure galaxy bias using tomography instead of bias parameterizations. The correlation between kg and the true lensing field k allows us to measure galaxy bias using different zero-lag correlations, such as / or /. Our method measures the linear bias factor on linear scales under the assumption of no stochasticity between galaxies and matter. We use the MICE simulation to measure the linear galaxy bias for a flux-limited sample (i < 22.5) in tomographic redshift bins using this method. This paper is the first that studies the accuracy and systematic uncertainties associated with the implementation of the method, and the regime where it is consistent with the linear galaxy bias defined by projected 2-point correlation functions (2PCF). We find that our method is consistent with linear bias at the percent level for scales larger than 30 arcmin, while nonlinearities appear at smaller scales. This measurement is a good complement to other measurements of bias, since it does not depend strongly on sigma8 as the 2PCF measurements. We apply this method to the Dark Energy Survey Science Verification data in a follow-up paper., Comment: 15 pages, 9 figures

Compound strong gravitational lensing is a rare phenomenon, but a handful of such lensed systems are likely to be discovered in forthcoming surveys. In this work, we use a double SIS lens model to analytically understand how the properties of the system impact image multiplicity for the final source. We find that up to six images of a background source can form, but only if the second lens is multiply imaged by the first and the Einstein radius of the second lens is comparable to, but does not exceed that of the first. We then build a model of compound lensing masses in the Universe, using SIE lenses, and assess how the optical depth for multiple imaging by a galaxy-galaxy compound lens varies with source redshift. For a source redshift of 4, we find optical depths of $6 \times 10^{-6}$ for multiple imaging and $5 \times 10^{-8}$ for multiplicity of 6 or greater. We find that extreme magnifications are possible, with magnifications of 100 or more for $6 \times 10^{-9}$ of $z=10$ sources with 0.1 kpc radii. We show some of the image configurations that can be generated by compound lenses, and demonstrate that they are qualitatively different to those generated by single-plane lenses; dedicated compound lens finders will be necessary if these systems are to be discovered in forthcoming surveys., Comment: 11 pages, submitted to MNRAS. Comments gratefully received

In this work we study the relevance of the cosmic web and substructures on the matter and lensing power spectra measured from halo mock catalogues extracted from the N-body simulations. Since N-body simulations are computationally expensive, it is common to use faster methods that approximate the dark matter field as a set of halos. In this approximation, we replace mass concentrations in N-body simulations by a spherically symmetric Navarro-Frenk-White halo density profile. We also consider the full mass field as the sum of two distinct fields: dark matter halos ($M>9\times 10^{12}~M_{\odot}$/h) and particles not included into halos. Mock halos reproduce well the matter power spectrum, but underestimate the lensing power spectrum on large and small scales. For sources at $z_{\rm s}=1$ the lensing power spectrum is underestimated by up to 40% at $\ell\approx 10^4$ with respect to the simulated halos. The large scale effect can be alleviated by combining the mock catalogue with the dark matter distribution outside the halos. In addition, to evaluate the contribution of substructures we have smeared out the intra-halo substructures in a N-body simulation while keeping the halo density profiles unchanged. For the matter power spectrum the effect of this smoothing is only of the order of 5%, but for lensing substructures are much more important: for $\ell\approx 10^4$ the internal structures contribute 30% of the total spectrum. These findings have important implications in the way mock catalogues have to be created, suggesting that some approximate methods currently used for galaxy surveys will be inadequate for future weak lensing surveys., Comment: 16 pages, 18 figures, submitted to MNRAS

The Planck CMB experiment has delivered the best constraints so far on primordial non-Gaussianity, ruling out early-Universe models of inflation that generate large non-Gaussianity. Although small improvements in the CMB constraints are expected, the next frontier of precision will come from future large-scale surveys of the galaxy distribution. The advantage of such surveys is that they can measure many more modes than the CMB -- in particular, forthcoming radio surveys with the SKA will cover huge volumes. Radio continuum surveys deliver the largest volumes, but with the disadvantage of no redshift information. In order to mitigate this, we use two additional observables. First, the integrated Sachs-Wolfe effect -- the cross-correlation of the radio number counts with the CMB temperature anisotropies -- helps to reduce systematics on the large scales that are sensitive to non-Gaussianity. Second, optical data allows for cross-identification in order to gain some redshift information. We show that, while the single redshift bin case can provide a sigma(fNL) ~ 20, and is therefore not competitive with current and future constraints on non-Gaussianity, a tomographic analysis could improve the constraints by an order of magnitude, even with only two redshift bins. A huge improvement is provided by the addition of high-redshift sources, so having cross-ID for high-z galaxies and an even higher-z radio tail is key to enabling very precise measurements of fNL. Our results show that SKA continuum surveys could provide constraints competitive with CMB and forthcoming optical surveys, potentially allowing a measurement of sigma(fNL) ~ 1 to be made. Moreover, these measurements would act as a useful check of results obtained with other probes at other redshift ranges with other methods., Comment: 10 pages, 5 figures. Version matching the one accepted for publication on JCAP

Doppler lensing is the apparent change in object size and magnitude due to peculiar velocities. Objects falling into an overdensity appear larger on its near side, and smaller on its far side, than typical objects at the same redshifts. This effect dominates over the usual gravitational lensing magnification at low redshift. Doppler lensing is a promising new probe of cosmology, and we explore in detail how to utilize the effect with forthcoming surveys. We present cosmological simulations of the Doppler and gravitational lensing effects based on the Millennium simulation. We show that Doppler lensing can be detected around stacked voids or unvirialised over-densities. New power spectra and correlation functions are proposed which are designed to be sensitive to Doppler lensing. We consider the impact of gravitational lensing and intrinsic size correlations on these quantities. We compute the correlation functions and forecast the errors for realistic forthcoming surveys, providing predictions for constraints on cosmological parameters. Finally, we demonstrate how we can make 3-D potential maps of large volumes of the Universe using Doppler lensing., Comment: 17 pages, 14 figures. Minor corrections and improvements; version accepted by MNRAS

Using a sample of 608 Type Ia supernovae from the SDSS-II and BOSS surveys, combined with a sample of foreground galaxies from SDSS-II, we estimate the weak lensing convergence for each supernova line-of-sight. We find that the correlation between this measurement and the Hubble residuals is consistent with the prediction from lensing (at a significance of 1.7sigma. Strong correlations are also found between the residuals and supernova nuisance parameters after a linear correction is applied. When these other correlations are taken into account, the lensing signal is detected at 1.4sigma. We show for the first time that distance estimates from supernovae can be improved when lensing is incorporated by including a new parameter in the SALT2 methodology for determining distance moduli. The recovered value of the new parameter is consistent with the lensing prediction. Using CMB data from WMAP7, H0 data from HST and SDSS BAO measurements, we find the best-fit value of the new lensing parameter and show that the central values and uncertainties on Omega_m and w are unaffected. The lensing of supernovae, while only seen at marginal significance in this low redshift sample, will be of vital importance for the next generation of surveys, such as DES and LSST, which will be systematics dominated., Comment: Minor changes. Accepted for publication in ApJ

The available probes of the large scale structure in the Universe have distinct properties: galaxies are a high resolution but biased tracer of mass, while weak lensing avoids such biases but, due to low signal-to-noise ratio, has poor resolution. We investigate reconstructing the projected density field using the complementarity of weak lensing and galaxy positions. We propose a maximum-probability reconstruction of the 2D lensing convergence with a likelihood term for shear data and a prior on the Fourier phases constructed from the galaxy positions. By considering only the phases of the galaxy field, we evade the unknown value of the bias and allow it to be calibrated by lensing on a mode-by-mode basis. By applying this method to a realistic simulated galaxy shear catalogue, we find that a weak prior on phases provides a good quality reconstruction down to scales beyond l=1000, far into the noise domain of the lensing signal alone., Comment: 11 pages, 9 figures, published in MNRAS

We present a study of weak lensing shear measurements for simulated galaxy images at radio wavelengths. We construct a simulation pipeline into which we can input galaxy images of known ellipticity, and with which we then simulate observations with eMERLIN and the international LOFAR array. The simulations include the effects of the CLEAN algorithm, uv sampling, observing angle, and visibility noise, and produce realistic restored images of the galaxies. We apply a shapelet-based shear measurement method to these images and test our ability to recover the true source ellipticities. We model and deconvolve the effective PSF, and find suitable parameters for CLEAN and shapelet decomposition of galaxies. We demonstrate that ellipticities can be measured faithfully in these radio simulations, with no evidence of an additive bias and a modest (10%) multiplicative bias on the ellipticity measurements. Our simulation pipeline can be used to test shear measurement procedures and systematics for the next generation of radio telescopes., Comment: Accepted to MNRAS, some changes from submitted version

Telescope Point Spread Function (PSF) quality is critical for realising the potential of cosmic weak lensing observations to constrain dark energy and test General Relativity. In this paper we use quantitative weak gravitational lensing measures to inform the precision of lens optical alignment, with specific reference to the Dark Energy Survey (DES). We compute optics spot diagrams and calculate the shear and flexion of the PSF as a function of position on the focal plane. For perfect optical alignment we verify the high quality of the DES optical design, finding a maximum PSF contribution to the weak lensing shear of 0.04 near the edge of the focal plane. However this can be increased by a factor of approximately three if the lenses are only just aligned within their maximum specified tolerances. We calculate the E and B-mode shear and flexion variance as a function of de-centre or tilt of each lens in turn. We find tilt accuracy to be a few times more important than de-centre, depending on the lens considered. Finally we consider the compound effect of de-centre and tilt of multiple lenses simultaneously, by sampling from a plausible range of values of each parameter. We find that the compound effect can be around twice as detrimental as when considering any one lens alone. Furthermore, this combined effect changes the conclusions about which lens is most important to align accurately. For DES, the tilt of the first two lenses is the most important., Comment: 10 pages, 8 figures

In this paper, we explore how the forthcoming generation of large-scale radio continuum surveys, with the inclusion of some degree of redshift information, can constrain cosmological parameters. By cross-matching these radio surveys with shallow optical to near-infrared surveys, we can essentially separate the source distribution into a low- and a high-redshift sample, thus providing a constraint on the evolution of cosmological parameters such as those related to dark energy. We examine two radio surveys, the Evolutionary Map of the Universe (EMU) and the Westerbork Observations of the Deep APERTIF Northern sky (WODAN). A crucial advantage is their combined potential to provide a deep, full-sky survey. The surveys used for the cross-identifications are SkyMapper and SDSS, for the southern and northern skies, respectively. We concentrate on the galaxy clustering angular power spectrum as our benchmark observable, and find that the possibility of including such low redshift information yields major improvements in the determination of cosmological parameters. With this approach, and provided a good knowledge of the galaxy bias evolution, we are able to put strict constraints on the dark energy parameters, i.e. w_0=-0.9+/-0.041 and w_a=-0.24+/-0.13, with type Ia supernovae and CMB priors (with a one-parameter bias in this case); this corresponds to a Figure of Merit (FoM) > 600, which is twice better than what is obtained by using only the cross-identified sources and greater than four time better than the case without any redshift information at all., Comment: 12 pages, 6 figures, 6 tables; accepted for publication in MNRAS

We present non-linear weak lensing predictions for coupled dark energy models using the CoDECS simulations. We calculate the shear correlation function and error covariance expected for these models, for forthcoming ground-based (such as DES) and space-based (Euclid) weak lensing surveys. We obtain predictions for the discriminatory power of a ground-based survey similar to DES and a space-based survey such as Euclid in distinguishing between $\Lambda$CDM and coupled dark energy models; we show that using the non-linear lensing signal we could discriminate between $\Lambda$CDM and exponential constant coupling models with $\beta_0\geq0.1$ at $4\sigma$ confidence level with a DES-like survey, and $\beta_0\geq0.05$ at $5\sigma$ confidence level with Euclid. We also demonstrate that estimating the coupled dark energy models' non-linear power spectrum, using the $\Lambda$CDM Halofit fitting formula, results in biases in the shear correlation function that exceed the survey errors., Comment: 9 pages, 5 figures, v2: accepted for publication in MNRAS

We test Einstein gravity using cosmological observations of both expansion and structure growth, including the latest data from supernovae (Union2.1), CMB (WMAP7), weak lensing (CFHTLS) and peculiar velocity of galaxies (WiggleZ). We fit modified gravity parameters of the generalized Poisson equations simultaneously with the effective equation of state for the background evolution, exploring the covariances and model dependence. The results show that general relativity is a good fit to the combined data. Using a Pad{\'e} approximant form for the gravity deviations accurately captures the time and scale dependence for theories like $f(R)$ and DGP gravity, and weights high and low redshift probes fairly. For current observations, cosmic growth and expansion can be fit simultaneously with little degradation in accuracy, while removing the possibility of bias from holding one aspect fixed., Comment: 5 pages, 3 figures; Accepted to Phys. Rev. D

We present forecasts for constraints on cosmological models which can be obtained by forthcoming radio continuum surveys: the wide surveys with the LOw Frequency ARray (LOFAR), Australian Square Kilometre Array Pathfinder (ASKAP) and the Westerbork Observations of the Deep APERTIF Northern sky (WODAN). We use simulated catalogues appropriate to the planned surveys to predict measurements obtained with the source auto-correlation, the cross-correlation between radio sources and CMB maps (the Integrated Sachs-Wolfe effect), the cross-correlation of radio sources with foreground objects due to cosmic magnification, and a joint analysis together with the CMB power spectrum and supernovae. We show that near future radio surveys will bring complementary measurements to other experiments, probing different cosmological volumes, and having different systematics. Our results show that the unprecedented sky coverage of these surveys combined should provide the most significant measurement yet of the Integrated Sachs-Wolfe effect. In addition, we show that using the ISW effect will significantly tighten constraints on modified gravity parameters, while the best measurements of dark energy models will come from galaxy auto-correlation function analyses. Using the combination of EMU and WODAN to provide a full sky survey, it will be possible to measure the dark energy parameters with an uncertainty of \{$\sigma (w_0) = 0.05$, $\sigma (w_a) = 0.12$\} and the modified gravity parameters \{$\sigma (\eta_0) = 0.10$, $\sigma (\mu_0) = 0.05$\}, assuming Planck CMB+SN(current data) priors. Finally, we show that radio surveys would detect a primordial non-Gaussianity of $f_{\rm NL}$ = 8 at 1-$\sigma$ and we briefly discuss other promising probes., Comment: 19 pages, 16 figures, 2 tables; submitted to MNRAS

Weak lensing calculations are often made under the assumption of the Born approximation, where the ray path is approximated as a straight radial line. In addition, lens-lens couplings where there are several deflections along the light ray are often neglected. We examine the effect of dropping the Born approximation and taking lens-lens couplings into account, for weak lensing effects up to second order (cosmic flexion), by making a perturbative expansion in the light path. We present a diagrammatic representation of the resulting corrections to the lensing effects. The flexion signal, which measures the derivative of the density field, acquires correction terms proportional to the squared gravitational shear; we also find that by dropping the Born approximation, two further degrees of freedom of the lensing distortion can be excited (the twist components), in addition to the four standard flexion components. We derive angular power spectra of the flexion and twist, with and without the Born-approximation and lens-lens couplings and confirm that the Born approximation is an excellent approximation for weak cosmic flexions, except at very small scales., Comment: 12 pages, 5 figures, submitted to MNRAS

We test General Relativity (GR) using current cosmological data: the cosmic microwave background (CMB) from WMAP5 (Komatsu et al. 2009), the integrated Sachs-Wolfe (ISW) effect from the cross-correlation of the CMB with six galaxy catalogs (Giannantonio et al. 2008), a compilation of supernovae Type Ia (SNe) including the latest SDSS SNe (Kessler et al. 2009), and part of the weak lensing (WL) data from CFHTLS (Fu et al. 2008, Kilbinger et al. 2009) that probe linear and mildly non-linear scales. We first test a model where the effective Newton's constant, mu, and the ratio of the two gravitational potentials, eta, transit from the GR value to another constant at late times; in this case, we find that standard GR is fully consistent with the combined data. The strongest constraint comes from the ISW effect which would arise from this gravitational transition; the observed ISW signal imposes a tight constraint on a combination of mu and eta that characterizes the lensing potential. Next, we consider four pixels in time and space for each function mu and eta, and perform a Principal Component Analysis (PCA) finding that seven of the resulting eight eigenmodes are consistent with GR within the errors. Only one eigenmode shows a 2-sigma deviation from the GR prediction, which is likely to be due to a systematic effect. However, the detection of such a deviation demonstrates the power of our time- and scale-dependent PCA methodology when combining observations of structure formation and expansion history to test GR., Comment: 14 pages, 10 figures. Minor modifications, version published by Phys. Rev. D

We present a set of predictions for weak lensing correlation functions in the context of modified gravity models, including a prescription for the impact of the nonlinear power spectrum regime in these models. We consider the DGP and f(R) models, together with dark energy models with the same expansion history. We use the requirement that gravity is close to GR on small scales to estimate the non-linear power for these models. We then calculate weak lensing statistics, showing their behaviour as a function of scale and redshift, and present predictions for measurement accuracy with future lensing surveys, taking into account cosmic variance and galaxy shape noise. We demonstrate the improved discriminatory power of weak lensing for testing modified gravities once the nonlinear power spectrum contribution has been included. We also examine the ability of future lensing surveys to constrain a parameterisation of the non-linear power spectrum, including sensitivity to the growth factor., Comment: 10 pages, 9 figures, 6 tables; v2: updated references; v3: accepted for publication in MNRAS

We account for all the image distortions relevant to weak gravitational lensing to second order. Besides the familiar shear, convergence, rotation and flexions, we find a new image distortion with two distinct descriptions, the twist and the turn. Like rotation, this distortion is not activated gravitationally to first order, but will be activated by systematic effects. We examine the rotational properties of twist and turn, and their effect on images in real and shapelet space. We construct estimators for the new distortion, taking into account the centroid shift which it generates. We then use these estimators to make first constraints on twist using the STAGES HST survey; we find that the mean twist estimator is consistent with zero. We measure correlation functions for our twist estimator on the survey, again finding no evidence of systematic effects., Comment: 9 pages, 9 figures. Accepted by MNRAS; expands discussion of distortions and estimators

We derive expressions, in terms of "polar shapelets", for the image distortion operations associated with weak gravitational lensing. Shear causes galaxy shapes to become elongated, and is sensitive to the second derivative of the projected gravitational potential along their line of sight; flexion bends galaxy shapes into arcs, and is sensitive to the third derivative. Polar shapelets provide a natural representation, in which both shear and flexion transformations are compact. Through this tool, we understand progress in several weak lensing methods. We then exploit various symmetries of shapelets to construct a range of shear estimators with useful properties. Through an analogous investigation, we also explore several flexion estimators. In particular, some of the estimators can be measured simultaneously and independently for every galaxy, and will provide unique checks for systematics in future weak lensing analyses. Using simulated images from the Shear TEsting Programme (STEP), we show that we can recover input shears with no significant bias. A complete software package to parametrize astronomical images in terms of polar shapelets, and to perform a full weak lensing analysis, is available at http://www.astro.caltech.edu/~rjm/shapelets/ ., Comment: 17 pages, 3 figures. Matches published version

We propose to use multiple-imaged gravitational lenses to set limits on gravity theories without dark matter, specificly TeVeS (Bekenstein 2004), a theory which is consistent with fundamental relativistic principles and the phenomenology of MOdified Newtonian Dynamics (MOND) theory. After setting the framework for lensing and cosmology, we derive analytically the deflection angle for the point lens and the Hernquist galaxy profile, and fit galaxy-quasar lenses in the CASTLES sample. We do this with three methods, fitting the observed Einstein ring sizes, the image positions, or the flux ratios. In all cases we consistently find that stars in galaxies in MOND/TeVeS provide adequate lensing. Bekenstein's toy $\mu$ function provides more efficient lensing than the standard MOND $\mu$ function. But for a handful of lenses [indicated in Table 2,3, fig 16] a good fit would require a lens mass orders of magnitude larger/smaller than the stellar mass derived from luminosity unless the modification function $\mu$ and modification scale $a_0$ for the universal gravity were allowed to be very different from what spiral galaxy rotation curves normally imply. We discuss the limitation of present data and summarize constraints on the MOND $\mu$ function. We also show that the simplest TeVeS "minimal-matter" cosmology, a baryonic universe with a cosmological constant, can fit the distance-redshift relation from the supernova data, but underpredicts the sound horizon size at the last scattering. We conclude that lensing is a promising approach to differentiate laws of gravity (see also astro-ph/0512425)., Comment: reduced to 17p, 16 figs, discussed cosmology and constraints on mu-function, MNRAS accepted

In this paper, we develop a new gravitational lensing inversion technique. While traditional approaches assume that the lensing field varies little across a galaxy image, we note that this variation in the field can give rise to a ``Flexion'' or bending of a galaxy image, which may then be used to detect a lensing signal with increased signal to noise. Since the significance of the Flexion signal increases on small scales, this is ideally suited to galaxy-galaxy lensing. We develop an inversion technique based on the ``Shapelets'' formalism of Refregier (2003). We then demonstrate the proof of this concept by measuring a Flexion signal in the Deep Lens Survey. Assuming an intrinsically isothermal distribution, we find from the Flexion signal alone a velocity width of v_c=221\pm 12 km/s for lens galaxies of r < 21.5, subject to uncertainties in the intrinsic Flexion distribution., Comment: 11 pages, Latex, 4 figures. Accepted by ApJ, changes include revision of errors from previous draft

We report the results of a cosmic shear survey using the 4.2m William Herschel Telescope on La Palma, to a depth of R=25.8 (z~0.8), over 4 square degrees. The shear correlation functions are measured on scales from 1' to 15', and are used to constrain cosmological parameters. We ensure that our measurements are free from instrumental systematics by performing a series of tests, including a decomposition of the signal into E- and B-modes. We also reanalyse the data independently, using the shear measurement pipeline developed for the COMBO-17 survey. This confirms our results and also highlights various effects introduced by different implementations of the basic "KSB" shear measurement method. We find that the normalisation of the matter power spectrum on 8 h^{-1}Mpc scales is sigma_8=(1.02+/-0.15)(0.3/Omega_m)^{0.5}, where the 68%CL error includes noise, sample variance, covariance between angular scales, systematic effects, redshift uncertainty and marginalisation over other parameters. We compare these results with other cosmic shear surveys and with recent constraints from the WMAP experiment., Comment: 11 pages, 13 figures. Accepted version. Now includes a second, independent analysis of the WHT data using the COMBO-17 pipeline. This confirms our results, within statistical errors. A meticulous comparison of the two methods also highlights some important details of weak shear measurement for the first time

We present a method to simulate deep sky images, including realistic galaxy morphologies and telescope characteristics. To achieve a wide diversity of simulated galaxy morphologies, we first use the shapelets formalism to parametrize the shapes of all objects in the Hubble Deep Fields. We measure this distribution of real galaxy morphologies in shapelet parameter space, then resample it to generate a new population of objects. These simulated galaxies can contain spiral arms, bars, discs, arbitrary radial profiles and even dust lanes or knots. To create a final image, we also model observational effects, including noise, pixellisation, astrometric distortions and a Point-Spread Function. We demonstrate that they are realistic by showing that simulated and real data have consistent distributions of morphology diagnostics: including galaxy size, ellipticity, concentration and asymmetry statistics. Sample images are made available on the world wide web. These simulations are useful to develop and calibrate precision image analysis techniques for photometry, astrometry, and shape measurement. They can also be used to assess the sensitivity of future telescopes and surveys for applications such as supernova searches, microlensing, proper motions, and weak gravitational lensing., Comment: MNRAS in press. Updated to reflect accepted version, including extra statistical tests