Weak Lensing Statistics Research Articles

Forecast constraints on the baryonic feedback effect from the future kinetic Sunyaev-Zel'dovich effect detection

The baryonic feedback effect is an important systematic error in the weak lensing (WL) analysis. It contributes partly to the S 8 tension in the literature. With the next generations of large scale structure (LSS) and CMB experiments, the high signal-to-noise kinetic Sunyaev-Zel'dovich (kSZ) effect detection can tightly constrain the baryon distribution in and around dark matter halos, and quantify the baryonic effect in the weak lensing statistics. In this work, we apply the Fisher matrix technique to predict the future kSZ constraints on 3 kSZ-sensitive Baryon Correction Model (BCM) parameters. Our calculations show that, in combination with next generation LSS surveys, the 3rd generation CMB experiments such as AdvACT and Simon Observatory can constrain the matter power spectrum damping S(k) to the precision of σ S (k) < 0.8%√(37.8 Gpc3h-3-3/V) at k ≲ 10h/Mpc, where V is the overlapped survey volume between the future LSS and CMB surveys. For the 4th generation CMB surveys such as CMB-S4 and CMB-HD, the constraint will be enhanced to σ S (k) < 0.4%√(37.8 Gpc3h-3/V). If extra-observations, e.g. X-ray detection and thermal SZ observation, can effectively fix the gas density profile slope parameter δ, the constraint on S(k) will be further boosted to σ S (k) < 0.3%√(37.8 Gpc3 h -3/V) and σ S (k) < 0.1%√(37.8 Gpc3 h -3/V) for the 3rd and 4th generation CMB surveys.

Forecasting the power of higher order weak-lensing statistics with automatically differentiable simulations

Aims. We present the fully differentiable physical Differentiable Lensing Lightcone (DLL) model, designed for use as a forward model in Bayesian inference algorithms that require access to derivatives of lensing observables with respect to cosmological parameters. Methods. We extended the public FlowPM N-body code, a particle-mesh N-body solver, while simulating the lensing lightcones and implementing the Born approximation in the Tensorflow framework. Furthermore, DLL is aimed at achieving high accuracy with low computational costs. As such, it integrates a novel hybrid physical-neural (HPN) parameterization that is able to compensate for the small-scale approximations resulting from particle-mesh schemes for cosmological N-body simulations. We validated our simulations in the context of the Vera C. Rubin Observatory’s Legacy Survey of Space and Time (LSST) against high-resolution κTNG-Dark simulations by comparing both the lensing angular power spectrum and multiscale peak counts. We demonstrated its ability to recover lensing Cℓ up to a 10% accuracy at ℓ = 1000 for sources at a redshift of 1, with as few as ∼0.6 particles per Mpc h−1. As a first-use case, we applied this tool to an investigation of the relative constraining power of the angular power spectrum and peak counts statistic in an LSST setting. Such comparisons are typically very costly as they require a large number of simulations and do not scale appropriately with an increasing number of cosmological parameters. As opposed to forecasts based on finite differences, these statistics can be analytically differentiated with respect to cosmology or any systematics included in the simulations at the same computational cost of the forward simulation. Results. We find that the peak counts outperform the power spectrum in terms of the cold dark matter parameter, Ωc, as well as on the amplitude of density fluctuations, σ8, and the amplitude of the intrinsic alignment signal, AIA.

The MillenniumTNG Project: the impact of baryons and massive neutrinos on high-resolution weak gravitational lensing convergence maps

ABSTRACT We study weak gravitational lensing convergence maps produced from the MillenniumTNG simulations by direct projection of the mass distribution on the past backwards lightcone of a fiducial observer. We explore the lensing maps over a large dynamic range in simulation mass and angular resolution, allowing us to establish a clear assessment of numerical convergence. By comparing full physics hydrodynamical simulations with corresponding dark-matter-only runs, we quantify the impact of baryonic physics on the most important weak lensing statistics. Likewise, we predict the impact of massive neutrinos reliably far into the non-linear regime. We also demonstrate that the ‘fixed &amp; paired’ variance suppression technique increases the statistical robustness of the simulation predictions on large scales not only for time slices but also for continuously output lightcone data. We find that both baryonic and neutrino effects substantially impact weak lensing shear measurements, with the latter dominating over the former on large angular scales. Thus, both effects must explicitly be included to obtain sufficiently accurate predictions for stage IV lensing surveys. Reassuringly, our results agree accurately with other simulation results where available, supporting the promise of simulation modelling for precision cosmology far into the non-linear regime.

Euclidpreparation

Recent cosmic shear studies have shown that higher-order statistics (HOS) developed by independent teams now outperform standard two-point estimators in terms of statistical precision thanks to their sensitivity to the non-Gaussian features of large-scale structure. The aim of the Higher-Order Weak Lensing Statistics (HOWLS) project is to assess, compare, and combine the constraining power of ten different HOS on a common set ofEuclid-like mocks, derived fromN-body simulations. In this first paper of the HOWLS series, we computed the nontomographic (Ωm,σ8) Fisher information for the one-point probability distribution function, peak counts, Minkowski functionals, Betti numbers, persistent homology Betti numbers and heatmap, and scattering transform coefficients, and we compare them to the shear and convergence two-point correlation functions in the absence of any systematic bias. We also include forecasts for three implementations of higher-order moments, but these cannot be robustly interpreted as the Gaussian likelihood assumption breaks down for these statistics. Taken individually, we find that each HOS outperforms the two-point statistics by a factor of around two in the precision of the forecasts with some variations across statistics and cosmological parameters. When combining all the HOS, this increases to a 4.5 times improvement, highlighting the immense potential of HOS for cosmic shear cosmological analyses withEuclid. The data used in this analysis are publicly released with the paper.

Assessing theoretical uncertainties for cosmological constraints from weak lensing surveys

ABSTRACT Weak gravitational lensing is a powerful probe, which is used to constrain the standard cosmological model and its extensions. With the enhanced statistical precision of current and upcoming surveys, high-accuracy predictions for weak lensing statistics are needed to limit the impact of theoretical uncertainties on cosmological parameter constraints. For this purpose, we present a comparison of the theoretical predictions for the non-linear matter and weak lensing power spectra, based on the widely used fitting functions ($\texttt {mead}$ and $\texttt {rev-halofit}$ ), emulators ($\texttt {EuclidEmulator}$ , $\texttt {EuclidEmulator2}$ , $\texttt {BaccoEmulator}$ , and $\texttt {CosmicEmulator}$ ), and N-body simulations (pkdgrav3). We consider the forecasted constraints on the $\Lambda \texttt {CDM}$ and $\texttt {wCDM}$ models from weak lensing for stage III and stage IV surveys. We study the relative bias on the constraints and their dependence on the assumed prescriptions. Assuming a $\Lambda \texttt {CDM}$ cosmology, we find that the relative agreement on the S8 parameter is between 0.2 and 0.3σ for a stage III-like survey between the above predictors. For a stage IV-like survey the agreement becomes 1.4–3.0σ. In the $\texttt {wCDM}$ scenario, we find broader S8 constraints, and agreements of 0.18–0.26σ and 0.7–1.7σ for stage III and stage IV surveys, respectively. The accuracies of the above predictors therefore appear adequate for stage III surveys, whereas the fitting functions would need improvements for future stage IV surveys. Furthermore, we find that, of the fitting functions, $\texttt {mead}$ provides the best agreement with the emulators. We discuss the implication of these findings for the preparation of future weak lensing surveys, and the relative impact of theoretical uncertainties to other systematics.

A roadmap to cosmological parameter analysis with third-order shear statistics

Context. Third-order weak lensing statistics are a promising tool for cosmological analyses since they extract cosmological information in the non-Gaussianity of the cosmic large-scale structure. However, such analyses require precise and accurate models for the covariance of the statistics. Aims. In this second paper of a series on third-order weak lensing statistics, we derive and validate an analytic model for the covariance of the third-order aperture statistics 〈Map3〉. Methods. We derive the covariance model from a real-space estimator for 〈Map3〉, including the Gaussian and non-Gaussian parts. We validate the model by comparing it to estimates from simulated Gaussian random fields (GRFs) and two sets of N-body simulations. Finally, we perform mock cosmological analyses with the model covariance and the simulation estimate to compare the resulting parameter constraints. Results. We find good agreement between the analytic model and the simulations, both for the GRFs and the N-body simulations. The figure of merit in the S8 − Ωm plane from our covariance model is within 3% of the one obtained from the simulated covariances. We also show that our model, which is based on an estimator using convergence maps, can be used to obtain upper and lower bounds for the covariance of an estimator based on three-point shear correlation functions. This second estimator is required to measure 〈Map3〉 in realistic survey data. In our derivation, we find that the covariance of 〈Map3〉 cannot be obtained from the bispectrum covariance and that it includes several ‘finite-field terms’ that do not scale with the inverse survey area. Conclusions. Our covariance model is sufficiently accurate for analysing stage III surveys. Covariances for statistics in Fourier space cannot always be straightforwardly converted into covariance for real-space statistics.

GLASS: Generator for Large Scale Structure

We present GLASS, the Generator for Large Scale Structure, a new code for the simulation of galaxy surveys for cosmology, which iteratively builds a light cone with matter, galaxies, and weak gravitational lensing signals as a sequence of nested shells. This allows us to create deep and realistic simulations of galaxy surveys at high angular resolution on standard computer hardware and with low resource consumption. GLASS also introduces a new technique to generate transformations of Gaussian random fields (including lognormal) to essentially arbitrary precision, an iterative line-of-sight integration over matter shells to obtain weak lensing fields, and flexible modelling of the galaxies sector. We demonstrate that GLASS readily produces simulated data sets with per cent-level accurate two-point statistics of galaxy clustering and weak lensing, thus enabling simulation-based validation and inference that is limited only by our current knowledge of the input matter and galaxy properties. The code described in this paper is available <a href="https://github.com/glass-dev/glass">here</a>.

GLASS: Generator for Large Scale Structure

We present GLASS, the Generator for Large Scale Structure, a new code for the simulation of galaxy surveys for cosmology, which iteratively builds a light cone with matter, galaxies, and weak gravitational lensing signals as a sequence of nested shells. This allows us to create deep and realistic simulations of galaxy surveys at high angular resolution on standard computer hardware and with low resource consumption. GLASS also introduces a new technique to generate transformations of Gaussian random fields (including lognormal) to essentially arbitrary precision, an iterative line-of-sight integration over matter shells to obtain weak lensing fields, and flexible modelling of the galaxies sector. We demonstrate that GLASS readily produces simulated data sets with per cent-level accurate two-point statistics of galaxy clustering and weak lensing, thus enabling simulation-based validation and inference that is limited only by our current knowledge of the input matter and galaxy properties.

On weak lensing response functions

We introduce the response function approach to model the weak lensing statistics in the context of separate universe formalism. Numerical results for the RFs are presented for various semi-analytical models that includes perturbative modelling and variants of halo models. These results extend the recent studies of the Integrated Bispectrum and Trispectrum to arbitrary order. We find that due to the line-of-sight projection effects, the expressions for RFs are not identical to the squeezed correlation functions of the same order. We compute the RFs in three-dimensions using the spherical Fourier-Bessel formalism which provides a natural framework for incorporating photometric redshifts, and relate these expressions to tomographic and projected statistics. We generalise the concept of k-cut power spectrum to k-cut response functions. In addition to response functions, we also define their counterparts in real space, since they are easier to estimate from surveys with low sky-coverage and non-trivial survey boundaries.

Dark Energy Survey Year 3 results: Cosmology from combined galaxy clustering and lensing validation on cosmological simulations

We present a validation of the Dark Energy Survey Year 3 (DES Y3) $3\times2$-point analysis choices by testing them on Buzzard v2.0, a new suite of cosmological simulations that is tailored for the testing and validation of combined galaxy clustering and weak lensing analyses. We show that the Buzzard v2.0 simulations accurately reproduce many important aspects of the DES Y3 data, including photometric redshift and magnitude distributions, and the relevant set of two-point clustering and weak lensing statistics. We then show that our model for the $3\times2$-point data vector is accurate enough to recover the true cosmology in simulated surveys assuming the true redshift distributions for our source and lens samples, demonstrating robustness to uncertainties in the modeling of the non-linear matter power spectrum, non-linear galaxy bias and higher-order lensing corrections. Additionally, we demonstrate for the first time that our photometric redshift calibration methodology, including information from photometry, spectroscopy, clustering cross-correlations, and galaxy-galaxy lensing ratios, is accurate enough to recover the true cosmology in simulated surveys in the presence of realistic photometric redshift uncertainties.

ADDGALS: Simulated Sky Catalogs for Wide Field Galaxy Surveys

We present a method for creating simulated galaxy catalogs with realistic galaxy luminosities, broadband colors, and projected clustering over large cosmic volumes. The technique, denoted Addgals (Adding Density Dependent GAlaxies to Lightcone Simulations), uses an empirical approach to place galaxies within lightcone outputs of cosmological simulations. It can be applied to significantly lower-resolution simulations than those required for commonly used methods such as halo occupation distributions, subhalo abundance matching, and semi-analytic models, while still accurately reproducing projected galaxy clustering statistics down to scales of r ∼ 100 h −1kpc . We show that Addgals catalogs reproduce several statistical properties of the galaxy distribution as measured by the Sloan Digital Sky Survey (SDSS) main galaxy sample, including galaxy number densities, observed magnitude and color distributions, as well as luminosity- and color-dependent clustering. We also compare to cluster–galaxy cross correlations, where we find significant discrepancies with measurements from SDSS that are likely linked to artificial subhalo disruption in the simulations. Applications of this model to simulations of deep wide-area photometric surveys, including modeling weak-lensing statistics, photometric redshifts, and galaxy cluster finding, are presented in DeRose et al., and an application to a full cosmology analysis of Dark Energy Survey (DES) Year 3 like data is presented in DeRose et al. We plan to publicly release a 10,313 square degree catalog constructed using Addgals with magnitudes appropriate for several existing and planned surveys, including SDSS, DES, VISTA, Wide-field Infrared Survey Explorer, and Rubin Observatory’s Legacy Survey of Space and Time.

Euclid: Constraining ensemble photometric redshift distributions with stacked spectroscopy

Context. The ESA Euclid mission will produce photometric galaxy samples over 15 000 square degrees of the sky that will be rich for clustering and weak lensing statistics. The accuracy of the cosmological constraints derived from these measurements will depend on the knowledge of the underlying redshift distributions based on photometric redshift calibrations. Aims. A new approach is proposed to use the stacked spectra from Euclid slitless spectroscopy to augment broad-band photometric information to constrain the redshift distribution with spectral energy distribution fitting. The high spectral resolution available in the stacked spectra complements the photometry and helps to break the colour-redshift degeneracy and constrain the redshift distribution of galaxy samples. Methods. We modelled the stacked spectra as a linear mixture of spectral templates. The mixture may be inverted to infer the underlying redshift distribution using constrained regression algorithms. We demonstrate the method on simulated Vera C. Rubin Observatory and Euclid mock survey data sets based on the Euclid Flagship mock galaxy catalogue. We assess the accuracy of the reconstruction by considering the inference of the baryon acoustic scale from angular two-point correlation function measurements. Results. We selected mock photometric galaxy samples at redshift z &gt; 1 using the self-organising map algorithm. Considering the idealised case without dust attenuation, we find that the redshift distributions of these samples can be recovered with 0.5% accuracy on the baryon acoustic scale. The estimates are not significantly degraded by the spectroscopic measurement noise due to the large sample size. However, the error degrades to 2% when the dust attenuation model is left free. We find that the colour degeneracies introduced by attenuation limit the accuracy considering the wavelength coverage of Euclid near-infrared spectroscopy.

Cosmic shear beyond 2-point statistics: Accounting for galaxy intrinsic alignment with projected tidal fields

ABSTRACT Developing analysis pipelines based on statistics beyond two-point functions is critical for extracting a maximal amount of cosmological information from current and upcoming weak lensing surveys. In this paper, we study the impact of the intrinsic alignment of galaxies (IA) on three promising probes measured from aperture mass maps – the lensing peaks, minima, and full PDF. Our 2D IA infusion method converts the light-cone-projected mass sheets into projected tidal tensors, which are then linearly coupled to an intrinsic ellipticity component with a strength controlled by the coupling parameter AIA. We validate our method with the γ-2PCFs statistics, recovering well the linear alignment model of Bridle &amp; King in a full tomographic setting, and for different AIA values. We next use our method to infuse at the galaxy catalogue level a non-linear IA model that includes the density-weighting term introduced in Blazek et al., and compute the impact on the three aperture mass map statistics. We find that large $\mathcal {S}/\mathcal {N}$ peaks are maximally affected, with deviations reaching 30 per cent (10 per cent) for a Euclid-like (KiDS-like) survey. Modelling the signal in a wCDM cosmology universe with N-body simulations, we forecast the cosmological bias caused by unmodelled IA for 100 deg2 of Euclid-like data, finding very large offsets in w0 (5-10σstat), Ωm (4-6σstat), and $S_8 \equiv \sigma _8\sqrt{\Omega _{\rm m}/0.3}$ (∼3σstat). The method presented in this paper offers a compelling avenue to account for IA in beyond-two-point weak lensing statistics, with a flexibility comparable to that of current γ-2PCFs IA analytical models.

The density distributions of cosmic structures: impact of the local environment on weak-lensing convergence

ABSTRACT Whilst the underlying assumption of the Friedman-Lemaître-Robertson-Walker (FLRW) cosmological model is that matter is homogeneously distributed throughout the universe, gravitational influences over the life of the universe have resulted in mass clustered on a range of scales. Hence we expect that, in our inhomogeneous Universe, the view of an observer will be influenced by the location and local environment. Here, we analyse the one-point probability distribution functions and angular power spectra of weak-lensing (WL) convergence and magnification numerically to investigate the influence of our local environment on WL statistics in relativistic N-body simulations. To achieve this, we numerically solve the null geodesic equations which describe the propagation of light bundles backwards in time from today, and develop a ray-tracing algorithm, and from these calculate various WL properties. Our findings demonstrate how cosmological observations of large-scale structure through WL can be impacted by the locality of the observer. We also calculate the constraints on the cosmological parameters as a function of redshift from the theoretical and numerical study of the angular power spectrum of WL convergence. This study concludes the minimal redshift for the constraint on the parameter Ωm (H0) is $z$ ∼ 0.2 ($z$ ∼ 0.6) beyond which the local environment’s effect is negligible and the data from WL surveys are more meaningful above that redshift. The outcomes of this study will have direct consequences for future surveys, where per cent-level-precision is necessary.

Constraining cosmology with weak lensing voids

Abstract Upcoming surveys such as lsst and euclid will significantly improve the power of weak lensing as a cosmological probe. To maximise the information that can be extracted from these surveys, it is important to explore novel statistics that complement standard weak lensing statistics such as the shear-shear correlation function and peak counts. In this work, we use a recently proposed weak lensing observable — weak lensing voids — to make parameter constraint forecasts for an $\rm \small {LSST}$-like survey. We use the cosmo-SLICS wCDM simulation suite to measure void statistics as a function of cosmological parameters. The simulation data is used to train a Gaussian process regression emulator that we use to generate likelihood contours and provide parameter constraints from mock observations. We find that the void abundance is more constraining than the tangential shear profiles, though the combination of the two gives additional constraining power. We forecast that without tomographic decomposition, these void statistics can constrain the matter fluctuation amplitude, S8 within 0.3 per cent (68 per cent confidence interval), while offering 1.5, 1.5 and 2.7 per cent precision on the matter density parameter, Ωm, the reduced Hubble constant, h, and the dark energy equation of state parameter, w0, respectively. These results are tighter than the constraints from the shear-shear correlation function with the same observational specifications for Ωm, S8 and w0. The constraints from the WL voids also have complementary parameter degeneracy directions to the shear 2PCF for all combinations of parameters that include h, making weak lensing void statistics a promising cosmological probe.

The impact of baryons on cosmological inference from weak lensing statistics

ABSTRACT As weak lensing surveys are becoming deeper and cover larger areas, information will be available on small angular scales down to the arcmin level. To extract this extra information, accurate modelling of baryonic effects is necessary. In this work, we adopt a baryonic correction model, which includes gas both bound inside and ejected from dark matter (DM) haloes, a central galaxy, and changes in the DM profile induced by baryons. We use this model to incorporate baryons into a large suite of DM-only N-body simulations, covering a grid of 75 cosmologies in the Ωm–σ8 parameter space. We investigate how baryons affect Gaussian and non-Gaussian weak lensing statistics and the cosmological parameter inferences from these statistics. Our results show that marginalizing over baryonic parameters degrades the constraints in Ωm–σ8 space by a factor of 2–5 compared to those with baryonic parameters fixed. We also find that combining the lensing power spectrum and peak counts can break the degeneracy between cosmological and baryonic parameters and mitigate the impact of the uncertainty in baryonic physics.

Interpreting deep learning models for weak lensing

Deep Neural Networks (DNNs) are powerful algorithms that have been proven capable of extracting non-Gaussian information from weak lensing (WL) data sets. Understanding which features in the data determine the output of these nested, non-linear algorithms is an important but challenging task. We analyze a DNN that has been found in previous work to accurately recover cosmological parameters in simulated maps of the WL convergence ($\kappa$). We derive constraints on the cosmological parameter pair $(\Omega_m,\sigma_8)$ from a combination of three commonly used WL statistics (power spectrum, lensing peaks, and Minkowski functionals), using ray-traced simulated $\kappa$ maps. We show that the network can improve the inferred parameter constraints relative to this combination by $20\%$ even in the presence of realistic levels of shape noise. We apply a series of well established saliency methods to interpret the DNN and find that the most relevant pixels are those with extreme $\kappa$ values. For noiseless maps, regions with negative $\kappa$ account for $86-69\%$ of the attribution of the DNN output, defined as the square of the saliency in input space. In the presence of shape nose, the attribution concentrates in high convergence regions, with $36-68\%$ of the attribution in regions with $\kappa > 3 \sigma_{\kappa}$.

Optimizing Simulation Parameters for Weak Lensing Analyses Involving Non-Gaussian Observables

Abstract We performed a series of numerical experiments to quantify the sensitivity of the predictions for weak lensing statistics obtained in ray-tracing dark matter (DM)-only simulations, to two hyper-parameters that influence the accuracy as well as the computational cost of the predictions: the thickness of the lens planes used to build past light cones and the mass resolution of the underlying DM simulation. The statistics considered are the power spectrum (PS) and a series of non-Gaussian observables, including the one-point probability density function, lensing peaks, and Minkowski functionals. Counterintuitively, we find that using thin lens planes (&lt; 60 h −1 Mpc on a 240 h −1 Mpc simulation box) suppresses the PS over a broad range of scales beyond what would be acceptable for a survey comparable to the Large Synoptic Survey Telescope (LSST). A mass resolution of 7.2 × 1011 h −1 M ⊙ per DM particle (or 2563 particles in a (240 h −1 Mpc)3 box) is sufficient to extract information using the PS and non-Gaussian statistics from weak lensing data at angular scales down to 1′ with LSST-like levels of shape noise.

Breaking degeneracies in modified gravity with higher (than 2nd) order weak-lensing statistics

General relativity (GR) has been well tested up to solar system scales, but it is much less certain that standard gravity remains an accurate description on the largest, that is cosmological, scales. Many extensions to GR have been studied that are not yet ruled out by the data, including by that of the recent direct gravitational wave detections. Degeneracies among the standard model (ΛCDM) and modified gravity (MG) models, as well as among different MG parameters, must be addressed in order to best exploit information from current and future surveys and to unveil the nature of dark energy. We propose various higher-order statistics in the weak-lensing signal as a new set of observables able to break degeneracies between massive neutrinos and MG parameters. We have tested our methodology on so-called f(R) models, which constitute a class of viable models that can explain the accelerated universal expansion by a modification of the fundamental gravitational interaction. We have explored a range of these models that still fit current observations at the background and linear level, and we show using numerical simulations that certain models which include massive neutrinos are able to mimic ΛCDM in terms of the 3D power spectrum of matter density fluctuations. We find that depending on the redshift and angular scale of observation, non-Gaussian information accessed by higher-order weak-lensing statistics can be used to break the degeneracy between f(R) models and ΛCDM. In particular, peak counts computed in aperture mass maps outperform third- and fourth-order moments.

Weak lensing light-cones in modified gravity simulations with and without massive neutrinos

We present a novel suite of cosmological N-body simulations called the DUSTGRAIN-pathfinder, implementing simultaneously the effects of an extension to General Relativity in the form of $f(R)$ gravity and of a non-negligible fraction of massive neutrinos. We describe the generation of simulated weak lensing and cluster counts observables within a past light-cone extracted from these simulations. The simulations have been performed by means of a combination of the MG-GADGET code and a particle-based implementation of massive neutrinos, while the light-cones have been generated using the MapSim pipeline allowing us to compute weak lensing maps through a ray-tracing algorithm for different values of the source plane redshift. The mock observables extracted from our simulations will be employed for a series of papers focussed on understanding and possibly breaking the well-known observational degeneracy between $f(R)$ gravity and massive neutrinos, i.e. the fact that some specific combinations of the characteristic parameters for these two phenomena (the $f_{R0}$ scalar amplitude and the total neutrino mass $\Sigma m_{\nu}$) may result indistinguishable from the standard $\mathrm{\Lambda CDM}$ cosmology through several standard observational probes. In particular, in the present work we show how a tomographic approach to weak lensing statistics could allow - especially for the next generation of wide-field surveys - to disentangle some of the models that appear statistically indistinguishable through standard single-redshift weak lensing probe.