Main

Despite its established role in the Standard Cosmological Model (ΛCDM), the microscopic nature of dark matter (DM) remains unknown. It is assumed to be cold—that is, non-relativistic at decoupling—and to interact, at most, very weakly with baryonic matter1,2,3. Cosmology offers a powerful tool for probing the nature of DM, especially in the context of neutrino–DM interactions (νDM). Both the astrophysical and terrestrial searches for νDM interactions pose a challenge. These interactions can only be indirectly constrained by studying small deviations in neutrino properties from the Standard Model predictions due to new physics4, or by searching for an excess in the astrophysical neutrino flux caused by DM annihilations in the Galactic centre5.

Instead, in the early Universe, neutrinos contributed substantially to the radiation components, with a number density much higher than that of baryons. The νDM interactions induce diffusion-damped dark acoustic oscillations (DAO) in the matter power spectrum6,7. Therefore, such sizable couplings lead to deviations from the ΛCDM model, affecting the cosmic microwave background (CMB) radiation and large-scale structure (LSS) of the Universe. Consequently, cosmological observations are highly sensitive to νDM interactions6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32.

Interestingly, recent analyses of CMB data have revealed a preference for non-zero νDM couplings, specifically in the high-multipole regime22,23,27, which is consistent with earlier findings in the Lyman-α flux power spectrum20. To further explore these interactions, we test νDM scenario predictions by incorporating weak lensing (WL) data, a low-redshift observation (z < 3.5), as a supplement to the high-redshift CMB data. Because the relative impact of νDM interactions grows at small scales, where nonlinear effects in structure formation become significant, we extend previous analyses by going beyond the linear evolution and including results of N-body simulations obtained on the basis of input matter power spectra modified in the presence of νDM interactions. To make such an analysis feasible, we follow a flexible approach introduced in ref. 33, which allows for the convenient reuse of results from previous simulations across various DAO scenarios and global parameter scans.

WL data are crucial for constraining cosmological parameters, especially for the S8 amplitude defined as \({S}_{8}={\sigma }_{8}\sqrt{{\varOmega }_{\rm{m}}/0.3}\) (ref. 34), where σ8 is the mass dispersion on a scale around 8h−1 Mpc and Ωm is the total matter abundance. In the standard ΛCDM framework, the S8 value derived from Planck CMB data is larger than the low-redshift measurements from WL surveys, leading to a 2–3σ tension35,36,37. In this work, we revisit this open question within the framework of the νDM model. By fitting the current 3-year Dark Energy Survey (DES) cosmic shear data alone35, we identify a preferred region for non-zero νDM interaction strength. Intriguingly, this preferred region is consistent with that favoured by Atacama Cosmology Telescope (ACT) data. When combining all early- and late-Universe observational data, we find a nearly 3σ detection of the non-zero νDM interactions. We show that, for the preferred value of the νDM interaction strength, both the CMB and WL data lead to consistent fits of the S8 parameter, therefore alleviating the persisting discrepancy.

To further explore the potential of next-generation observations, we generate mock cosmic shear data for upcoming surveys, including the Vera C. Rubin Observatory (formerly known as the Large Synoptic Survey Telescope, LSST)38 and the China Space Station Telescope (CSST)39. Our results demonstrate that, with the improved sensitivity of these future surveys, the favoured interaction region will be either robustly confirmed or excluded.

The Article is organized as follows. In the Modelling νDM interactions section, we briefly discuss how νDM interactions are modelled in our study. The Results section is devoted to presenting the results of our study, and we conclude in the Discussion section. The Methods section discusses the implementation of the cosmological datasets in the analysis. Supplementary Information analyses the expected impact of νDM scatterings on the matter power spectrum beyond our main assumptions and presents our treatment of the WL data.

Modelling νDM interactions

In the linear regime of perturbation growth, the shape of the matter power spectrum is determined by solving the Boltzmann equation, which describes the phase-space evolution of the distribution function for various Standard Model species and DM, along with the coupled Einstein and fluid equations40,41. In the presence of νDM interactions, additional terms appear in the Boltzmann hierarchy, altering the evolution of perturbations. These interaction terms modify the energy transfer and momentum exchange between DM and neutrinos, leading to distinct imprints on the CMB anisotropies and the matter power spectrum, as detailed in refs. 11,42,43,44. The corresponding equations are readily solved for cold (non-relativistic) DM species after integrating over momentum. In particular, the equations describing the evolution of the density fluctuations δχ and the divergence of fluid velocity θχ are given by

$${\dot{\delta }}_{\chi }=-{\theta }_{\chi }+3\,\dot{\phi },$$
(1)
$${\dot{\theta }}_{\chi }={k}^{2}\psi -{\mathscr{H}}{\theta }_{\chi }-{K}_{\chi }\,{\dot{\mu }}_{\chi }\,({\theta }_{\chi }-{\theta }_{\nu }),$$
(2)

where ϕ and ψ are scalar potentials appearing in the line element of the perturbed flat Friedmann–Lemaître–Robertson–Walker Universe, and \({\mathscr{H}}=\dot{a}/a\) is the Hubble rate. We define Kχ = (1 + wν) ρν/ρχ, where ρχ and ρν are the DM and neutrino energy densities, respectively, and wν is the neutrino equation of state parameter. For massless neutrinos, one finds wν = 1/3 and Kχ = (4/3)ρν/ρχ. From equation (2), the evolution of θχ is modified in the presence of the νDM interaction term, which is proportional to \({\dot{\mu }}_{\chi }\). In the massless neutrino case, this is given by \({\dot{\mu }}_{\chi }=a\,{n}_{\chi }{\sigma }_{\nu {\rm{DM}}}\), where the cold DM number density is nχ = ρχ/mχ, the νDM scattering cross-section is denoted by σνDM, and mχ is the DM particle mass. Therefore, \({K}_{\chi }{\dot{\mu }}_{\chi }\) depends on the cross-section and the inverse of the DM mass. This dependence is commonly parameterized by the dimensionless quantity11

$${u}_{\nu {\rm{DM}}}=\frac{{\sigma }_{\nu {\rm{DM}}}}{{\sigma }_{\rm{T}}}{\left(\frac{{m}_{\chi }}{100\,{\rm{GeV}}}\right)}^{-1},$$
(3)

where σT is the Thomson scattering cross-section. The general expression for \({\dot{\mu }}_{\chi }\) is more complex for massive neutrinos, but the impact of the νDM interactions on perturbation evolution can still be effectively described by uνDM in the cold DM regime. In this work, we consider the most thoroughly studied scenario, in which the neutrinos are massless, and the νDM interaction cross-section is independent of temperature. We refer to Supplementary Information for a discussion beyond this approximation and to the Methods section for details of our cosmological data analysis.

Results

Possible evidence of non-zero νDM interaction strength

As mentioned above, hints of non-negligible νDM interaction strength have been found in high-multipole ACT22,23,27 and Lyman-α20 data. For the purpose of this study, we have re-examined the CMB analysis including data from the Planck and ACT collaborations, and baryon acoustic oscillation (BAO) data (Planck+BAO+ACT likelihoods), by using the flat priors, shown in Supplementary Table 1. The relevant one-dimensional posterior distribution for uνDM is shown as a solid black line in Fig. 1. We observe a preference for non-zero uνDM within the 68% credible region, consistent with previous findings, which is driven by the high-ℓACT data. We note that our results for uνDM are slightly shifted to higher values compared with previous works27, as we used the full Plik likelihood with a cut at \({\ell }_{\max }=650\) rather than the lite version. The preferred parameter regions are reported in Table 1, with a central value of \({\log }_{10}\,{u}_{\nu {\rm{DM}}}\approx -4.24\).

Fig. 1: Posterior distributions of the DM–neutrino interaction parameter uνDM.
figure 1

The dash-dotted red (dotted blue) line represents the results obtained using the Planck+BAO+ACT (DES Y3 cosmic shear) likelihood. The combined results for the likelihood Planck+BAO+ACT+DES Y3 cosmic shear are presented as a solid green line.

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Table 1 The 68% credible intervals for the cosmological parameters
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We now examine this anomaly using cosmic shear data. The posterior distribution obtained when fitting the DES Y3 cosmic shear likelihood only is shown with the dotted blue line in Fig. 1. In this case, we also find a mild preference towards non-zero uνDM, albeit with a lower statistical significance (<1σ). We discuss details of our cosmic shear analysis in the ‘Weak lensing’ section in Methods and further illustrate it in Supplementary Figs. 2 and 3. To test the interplay between the different datasets with regard to this anomaly, we next incorporate a combination of both early- and late-Universe observational data, Planck+BAO+ACT+DES Y3 cosmic shear. By using the combined dataset, we find robust evidence for a non-zero νDM interaction strength at nearly 3σ significance, with uνDM ≈ 10−4. This strengthens the preference found in the Planck+BAO+ACT and DES Y3 cosmic shear data. The corresponding posterior distribution for uνDM is shown with the solid green line in Fig. 1, and the relevant parameter ranges are given in Table 1. The relevant χ2 values and triangle posterior distributions of the model parameters are presented in Supplementary Table 2 and Supplementary Fig. 4.

For a complementary perspective, the right panel of Fig. 2 also shows the Δχ2 curves obtained from each case using the profile likelihood method. This demonstrates the robustness of the preferred parameter region under different statistical approaches. A detailed breakdown of the χ2 values for each component is provided in Supplementary Table 1.

Fig. 2: Profile likelihood distribution and marginalized 2D posterior distribution in the (S8, uνDM) plane.
figure 2

Left: marginalized 2D posterior distribution in the (S8, uνDM) plane. The red and blue contours show the results for the Planck+BAO+ACT and DES Y3 cosmic shear datasets, respectively. The green region represents the results for the combined Planck+BAO+ACT+DES Y3 cosmic shear dataset. Right: the Δχ2 with the parameter uνDM obtained using the profile likelihood method from the analysis of Planck+BAO+ACT, DES Y3 cosmic shear and combined datasets.

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This result suggests that the νDM interaction with uνDM ≈ 10−4 is consistently supported by both CMB and WL cosmological data, despite these being independent observational probes spanning different epochs in cosmic history. This convergence highlights the potential of νDM interactions as a compelling extension beyond the standard ΛCDM paradigm, offering new insights into the fundamental nature of DM and its role in cosmic evolution.

It is important to note that interpreting the observed preference in terms of a constant uνDM parameter could face challenges from small-scale observations, such as the Lyman-α forest20, dwarf galaxy counts28 and galaxy luminosity functions45. We note, however, that these small-scale probes are subject to considerable astrophysical uncertainties, particularly those arising from baryonic feedback processes. Such effects can alter the interpretation of structure formation and may introduce non-negligible, model-dependent systematics into the derived constraints on νDM interactions.

More importantly, the cosmological observables used in our analysis—the CMB and cosmic shear—probe perturbations at different scales and epochs compared with those examined by the Lyman-α forest or galaxy luminosity functions. This apparent tension could be alleviated if the νDM interaction is not constant but instead varies with redshift, for example, through an energy-dependent scattering cross-section as motivated by specific particle physics models46. Therefore, the working assumption of a constant νDM cross-section applied in our study should be considered a useful and widely adopted phenomenological approximation. It allows us to capture the essential preferences in the considered datasets, while acknowledging that further investigations into specific νDM model implementations are warranted.

S 8 discrepancy

As mentioned in the main text, suppression of perturbations at scales probed by WL surveys has an important effect on the matter clustering parameter \({S}_{8}={\sigma }_{8}\,\sqrt{{\varOmega }_{\rm{m}}/0.3}\). It has been shown that the persisting tension between the CMB and WL estimates of this parameter, known as the S8 discrepancy (cf. refs. 47,48,49 for review), can be alleviated by νDM interactions15. We revisit this possibility by consistently including the entire Planck+BAO+ACT+DES Y3 cosmic shear dataset in the analysis.

The results of the marginalized two-dimensional (2D) posterior distribution in the (S8, uνDM) plane are presented in the left panel of Fig. 2. In the plot, we present the results obtained separately for Planck+BAO+ACT and DES Y3 cosmic shear data and the combined analysis. As can be seen, for small values of uνDM < 10−6, the impact of νDM interactions is negligible at perturbation scales characteristic to S8. In this case, the ΛCDM regime is effectively recovered for both the CMB and WL data, and the 2σ regions obtained for the early and late Universe datasets show no overlap. Hence, the S8 discrepancy persists, as expected.

However, for larger values of uνDM, the data are consistent with lower values of S8, leading to a better agreement between CMB and WL observations. When combining datasets (Planck+BAO+ACT+DES Y3 cosmic shear), we resolve the S8 tension, as shown with green-shaded regions in the plot. Remarkably, the value of the νDM interaction strength required for this, uνDM ≈ 10−4, corresponds to the previously reported 3σ evidence found in the combined dataset (cf. also Table 1).

Future prospects

The above results highlight the potential of νDM interactions to address persisting discrepancies in cosmological data that will be decisively studied in next-generation cosmological surveys. To investigate the relevant prospects of future WL observations, we additionally perform Markov Chain Monte Carlo (MCMC) scans, combining the mock data with the Planck+BAO+CSST and Planck+BAO+LSST likelihoods. The resulting likelihood profiles, shown in Fig. 3 (light-green and grey lines), indicate that these future WL surveys have the potential to constrain the νDM interaction parameter to \({\log }_{10}\,{u}_{\nu {\rm{DM}}}\lesssim -5.3\) (CSST) or even \({\log }_{10}\,{u}_{\nu {\rm{DM}}}\lesssim -5.9\) (LSST) at 95% confidence level, assuming the peak we observe is a spurious result and the true cosmology is ΛCDM, that is, DM is effectively not interacting with neutrinos at redshifts relevant to our analysis. As can be seen, a substantial improvement in sensitivity is expected from these next-generation WL surveys. In particular, the preferred parameter region obtained by fitting ACT and DES Y3 cosmic shear data, as indicated with an orange shading in the plot, will be either thoroughly confirmed or excluded by these surveys. When using mock data generated from a νDM interacting scenario, the 1σ error bar on \({\log }_{10}\,{u}_{\nu {\rm{DM}}}\) is reduced from ±0.55 (DES) to ±0.08 (CSST), demonstrating the promising discovery potential of upcoming WL surveys.

Fig. 3: Forecasted constraints on the DM–neutrino interaction strength from future WL surveys.
figure 3

Variation of Δχ2 with the parameter uνDM obtained using the profile likelihood method92. The brown line represents the Planck+BAO likelihood, while the light-green and grey lines additionally include mock cosmic shear data from CSST and LSST, respectively. The dashed black line indicates Δχ2 = 2.71, corresponding to the 2σ upper limit. The orange-shaded region indicates the 95% confidence level preferred range of the uνDM parameter found in the Planck+BAO+ACT+DES Y3 cosmic shear data.

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Discussion

Cosmological surveys and gravitational lensing observations provide compelling evidence for the existence of DM, but they may also offer critical insights into its fundamental nature. Probing possible interactions of DM with neutrinos remains particularly challenging in terrestrial searches (see refs. 50,51 for reviews), although this challenge can be mitigated by studying the impact of νDM scatterings on the matter power spectrum in the early Universe. Recent studies have uncovered a slight preference for non-negligible νDM interactions in high-multipole CMB data and Lyman-α forest observations.

In this study, we utilized WL surveys to investigate νDM interactions further. We computed the matter power spectrum incorporating nonlinear corrections from N-body simulations. These simulations evolve perturbations solely through gravity, as the νDM interactions are expected to decouple at early times and do not affect matter distributions at the scales probed in our study. We used an emulator that interpolates matter power spectra from predefined simulations to apply N-body results in cosmological parameter scans.

DES Y3 cosmic shear data alone, which are free from galaxy bias, reveal a preference for non-zero DM–neutrino interaction strength. This preference endures even when combining WL data with CMB and BAO datasets. We find that the Planck+BAO+ACT+DES Y3 cosmic shear data favour non-zero uνDM at nearly the 3σ level. This preferred interaction strength, uνDM ≈ 10−4, can also simultaneously alleviate the persistent S8 tension. The preference for non-zero uνDM in the data is additionally linked to a broadening of the Ωm distribution, as shown in Supplementary Fig. 4. While the νDM scenario permits a larger value for this parameter, the amount of structures does not increase proportionally. This leads to an overall improved cosmological fit.

Although the statistical significance of these anomalies is not yet sufficient to definitively rule out the standard cosmological scenario, the discrepancies across different observables and datasets underscore the importance of further investigation. Future high-precision WL surveys are expected to provide deeper insights into the mass distribution, particularly at small scales, enabling more stringent tests of νDM interactions—especially in parameter regions suggested by ACT and DES Y3 cosmic shear observations.

The suppression in the matter power spectrum favoured by our analysis could potentially arise in other well-motivated extensions of the ΛCDM model, beyond νDM interactions. These include DM interactions with baryons52, photons53 or dark radiation54, as well as models with warm DM55 or ultralight (fuzzy) DM56. While these models can produce qualitatively similar effects on the linear matter power spectrum, νDM interactions offer distinct advantages. First, this scenario is less constrained by CMB observations compared with DM interactions with other Standard Model species. Second, unlike warm DM or fuzzy DM—where the suppression scale is typically fixed by the DM particle mass—the νDM interaction can exhibit redshift dependence or affect only a fraction of the DM, providing greater flexibility to avoid small-scale bounds (cf. discussion in Supplementary Information). While νDM interactions offer a particularly compelling explanation for the observed deviations, which can also be independently tested in future terrestrial searches, other beyond-ΛCDM models predicting scale-dependent suppression of the power spectrum could provide alternative explanations that should likewise be tested (cf., for example, refs. 57,58). The standard cosmological model is under growing pressure, but new hints in cosmological data are driving us towards finding a valid extension.

Note added

After the submission of this Article, the KiDS-Legacy survey reported a higher value for the structure growth parameter, \({S}_{8}=0.81{5}_{-0.021}^{+0.016}\), which is in good agreement with the Planck ΛCDM prediction. As these data are not yet publicly available, we cannot assess their impact on our results. However, we stress that the preference we find in our data is not driven by the global S8 tension. Our constraints are primarily informed by cosmic shear measurements sensitive to both quasi-nonlinear scales around (k ≈ 1h Mpc−1) and the S8 more linear scales (for example, (k ≲ 0.7h Mpc−1)). We do expect that, if larger values of S8 are consistently favoured by the new data and other WL surveys in the future, then smaller—yet non-vanishing—values of uνDM might be preferred in the fit, in line with previous findings based on CMB data alone22,23,27 and Lyman-α observations20. A status review of this discrepancy can be found in ref. 59.

Methods

Cosmological data analysis

We use a modified version of the CLASS code to model the evolution of the Universe, specifically accounting for νDM interactions43,44. In our analysis, we vary uνDM. We also include the six ΛCDM parameters: the baryon Ωb and DM ΩDM energy densities (assuming all of DM interacts with neutrinos), the amplitude As and spectral index ns of primordial scalar perturbations, the optical depth to reionization τreio, and the angular size of the horizon at the last scattering surface θ. The prior ranges of each parameters are presented in Supplementary Table 1. We have verified that using a flat linear prior on the parameter uνDM does not alter our main conclusions. The effective number of relativistic degrees of freedom is fixed to ΔNeff = 3.044. The following cosmological data are included in the likelihood:

  1. (1)

    The DES 3-year cosmic shear likelihood35. We build an emulator to model the nonlinear correction to the matter power spectrum, calibrated on 200 N-body simulations generated with DAO-modified initial conditions.The linear matter power spectrum is first computed using the modified CLASS code, and the emulator is then used to obtain its nonlinear counterpart (cf. ref. 33 for further details). The resulting nonlinear power spectrum is used to predict the cosmic shear signal for a given intrinsic-alignment model (see ‘Weak lensing’ section for more details). We refer to this dataset as DES Y3 cosmic shear throughout this work. We account for nonlinear effects of the gravitational potential on the matter power spectrum at small scales, k ≳ 1h Mpc−1 using N-body simulations. Notably, on top of the cosmic shear data, the DES Y3 dataset contains galaxy clustering and galaxy–galaxy lensing data. These are, however, subject to unknown galaxy bias, which describes the bias arising from using galaxies as tracers of matter36,60. In this Article, we focus on the most robust conclusions based solely on cosmic shear. Further details on the analysis of the DES Y3 dataset and the implementation of nonlinear effects in the matter power spectrum are given in the ‘Weak lensing’ section.

  2. (2)

    The CMB likelihoods from Planck 2018 Legacy (P18)61, including high-ℓ power spectra (TT, TE and EE), low-ℓ power spectra (TT and EE) and the Planck lensing reconstruction. The official Planck likelihoods are used directly, and their implementation is interfaced through Montepython. We refer to this dataset as Planck.

  3. (3)

    We use the BOSS DR12 BAO likelihood, which combines distance measurements at z = 0.106, 0.15 and 0.2–0.75 (refs. 62,63,64), referred to as BAO. The likelihood is implemented following the public SDSS likelihood module, assuming Gaussian priors on the measured distance ratios.

    For comparison, we also included the new BAO likelihood incorporating the BOSS DR16 dataset65,66,67,68,69 in the data analysis. Including the updated BAO dataset yields nearly identical bounds on uνDM as those obtained with DR12, demonstrating the robustness of our results to this update.

  4. (4)

    The full ACT temperature and polarization DR4 likelihood70. We use HMCode71 for nonlinear correction to the matter power spectrum. We have verified that the angular power spectra obtained from HMCode are consistent with those from our emulator at percent level. We refer to this dataset as ACT. When combining the Planck and ACT datasets, we applied a conservative cut of ℓ < 650 on the Planck data to avoid double-counting in the overlapping multipole range. In this way, the combined dataset utilizes the large-scale information from Planck and the small-scale measurements from ACT. We have additionally confirmed with a sample scan that including the ACT CMB lensing DR6 likelihood72,73,74 does not alter our results. The ACT DR6 lensing data were cut at ℓ < 800 for this purpose.

  5. (5)

    To further investigate the potential of future WL observations, we utilize the expected sensitivity of the upcoming CSST and LSST cosmic shear surveys. Using the publicly available code CosmoCov75,76, we compute the covariance matrix to represent cosmic shear sensitivity, incorporating the CSST and LSST window functions. The fiducial model we used for these forecasts is the ΛCDM with Planck cosmological parameters.

Weak lensing

Weak gravitational lensing enables the direct mapping of the late-time LSS of the Universe by statistically analysing the shape distortions of numerous galaxies induced by foreground matter fields. The comprehensive set of WL measurements, known as 3 × 2pt, consists of three two-point correlation functions with angular separation θ of galaxy pairs: galaxy clustering w(θ) (position–position), galaxy–galaxy lensing γt(θ) (position–shape) and cosmic shear ξ±(θ) (shape–shape). The quantity w(θ) measures the angular clustering of foreground lens galaxies, while γt(θ) measures the correlation between the positions of foreground lens galaxies and the shape distortions of background source galaxies at an angular separation θ. Finally, ξ±(θ) measures cosmic shear, that is, the correlation between the shape distortions of background source galaxies due to the foreground LSS. Compared with the galaxy–galaxy lensing and galaxy clustering, the cosmic shear is independent of the galaxy bias, which describes the bias arising from using galaxies as tracers of matter36,60.

Therefore, the analyses based solely on cosmic shear data lead to the most robust conclusions that we present in the following. When analysing cosmic shear data, nonlinear effects of the gravitational potential play an important role in the evolution of LSS at small scales, k ≳ 1h Mpc−1. We account for these nonlinear effects using N-body simulations.

N-body simulation

As discussed above, νDM interactions primarily affect WL data through DAO, which modify the initial matter power spectrum used in N-body simulations. Following ref. 33 (cf. equations (3.1) and (3.2) therein), we use the modified Boltzmann code CLASS44 to compute the ratio of linear matter power spectra between ΛCDM and the νDM scenario. While this ratio depends on k, we effectively reduce its dimensionality to two parameters using principal component analysis77. This allows us to construct a two-parameter grid mapping linear to nonlinear matter power spectra, based on 205 N-body simulations run with the GIZMO code78,79. These simulations were initialized with different matter power spectra corresponding to the interacting DM model. For arbitrary values of uνDM, we map the corresponding linear power spectrum ratio onto this grid and deduce the nonlinear result through interpolation. Finally, we obtain the nonlinear matter power spectrum for the νDM scenario by multiplying this nonlinear ratio with the nonlinear ΛCDM power spectrum from Halofit80.

Although the original map of nonlinear power spectrum ratios in ref. 33 used DM–baryon interactions, a similar procedure applies to the νDM case. This is because the parameterization of the linear matter power spectrum ratios via principal component analysis is the same, and the N-body simulations evolve solely through gravity. To verify this, we performed an N-body simulation for the νDM scenario with \({\log }_{10}{u}_{\nu {\rm{DM}}}=-4.6\) and compared the resulting nonlinear matter power spectrum with that obtained from the emulator (that is, by interpolating on the grid). The comparison is shown in the left panel of Supplementary Fig. 2. This plot has been obtained by neglecting the impact of Halofit. We also present the uncertainty of the simulation in the plot. Because our simulations are performed within a finite comoving volume, the large-scale density fluctuations on scales comparable to or larger than the box size are dominated by the cosmic variance. The relative uncertainty scales approximately as \(\Delta P/P \sim 1/\sqrt{{N}_{\rm{modes}}}\approx 1/{L}_{\rm{box}}^{3/2}\), highlighting that a larger box volume is required to reduce this large-scale variance, where Nmodes is the number of independent Fourier modes available in a bin centred at wavenumber k and Lbox is the box size 200h−1 Mpc. The two results agree well, matching within nearly 15% uncertainty for k ≈ 1h Mpc−1.

We also show the uncertainty in ΔP(k) = PN-body(k) − Pem(k) in the right panel of Supplementary Fig. 2. These results were obtained for the best-fit point in our analysis and for a similar scenario with the same cosmological parameters, except for a lower νDM interaction strength of uνDM = 10−5. As can be seen, both results correspond to qualitatively distinct behaviours. This indicates a lack of systematic bias in the emulator results.

To quantify the impact of these differences, we computed the corresponding χ2 values using the DES Y3 cosmic shear likelihood. For the best-fit point, we found \({\chi }_{{\rm{emu}}}^{2}=240.6\) and \({\chi }_{N\text{-}\text{body}}^{2}=239.1\) for the most compatible N-body simulation result within the uncertainty bars. This difference of Δχ2 ≈ 1.5 is well within the statistical uncertainties of the dataset and smaller than the discrepancy introduced by using more approximate nonlinear tools, such as \({\chi }_{{\rm{HMCode}}}^{2}=399.8\) and \({\chi }_{{\rm{Halofit}}}^{2}=\text{8,246.6}\). Therefore, while the emulator does introduce a modelling uncertainty, it provides a substantially more accurate and reliable nonlinear correction compared with HMCode or Halofit, while maintaining the flexibility needed for MCMC scans.

We note, however, that a stronger bias might be introduced by using the Halofit nonlinear power spectrum (obtained on the basis of Gadget-2), when accounting for the impact of variations in other cosmological parameters, as discussed above and in ref. 33. In particular, for the specific points in the parameter space tested in Supplementary Fig. 2, we have found a systematic bias between GIZMO and Halofit results of order \({\mathscr{O}}(10 \% )\) for k ≈ 0.1–1h Mpc−1. This may impact the precise value of the best-fit point uνDM parameter obtained in the MCMC scan in our analysis, as it appears slightly sensitive to the choice of the baseline simulation results (the difference between \(\log {u}_{\nu {\rm{DM}}}=-3.7\) and −4.0 obtained in additional tests).

WL data

We use the current DES Y3 cosmic shear data in our analysis. This dataset contains the shapes of over 108 source galaxies across an effective area of 4,143 deg2. The shape catalogue METACALIBRATION used in the DES Y3 analysis is divided into four redshift bins in the redshift range of 0 < z < 3 (ref. 35). Following ref. 35, we mask small angular scales to reduce uncertainties from baryonic effects. We also utilize cosmic shear mock data from CSST and LSST for future forecasts. The redshift distributions for CSST and DES are different; thus, the CSST mask may not precisely reflect real conditions. However, the capabilities of the future telescope to detect distant galaxies make this mask a conservative estimate. For LSST, we present results with the masking scale set at \(l < {l}_{\max }=\text{3,000}\) following refs. 81,82.

Supplementary Fig. 3 shows the impact of νDM interactions on the cosmic shear signal. It illustrates the deviation in the expected cosmic shear signal (4th–4th bin) for two selected values of the νDM interaction strength, \({\log }_{10}({u}_{\nu {\rm{DM}}})=-4.6\) and −3.3, along with the DES Y3 data points. Nonlinear corrections are applied, as previously described. Stronger interactions lead to greater suppression of the matter power spectrum, which determines the shape of the blue and red curves. For comparison, the linear results are also shown with dotted lines. The nonlinear effects are significant, enhancing the signal at small angular scales. This effect is opposite to that of νDM interactions; the signal enhancement due to nonlinear effects is partially offset by increasing uνDM.

By treating neutrinos as massless in our analysis, we neglect the impact of their gravitational potential in the N-body simulations. We stress that, for a total neutrino mass ∑mν = 0.06 eV, the resulting suppression of the nonlinear matter power spectrum is expected to be less than 5% at k ≈ 1h Mpc−1 (ref. 83). This effect is smaller than the uncertainty introduced by our emulator.

It is worth noting that increasing the neutrino mass beyond this limit can impact the matter power spectrum, particularly at late times and on small scales, and could even affect the inferred value of S8 (ref. 84). Moreover, because ∑mν is negatively correlated with H0 (refs. 85,86), its inclusion could shift the preferred H0 value downwards, potentially exacerbating the H0 tension. However, because the cosmological upper bound on the neutrino mass is primarily driven by BAO data—and these constraints are becoming increasingly stringent68,87,88,89 (if not favouring a negative mass90,91)—we adopt a massless neutrino approximation for simplicity.

While our main results are derived from cosmic shear data, we also analysed the full DES Y3 3 × 2pt dataset for completeness. This analysis also indicates a preference for a non-vanishing uνDM, although the statistical significance is reduced from nearly 3σ to below 2σ. In this case, the peak of the posterior distribution for the neutrino interaction parameter is also shifted, favouring a lower interaction strength of \({\log }_{10}{u}_{\nu {\rm{DM}}}=-4.6{0}_{-3.17}^{+0.55}\). We attribute this discrepancy to the limitations of applying a ΛCDM-based galaxy bias model within our interacting dark sector scenario. Therefore, a more robust and model-compatible treatment of galaxy bias is necessary to draw stronger conclusions from the full 3 × 2pt dataset.