How to Weigh the Invisible: Redshift Tomography of Unresolved Galaxies from Euclid and LSST Data ✛ ✎
Context
Why does it matter? Precise knowledge of the redshift distribution of unresolved galaxies is key to extracting cosmological information from the cosmic optical background. Unlike the well-studied cosmic microwave background, the optical background contains the combined light of all stars and star formation processes over the history of the expansion of the universe. This makes it a potential window into the reionization epoch and a testbed for dark matter hypotheses. However, the bright foreground from interstellar dust (zodiacal light) long hindered observations. Now, thanks to space telescopes like Hubble and James Webb, along with ground-based surveys like LSST, we can finally study this background. It is here that the work of Nancy Grace Roman, a pioneer of space telescopes, gains new resonance.
Methods
How was it done? Researchers created realistic simulations of multi-band images combining data from the Euclid space mission and the LSST ground survey, using numerical simulations based on the Flagship catalog. They then applied a modern machine learning technique — conditional normalizing flows — to estimate redshift distributions from pixel values in multi-band photometry. The key idea: a neural network learns to transform a simple distribution into a complex target distribution, conditioned on the observed fluxes in ten filters. The model builds upon the Friedmann equations, describing the expansion of the universe, and Hubble's law, linking redshift to distance. We also note the contribution of Vera Rubin, whose observations of galaxy rotation indicated the existence of dark matter, which can be explored through background fluctuations.
Results
What did they find? The model achieved subpercent accuracy (error less than 1%) in determining the mean and standard deviation of the flux-weighted redshift distribution on an independent sample. Even when artificially removing 20% of the data or whole photometric bands, applying simple imputation strategies (replacing missing values with the mean or extrapolating) restored accuracy to the original level. When the noise level was systematically shifted by ±3σ, the network showed noticeable deviations in predicting the observable — the root-mean-square noise deviation — providing a built-in diagnostic indicator of model unreliability. This is especially important, as it's impossible to directly verify the correctness of redshift distributions in real data. Tomographic analysis — dividing pixels into four redshift bins — demonstrated errors at the subpercent level in all bins, except for edge effects at low and high z. Thus, Edwin Hubble, who discovered the expansion of the universe, could have assessed the evolution of large-scale structure with such maps.
Implications
Significance for science: The results mean that unresolved galaxies, which make up the majority in the universe and are usually lost in deep surveys, can now be used as full-fledged cosmological tracers. This opens a new observational window, complementing traditional catalogs of individual galaxies. It becomes possible to study the reionization era, the distribution of dark matter, and to test models of star formation through the statistics of spatial fluctuations in the optical background. The proposed approach, which includes observable diagnostic quantities in the target variables, sets a new standard for uncertainty quantification in machine learning-based problems in astrophysics.
Future development
Future developments: In the future, one could train ensembles of models on various cosmological simulations (hydrodynamic, semi-analytic) to estimate systematic errors. Accounting for additional astrophysical backgrounds — from Galactic cirrus to intracluster light — would bring the method closer to real data. Increasing map resolution (pixels with fewer galaxies) will test the method's limits and provide access to small scales. Integration with radio observations and cross-correlations with catalogs of resolved galaxies promise breakthroughs in understanding the early epoch of star formation and the nature of dark matter.
Impact
Will impact observational cosmology, extragalactic astrophysics, data analysis from major surveys (Euclid, LSST, Roman Space Telescope), as well as the development of machine learning methods in astronomy.
Next steps
Next steps include validation on real Euclid Q1 data, developing methods for background subtraction, and calibration on hydrodynamic simulations with more complete treatment of the interstellar medium.
Key open problems
Connection to unsolved problems: The method directly relates to the nature of dark matter (axions, dark photons) through their hypothetical glow in the optical band, as well as the problem of missing light in the ultraviolet and infrared backgrounds. Refining redshift distributions for unresolved galaxies will help alleviate tensions in measurements of the cosmic star formation rate and better understand the expansion of the universe.
The knowledge machine's view
This section is addressed to the author of the paper and their colleagues. Neighbouring works were found by meaning-based search across our archive, not by word overlap. We do not review: we show the field around the work.
What the work does
The paper introduces a method for estimating the redshift distribution of unresolved galaxies from multi-band photometry using conditional normalizing flows. The model is trained on simulated Euclid and LSST data, achieves sub-percent accuracy, is robust to missing data, and includes a built-in diagnostic indicator for noise shifts.
Where its strength is
The main strength is the combination of realistic simulations and a modern probabilistic approach that not only provides accurate predictions but can also flag its own unreliability under systematic shifts. This paves the way for reliable tomographic analysis of the cosmic optical background without direct redshift measurements.
Where it could go next
- It might be interesting to see how a similar approach to extracting faint signals at the resolution limit is applied to finding rare objects in deep surveys. In our archive, there is a nearby work where an unsupervised neural network finds new galaxies by anomalies in the data—this could suggest strategies for detecting unusual source populations in the optical background.based on: Neural Network Discovers New Galaxies Without Any Guidance arXiv:2511.05439
- Since your method relies on multi-band photometry, it may be useful to look at experience in separating populations with similar colors in crowded fields. We have a review where spectral deconvolution methods were used to identify 'red dots' without clear color boundaries—this might enhance tomographic separation at the edges of redshift ranges.based on: Archipelago in the Ocean of Data: Red Points Without Color Boundaries arXiv:2607.22835v1
- An interesting development could be adapting the method to estimate dark matter contributions through background fluctuations. Nearby, there is a work where a neural network learns to see dark matter from image distortions—combining it with your approach could provide an independent check of the link between redshift distributions and large-scale structure.based on: Neural Network Learns to See Dark Matter arXiv:2603.14503
Worth trying
- Test the model on real data with known redshifts (e.g., fields with deep spectroscopy) to calibrate the noise diagnostic indicator.
- Apply spectral deconvolution techniques to improve tomography at redshift boundaries where the model currently shows edge effects.
- Combine redshift distribution predictions with dark matter maps from weak lensing for cross-validation.
Why this may matter
If the method proves accurate on real data, it could become a key tool for extracting cosmological information from the optical background, potentially opening a window into the epoch of reionization and allowing tests of dark matter hypotheses without resolving individual galaxies.
Nearby works in our archive
- How to See the Invisible Web of the Cosmossimilarity 0.67
- A Dark Matter Map Without a Safety Netsimilarity 0.64
- Neural Network Discovers New Galaxies Without Any Guidancesimilarity 0.63
- How to Weigh the Universe with Color-Coded Tagssimilarity 0.63
- Neural Network Learns to See Dark Mattersimilarity 0.63
- How to Weigh the Universe Without a Scalesimilarity 0.63
- Archipelago in the Ocean of Data: Red Points Without Color Boundariessimilarity 0.62
The closest work in the archive sits at 0.67 by meaning — the usual level for our corpus.
Although the Hubble Telescope can see galaxies down to 30th magnitude, about 90% of galaxies in the universe remain unresolved even for it. Their combined light forms a faint diffuse background that carries information about the very first stars.
The idea of reading the cosmic background echoes Isaac Asimov's novel 'The End of Eternity,' where observers analyze 'temporal radiation' to understand time structures. Here, astrophysicists analyze the 'optical noise' of the universe to reconstruct its history.
Key numbers
- mean redshift accuracy: 0.15%
- average unresolved galaxies per pixel: 130
- depth in VIS filter: 25.7 mag
- training area: 100 sq. degrees
- map resolution (HEALPix Nside=4096): 0.86 arcminutes