What can a global neutrino-telescope network measure for H0, Omega_m, and w by 2030?

The 2030 gain is precision, not a new central value

The paper asks how far a global high-energy neutrino network could push cosmology by 2030. Its answer is a forecast, not a detection: with full-sky IceCube exposure plus KM3NeT-ARCA and Baikal-GVD, the neutrino-measured Hubble constant H0 would keep its central value of 66 km s-1 Mpc-1 but shrink its uncertainty from +44/-37 to +15/-13 km s-1 Mpc-1, a reduction of nearly 65%. The same configuration would constrain the disk-corona slope beta to 0.72 ± 0.04.

That distinction matters. The present-day fit already gives H0 = 66 +44/-37 km s-1 Mpc-1 and beta = 0.72 +0.14/-0.16 from 26 Seyfert galaxies using IceCube's 14-year public data release. The 2030 numbers come from injecting Asimov data on today's best-fit relation (H0 = 66, beta = 0.72) and summing each detector's day-averaged up-going response weighted by its projected exposure. They describe achievable precision under stated assumptions, not a measured value.

A sub-linear slope turns Seyferts into standardizable candles

The method rests on a measured power law between neutrino and X-ray luminosity, L_nu proportional to L_X^beta. The expected signal count from a source scales as kappa times detector response times F_X^beta times d_L^(2(beta-1)). Because beta is about 0.72 rather than 1, the predicted count depends on luminosity distance, and therefore on H0, through that distance factor.

For low-redshift Seyferts, d_L is approximately cz/H0, so H0 enters only as an overall scale that is degenerate with the normalization kappa. The degeneracy is broken by anchors: sources whose distances are known independently of H0. The per-source sensitivity to H0 then scales as |1 - beta| and vanishes at the calorimetric point beta = 1. This is why the slope measurement and the Hubble measurement are coupled rather than separate results.

The present analysis uses 26 Seyferts: 12 northern sources from the earlier neutrino-H0 analysis and 14 southern sources selected from IceCube's muon-neutrino southern-sky search. Two anchors set the absolute scale, NGC 1068 at 10.72 ± 0.52 Mpc (Cepheid) and NGC 4945 at 3.6 ± 0.2 Mpc (tip of the red giant branch). Inference uses per-source two-dimensional likelihood surfaces in signal count and spectral index, profiling over the spectral index.

Northern detectors switch on the southern Seyferts

IceCube sees the southern sky above the horizon, where atmospheric muons bury the signal. KM3NeT-ARCA in the Mediterranean and Baikal-GVD at Lake Baikal see that same sky below the horizon, so sources arrive as up-going neutrinos through the Earth, a direction where atmospheric muon background is suppressed. The paper maps IceCube's measured effective area through each detector's real horizon and scales by integrated exposure and a per-unit-exposure track efficiency.

That efficiency is not assumed equal. ARCA is taken as identical to IceCube per unit volume (eta = 1), but Baikal-GVD is treated conservatively at eta = 0.2 because it is a sparse array of optically independent clusters whose tracks are reconstructed within a single small cluster. The value comes from converting published per-cluster effective volumes to effective areas and comparing them with IceCube's, a ratio rising from about 0.1 at TeV energies to about 0.3 near a PeV.

With projected 2030 exposures of 20 km3 yr for IceCube, 2.3 for ARCA and 7.4 for Baikal-GVD, the bright southern sources switch on. NGC 4945 reaches a per-source signal-to-noise of about 20, Centaurus A, Circinus and ESO 138-1 reach 7 to 12 (up from 0.1 or less today), and NGC 5643 and NGC 7582 reach about 4 to 5. The remaining eight southern Seyferts stay at or below about 2 sigma even in 2030. The network's leading effect is to activate the southern sky and tighten beta; its effect on H0 is indirect, mediated by the anchors it brings online.

Anchor X-ray errors pass straight into H0

Because anchors break the kappa-H0 degeneracy, an error on an anchor's X-ray flux passes directly into H0. The sources that matter most are the three heavily Compton-thick anchors, NGC 1068, NGC 4945 and NGC 5643, whose fluxes are hardest to model. The paper's blanket assumption of 0.25 fractional X-ray flux uncertainty is described as already optimistic for these three, and the proposed campaign aims to bring them to 0.15.

The forecast promotes three more sources to anchors for a total of five: NGC 5643 at 13.4 ± 0.5 Mpc, NGC 4151 at 15.8 ± 0.4 Mpc and NGC 7469 at 58.2 ± 1.9 Mpc. They are promoted under the Asimov assumption that they lie on the L_nu-L_X relation, so added exposure makes them informative. Only redshift-independent distances are used, avoiding flow-field catalog values so the anchor set does not import an assumed H0. Centaurus A is excluded as an anchor despite its precise distance because its prominent radio jet means its neutrino emission need not trace the disk-corona relation.

The X-ray program is deliberately small. About 100 ks of NuSTAR with simultaneous XMM coverage on NGC 5643 would cut its statistical error by roughly a third; its first 42 ks of NuSTAR data give intrinsic luminosities of 0.8 to 1.7 x 10^42 erg s-1, a spread of about 30% driven mainly by slab versus torus reflection geometry. The other anchors need reanalysis rather than new data, and roughly 300 ks of targeted hard-X-ray time plus archival reanalysis captures most of the available improvement.

Beta = 1 becomes a 5-sigma testable threshold

The slope forecast is the paper's sharpest falsifiable claim. Current data give beta = 0.72 +0.14/-0.16; the 2030 configuration is projected to reach beta = 0.72 ± 0.04, which the authors say enables a 5 sigma or greater exclusion of the calorimetric value beta = 1. In the calorimetric limit the predicted count would be distance-independent, and the H0 sensitivity, which scales as |1 - beta|, would vanish.

This makes beta more than a nuisance parameter. A confirmed sub-linear slope is what keeps the ladder sensitive to distance at all, so the same data that sharpen beta also protect the H0 measurement's mechanism. The forecast assumes the southern Seyferts, which IceCube resolves mostly as down-going upper limits, follow the same relation once KM3NeT-ARCA and Baikal-GVD observe them as up-going tracks.

Little red dots could add Omega_m and w, with weaker w

The Omega_m and w result is conditional in a different way from the H0 forecast. It requires a high-redshift population of neutrino sources, such as JWST's little red dots, to be identified and to obey the same luminosity relation as Seyferts. The paper's Fisher forecast treats a population spread over z = 4 to 7 that supplies 30% of the diffuse neutrino flux, standardized by the low-redshift Seyferts, which fix the normalization, slope and H0.

Under an assumed order-of-magnitude improvement in flux-normalization and spectral-index uncertainties, the total error on the population flux is about 3%. Marginalizing over the resulting region gives sigma(Omega_m) approximately 0.14 and sigma(w) approximately 1.0. The matter density is pulled to roughly half its prior width, while the equation of state stays close to its prior. The paper is explicit that a dense gas envelope may absorb X-rays while neutrinos escape, which would let these sources remain neutrino-bright despite X-ray faintness; a high-redshift neutrino measurement would test that assumption directly.

The contour orientation differs from supernova and CMB constraints because each observable probes different redshift ranges. At Omega_m = 0.3 and w = -1, the local constant-distance slope is dw/dOmega_m of about -2.2 at z = 0.5 versus -7.2 at z = 5, so the high-redshift population tilts more steeply than the supernova constraint. This is a geometric argument about which parameter combination the data constrain, not evidence that the population exists.

The forecast rests on stated, checkable assumptions

The 2030 projection assumes a fully complete KM3NeT-ARCA and Baikal-GVD, improved X-ray calibration of the anchors, spectral-index precision on the anchors matching what NGC 1068 already achieves, a factor-two gain in per-source signal efficiency following the historical trend of IceCube reconstruction and event-selection improvements, and peculiar-velocity uncertainties reduced by a factor of 2.5. It also assumes no neutrino sources beyond those currently identified; new Seyferts, especially in the largely unexplored southern sky, could improve a 2030 H0 measurement further.

The paper's own framing is that the network's leading effect is activating the southern sky and tightening beta, with the H0 gain mediated by anchors. That ordering is the most useful way to read the results: the beta measurement is the most direct product of the new detectors, the H0 improvement depends on X-ray calibration of a handful of anchors, and the Omega_m and w projection depends on a source population that has not yet been confirmed to follow the relation.

Watch beta and the anchors before the dark-energy claim

If one number should be tracked, it is beta. A 2030 result near 0.72 ± 0.04 would both exclude the calorimetric value beta = 1 at 5 sigma or more and preserve the distance sensitivity that makes the H0 measurement possible; a result drifting toward 1 would weaken the ladder regardless of how much exposure is added. The second priority is the anchor set: five anchors with X-ray flux uncertainties near 0.15, rather than the current blanket 0.25, are what convert southern-sky detections into a tighter H0.

The Omega_m and w forecast sits behind a separate gate. It pays off only if little red dots are confirmed as neutrino sources and shown to obey the Seyfert relation, and even then the projected sigma(w) of about 1.0 leaves the equation of state near its prior while sigma(Omega_m) of about 0.14 pulls matter density to roughly half its prior width. The paper's own ordering, with beta and the anchors as the near-term products and dark energy as the conditional extension, is the right guide to what a 2030 network would actually deliver.

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