A theoretical model of modified gravity gives a weaker predicted 21-cm absorption signal than ΛCDM over the redshift range 15 < z < 20. The curves remain negative, so the model still predicts absorption, but the Horndeski result is less negative than the ΛCDM comparison, with the difference becoming more evident for larger absolute values of λ3.
The manuscript is an arXiv preprint identified as arXiv:2608.25159v1 and dated 25 Aug 2026. Its authors describe the small model-versus-ΛCDM difference as a possible additional cosmological observable for testing scalar-tensor theories, and call the calculation a first quantitative estimate that motivates self-consistent follow-up.
A difference that grows with redshift
The predicted expansion history shows a similar pattern. The modeled Hubble parameter H(z) is practically the same as ΛCDM at very low redshift, begins to diverge as redshift grows, and shows its main displayed difference among models around 5 < z < 30.
The model also reports a prolonged interval in which the unified-fluid equation-of-state parameter wU(z) remains zero, a behavior described as consistent with a pressureless component. The paper describes the derivative term as friction-like.
How the signal was built
Because the H(t) equation cannot generally be solved analytically, the authors solve it numerically. They use redshift z = −1 + a0/a as the independent variable and set a0 to 1.
The brightness-temperature calculation combines H(z) with the background-radiation temperature Tγ = 2.73(1 + z) and the gas spin temperature Ts. For Ts, the study uses 21cmFAST and represents values over 15 < z < 20 with a third-order polynomial fit. The reported fit has R2 = 0.999871356000939.
It also assumes a present-day neutral-hydrogen density nHI0 = 0.19 m−3 at z = 0 and a mean neutral fraction x̄HI ≈ 1 over 14 < z < 30.
Why the result remains provisional
That spin-temperature choice is the central limitation. 21cmFAST uses ΛCDM, so the adopted Ts is only a first approximation for the Horndeski calculation. The astrophysical sector is kept fixed to isolate the modeled contribution from the changed H(z); a self-consistent treatment would recalculate Ts.
The parameter scan is limited as well. The numerical illustration uses three representative λ3 values inside the stable region, with λ5 cases lying along the λ3−λ5 existence curve. The chosen subspace is set to satisfy H(z = 0) ≡ H0 ≈ 6 × 10−61 and wU(z = 0) ≈ −0.7, while a plotted bound is used to avoid Laplacian and ghost instabilities.
The paper reports no numerical uncertainty estimates for the comparison. The size of the departure is therefore conditional on the selected model cases and the fixed astrophysical input.
Taken together, the comparison is a conditional model result rather than a complete prediction of the modified-gravity signal. The authors frame 21-cm brightness temperature as an additional observable for testing scalar-tensor theories and describe the work as a first estimate that calls for self-consistent follow-up.
Paper data and sources
Original title: 21-cm Brightness Temperature in a Unified-Dark-Sector Horndeski Theory
Authors: Bertha Cuadros-Melgar, Thanasis Karakasis, Eleftherios Papantonopoulos, Maria Petronikolou
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-25
DOI: Not available
Original paper · Full text