The cosmological dispute resembles two craftsmen measuring the same room with different tape measures. One, looking at distant galaxies, gets one number. The other, peering into the ancient glow (the cosmic microwave background, the cooled light of the Big Bang) gets another, smaller number. This discrepancy is called the Hubble tension. It does not fit within random error and hints at something new in the workings of the world.
Recently, the ACT collaboration processed fresh data on the cosmic microwave background and announced: no extra invisible particles, dark radiation, are visible, and the expansion rate remains low. The dispute seemed to hit a dead end. But the authors of the new work noticed that ACT's conclusions are unusually sensitive to assumptions about how the early Universe inflated. Inflation is the ultra-fast expansion in the first moments that set the ripples that later became galaxies. Usually, it is assumed that the strength of this ripple, its spectral index, hardly changed from scale to scale. However, if one allows it to vary smoothly, adding parameters for the "run" and the "run of the run," the picture flips.
Moreover, dark radiation could have once exchanged energy with dark matter and decoupled around the epoch of matter-radiation equality. Then it would have generated its own sound waves — dark acoustic oscillations. Their "resistance horizon" would be about 60 megaparsecs. That distance light travels in 200 million years. In this scenario, the constraint softens even further: to 0.68 species, and the Hubble tension drops below 2 sigma. This level of significance is no longer considered a serious indication of new physics. Meanwhile, the spectral index indeed shows a preference for a positive run at the 2.9 sigma level.
Such a run could naturally arise if inflation consisted of two acts. The first ended, leaving a mark in the large-scale ripple that satellites like Planck and ground-based galaxy surveys catch. Small scales, on the other hand, retain the memory of the second act. The result is an elegant picture: dark radiation hides in the large spots of the cosmic microwave background, while the dynamics of inflation hide in the small ones. The tape measures are no longer lying: it's just that the room turned out to have a niche that was previously unnoticed.
as written by the authors arXiv:2604.26541
We point out that constraints on $$\Delta N_\mathrm{eff}$$ reported by the ACT collaboration in their DR6 data release are surprisingly sensitive to the assumptions made about the initial power spectrum from inflation. The ACT collaboration reports no evidence of new light degrees of freedom alongside a low value of the expansion rate, thus confirming the Hubble tension. However, as we show here, when considering self-interacting dark radiation and including running, $$\alpha_s$$, and running of the running, $$\beta_s$$, of the spectral index $$n_s$$, the picture changes significantly. Confronting this extended model with Planck, ACT DR6, DESI DR2, and uncalibrated Pantheon+ data, we find the significantly relaxed bound $$\Delta N_\text{eff}< 0.58$$ at 95$$\%$$ CL, together with a $$2.9 \sigma$$ ($$2.6 \sigma$$) preference for $$\alpha_s>0$$ ($$\beta_s>0$$), while the Hubble tension is reduced to $$2.2 \sigma$$ with only three more parameters compared to $$\Lambda$$CDM. If the dark radiation fluid is initially coupled to dark matter, and undergoes dark radiation-matter decoupling (DRMD) around matter-radiation equality, predicting dark acoustic oscillations with drag horizon $$r_{d,\mathrm{DAO}} \approx 60 \,\mathrm{Mpc}/h$$, the bound is further relaxed to $$\Delta N_\text{eff}< 0.68$$ at 95$$\%$$ CL, reducing the Hubble tension below $$2\sigma$$. We also discuss how $$\alpha_s$$ and $$\beta_s$$ could naturally appear in inflationary scenarios, possibly connected to the end of a first act of inflation. In this case dark radiation is mostly probed by scales covered by Planck and DESI, while smaller scales carry information on inflationary dynamics.
The "run of the run" parameter (βs) is the rate of change of the rate of change of the spectral slope. If the regular run shows how the color of the ripple changes when moving from large waves to small ones, the run of the run tells whether this change is uniform or accelerating. In everyday terms: the slope is the steepness of a hill, the run is how quickly the steepness changes, and the run of the run is whether that change becomes sharper or smoother.
The idea of dark acoustic oscillations echoes the "dark forest" from Liu Cixin's novel: hidden interactions in the dark sector create their own, invisible structure of space that affects the visible Universe only indirectly.