The End of the First Act: Spectral Running, Interacting Dark Radiation, and the Hubble Tension in Light of ACT DR6 Data

Abstract

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.