Cold New Early Dark Energy pulls the trigger on the $H_0$ and $S_8$ tensions: a simultaneous solution to both tensions without new ingredients

In this work, we show that the Cold New Early Dark Energy (Cold NEDE) model in its original form can solve both the Hubble tension and the $S_8$ tension without adding any new ingredients at the fundamental level. So far, it was assumed that the trigger field in the Cold NEDE model is completely subdominant. However, relaxing this assumption and letting the trigger field contribute a mere $0.5\%$ of the total energy density leads to a resolution of the $S_8$ tension while simultaneously improving it as a solution to the $H_0$ tension. Fitting this model to baryonic acoustic oscillations, large-scale-structure, supernovae (including a SH0ES prior), and cosmic microwave background data, we report a preferred NEDE fraction of $f_\mathrm{NEDE}= 0.134^{+0.032}_{-0.025}$ ($68\%$ C.L.), lifting its Gaussian evidence for the first time above $5\sigma$ (up from $4 \sigma$ when the trigger contribution to dark matter is negligible). At the same time, we find the new concordance values $H_0 = 71.71 \pm 0.88 \,\mathrm{km}\, \mathrm{sec}^{-1}\, \mathrm{Mpc}^{-1}$ and $S_8 = 0.793 \pm 0.018$. Excluding large-scale structure data and the SH$_0$ES prior, both Gaussian tensions are reduced below the $2 \sigma$ level.