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Testing $n_s=1$ in light of the latest ACT and SPT data

Ze-Yu Peng, Jun-Qian Jiang, Hao Wang, Yun-Song Piao

TL;DR

This study investigates whether the primordial scalar spectral index satisfies $n_s=1$ in light of the latest ACT DR6 and SPT-3G D1 data, within pre-recombination Early Dark Energy models designed to resolve the Hubble tension. By analyzing axion-like EDE and AdS-EDE using Planck, ACT, SPT, DESI BAO, Pantheon+, and SH0ES priors through MCMC with Cobaya/CLASS, the authors test the predicted $n_s\approx1$ outcome for $H_0\simeq73$ km s$^{-1}$ Mpc$^{-1}$. They find that the $n_s$–$H_0$ scaling remains robust: with SH0ES, $H_0$ rises to ~72–73 and $n_s$ stays near unity (within a few parts in $10^3$) for both EDE models; without SH0ES, $H_0$ decreases and $n_s$ can deviate modestly from unity depending on the model and dataset. These results reinforce the view that resolving the Hubble tension via EDE favors a scale-invariant Harrison–Zel’dovich spectrum and have meaningful implications for early-Universe physics and inflation.

Abstract

It is commonly recognized that the primordial scalar spectral index $n_s$ is approximately $0.96-0.975$, depending on the dataset. However, this view is being completely altered by the early dark energy (EDE) resolutions of the Hubble tension, known as the most prominent tension the standard $Λ$CDM model is suffering from. In corresponding models with pre-recombination EDE, resolving the Hubble tension (i.e., achieving $H_0\sim 73$km/s/Mpc) must be accompanied by a shift of $n_s$ towards unity to maintain consistency with the cosmological data, which thus implies a scale invariant Harrison-Zel'dovich spectrum with $n_s=1$ $(|n_s-1|\simeq {\cal O}(0.001))$. In this work, we strengthen and reconfirm this result with the latest ground-based CMB data from ACT DR6 and SPT-3G D1, the precise measurements at high multipoles beyond the Planck angular resolution and sensitivity. Our work again highlights the importance of re-examining our understanding on the very early Universe within the broader context of cosmological tensions.

Testing $n_s=1$ in light of the latest ACT and SPT data

TL;DR

This study investigates whether the primordial scalar spectral index satisfies in light of the latest ACT DR6 and SPT-3G D1 data, within pre-recombination Early Dark Energy models designed to resolve the Hubble tension. By analyzing axion-like EDE and AdS-EDE using Planck, ACT, SPT, DESI BAO, Pantheon+, and SH0ES priors through MCMC with Cobaya/CLASS, the authors test the predicted outcome for km s Mpc. They find that the – scaling remains robust: with SH0ES, rises to ~72–73 and stays near unity (within a few parts in ) for both EDE models; without SH0ES, decreases and can deviate modestly from unity depending on the model and dataset. These results reinforce the view that resolving the Hubble tension via EDE favors a scale-invariant Harrison–Zel’dovich spectrum and have meaningful implications for early-Universe physics and inflation.

Abstract

It is commonly recognized that the primordial scalar spectral index is approximately , depending on the dataset. However, this view is being completely altered by the early dark energy (EDE) resolutions of the Hubble tension, known as the most prominent tension the standard CDM model is suffering from. In corresponding models with pre-recombination EDE, resolving the Hubble tension (i.e., achieving km/s/Mpc) must be accompanied by a shift of towards unity to maintain consistency with the cosmological data, which thus implies a scale invariant Harrison-Zel'dovich spectrum with . In this work, we strengthen and reconfirm this result with the latest ground-based CMB data from ACT DR6 and SPT-3G D1, the precise measurements at high multipoles beyond the Planck angular resolution and sensitivity. Our work again highlights the importance of re-examining our understanding on the very early Universe within the broader context of cosmological tensions.

Paper Structure

This paper contains 8 sections, 8 equations, 3 figures, 4 tables.

Table of Contents

  1. Introduction
  2. $n_s= 1$
  3. Testing $n_s=1$ in light of latest data
  4. Datasets and Methods
  5. Result for both axion-like and AdS EDEs
  6. Discussion
  7. The EDE models
  8. The effects of $\tau_{\mathrm{reio}}$ prior and SN data

Figures (3)

  • Figure 1: 1D and 2D marginalized posterior distributions ($68\%$ and $95\%$ confidence range) of relevant parameters for axion-like EDE (left) and AdS-EDE (right), fitting to Planck and Planck+SPT+ACT datasets with and without SH0ES.
  • Figure 2: The $n_s-H_0$ scaling relation from Planck (left) and Planck+SPT+ACT (right). We present the $68\%$ and $95\%$ posterior distributions for axion-like EDE with and without SH0ES, AdS-EDE and $\Lambda$CDM. The purple lines are $\delta n_s=0.4\frac{\delta H_0}{H_0}$ (left) and $\delta n_s=0.3\frac{\delta H_0}{H_0}$ (right) for Planck and Planck+SPT+ACT, respectively. The grey bands are $1\sigma$ and $2\sigma$ regions of the latest $H_0$ measurement from SH0ES Riess:2021jrx.
  • Figure 3: 1D and 2D marginalized posterior distributions ($68\%$ and $95\%$ confidence range) of relevant parameters for axion-like EDE. The plot shows our baseline results against a reweighted analysis that excludes the SN data and adopts the $\tau_{\mathrm{reio}}$ prior from Ref. SPT-3G:2025vyw.