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A primordial origin to cosmic tensions: towards reconciling $H_0$ and $S_8$ with early dark energy and scale-dependent primordial non-Gaussianities
Cosmology and Nongalactic Astrophysics · Submitted 20 Feb 2025
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Here, we show how combining EDE with scale-dependent primordial non-Gaussianities (sPNG) can in principle both increase $H_0$ and decrease $S_8$ at once, even conceivably allowing to solve the potential $S_8$ tension between measurements of weak gravitational lensing and the $\Lambda$CDM expectation.
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The abstract, sentence by sentence
The Hubble ($H_0$) tension between direct measurements of the expansion rate and the prediction of the $\Lambda$CDM cosmological model calibrated on the Cosmic Microwave Background (CMB), is a strong motivation to explore alternative cosmological models. A popular class of such models includes an additional component of dark energy relevant in the early Universe, which solves the Hubble tension. These Early Dark Energy (EDE) models however typically overpredict the value of the $S_8$ parameter. Here, we show how combining EDE with scale-dependent primordial non-Gaussianities (sPNG) can in principle both increase $H_0$ and decrease $S_8$ at once, even conceivably allowing to solve the potential $S_8$ tension between measurements of weak gravitational lensing and the $\Lambda$CDM expectation. Such sPNG are related to non-trivial inflationary physics, and observationally affect the non-linear regime of structure formation while leaving the linear regime mostly untouched. Depending on the amplitude of the sPNG, such models can either yield back the $\Lambda$CDM expectation for the power spectrum in the non-linear regime, and hence an $S_8$ parameter compatible with $\Lambda$CDM, or can even reconcile the value of $S_8$ from old weak-lensing measurements with the CMB, while solving the Hubble tension in all cases. In such models, both tensions would then be entirely related to pre-CMB physics of the early Universe.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The Hubble ($H_0$) tension between direct measurements of the expansion rate and the prediction of the $\Lambda$CDM cosmological model calibrated on the Cosmic Microwave Background (CMB), is a strong motivation to explore alternative cosmological models. | background 1.00 | 0.04 | 0.03 | asserted 0.99 |
| s1 | A popular class of such models includes an additional component of dark energy relevant in the early Universe, which solves the Hubble tension. | background 1.00 | 0.04 | 0.04 | asserted 0.98 |
| s2 | These Early Dark Energy (EDE) models however typically overpredict the value of the $S_8$ parameter. | background 0.66 | 0.06 | 0.03 | asserted 0.91 |
| s3 | Here, we show how combining EDE with scale-dependent primordial non-Gaussianities (sPNG) can in principle both increase $H_0$ and decrease $S_8$ at once, even conceivably allowing to solve the potential $S_8$ tension between measurements of weak gravitational lensing and the $\Lambda$CDM expectation. | contribution 0.89 | 0.85 | 0.87 | asserted 0.57 |
| s4 | Such sPNG are related to non-trivial inflationary physics, and observationally affect the non-linear regime of structure formation while leaving the linear regime mostly untouched. | background 0.95 | 0.09 | 0.04 | asserted 0.99 |
| s5 | Depending on the amplitude of the sPNG, such models can either yield back the $\Lambda$CDM expectation for the power spectrum in the non-linear regime, and hence an $S_8$ parameter compatible with $\Lambda$CDM, or can even reconcile the value of $S_8$ from old weak-lensing measurements with the CMB, while solving the Hubble tension in all cases. | result 0.68 | 0.49 | 0.43 | hedged possibility 0.90 |
| s6 | In such models, both tensions would then be entirely related to pre-CMB physics of the early Universe. | interpretation 1.00 | 0.22 | 0.21 | asserted 0.53 |
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Original abstract
The Hubble ($H_0$) tension between direct measurements of the expansion rate and the prediction of the $\Lambda$CDM cosmological model calibrated on the Cosmic Microwave Background (CMB), is a strong motivation to explore alternative cosmological models. A popular class of such models includes an additional component of dark energy relevant in the early Universe, which solves the Hubble tension. These Early Dark Energy (EDE) models however typically overpredict the value of the $S_8$ parameter. Here, we show how combining EDE with scale-dependent primordial non-Gaussianities (sPNG) can in principle both increase $H_0$ and decrease $S_8$ at once, even conceivably allowing to solve the potential $S_8$ tension between measurements of weak gravitational lensing and the $\Lambda$CDM expectation. Such sPNG are related to non-trivial inflationary physics, and observationally affect the non-linear regime of structure formation while leaving the linear regime mostly untouched. Depending on the amplitude of the sPNG, such models can either yield back the $\Lambda$CDM expectation for the power spectrum in the non-linear regime, and hence an $S_8$ parameter compatible with $\Lambda$CDM, or can even reconcile the value of $S_8$ from old weak-lensing measurements with the CMB, while solving the Hubble tension in all cases. In such models, both tensions would then be entirely related to pre-CMB physics of the early Universe.
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References
How the literature uses it
8 arXiv papers cite this in 9 sentences
Papers citing it · 4 sentences without a confident label
Cites it as support 1 paper
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In particular, these non-linear effects introduce a damping of oscillatory primordial features, as demonstrated by numerical $N$-body simulations [ref] .
Primordial Features in light of the Effective Field Theory of Large Scale Structure · Introduction · 0.99
Cites it as background 4 papers
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The best known among these discrepancies, the Hubble tension, concerns the Hubble constant $H_0$, and is possibly the most convincing evidence for new physics beyond $Λ$CDM (see e.g. Refs. [ref] for reviews, and Refs. [ref] for examples of proposed solutions based on new physics beyond $Λ$CDM, with no claims as to completeness).
BAO miscalibration cannot rescue late-time solutions to the Hubble tension · Introduction · 0.97
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See [ref] for other promising scenarios of EDE models.
Imprint of swampland-inspired coupled early dark energy · Introduction · 0.98
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Nevertheless, we stress that several other EDE models beyond axion-like EDE are being developed and studied, such as (cold and hot) new EDE, AdS EDE, acoustic EDE, and rock 'n' roll EDE among others: we refer the reader to Refs. [ref] for examples in this direction, as well as various studies on EDE.
Running into tension: primordial black holes from ultra-slow-roll inflation, spectral running, and the Hubble tension · Axion-like early dark energy · 0.95
What it cites · 123 sentences without a confident label
Uses the method or tool of 7 papers
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Following Ref. [ref] , we will consider the following effective local template for scale-dependent PNG: [equation] where $α=tanh(k_min/σ )$, and $f_NL^0$, $k_min$, $σ$ describe the amplitude, scale and shape of the sPNG.
Scale-dependent local primordial non-Gaussianity as a solution to the $S_8$ tension · Scale dependent primordial non-Gaussianities · 0.86
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Following Ref. [ref] , we will consider the following effective local template for scale-dependent PNG: [equation] where $α=tanh(k_min/σ )$, and $f_NL^0$, $k_min$, $σ$ describe the amplitude, scale and shape of the sPNG.
A cosmic degeneracy story: structure formation with warm dark matter and scale-dependent primordial non-Gaussianities · Scale dependent primordial non-Gaussianities · 0.86
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The initial conditions of our numerical setup are generated using a modified version of the public code monofonIC https://bitbucket.org/ohahn/monofonic/ [ref] , customized to include sPNG (Eq.~[ref]) and to be able to call To that end, a specific version of AxiCLASS was devised and is available here https://github.com/PoulinV/AxiCLASS/releases/tag/monofonic_v1 AxiCLASS for linear cosmology.
Accurate initial conditions for cosmological N-body simulations: Minimizing truncation and discreteness errors · Numerical setup · 0.99
Uses data or values from 6 papers
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In this work, we use the results of the latest data analysis of the model in light of Planck NPIPE data (described with the CamSpec likelihood), SDSS BAO and Pantheon$^+$ data calibrated with S$H_0$ES performed in Ref. [ref] .
Improved Planck constraints on axion-like early dark energy as a resolution of the Hubble tension · Early Dark Energy · 0.96
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A tension was originally identified by the Kilo-Degree Survey (KiDS), which when combined with BOSS, yielded $S_8 = 0.766_-0.014^+0.020$ [ref] compared to the value expected in $Λ$CDM from Planck and SDSS BAO measurements $S_8=0.825±0.011$ [ref] , with a discrepancy at the 3$σ$ level.
KiDS-1000 Cosmology: Multi-probe weak gravitational lensing and spectroscopic galaxy clustering constraints · Introduction · 0.95
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A tension was originally identified by the Kilo-Degree Survey (KiDS), which when combined with BOSS, yielded $S_8 = 0.766_-0.014^+0.020$ [ref] compared to the value expected in $Λ$CDM from Planck and SDSS BAO measurements $S_8=0.825±0.011$ [ref] , with a discrepancy at the 3$σ$ level.
Planck 2018 results. VI. Cosmological parameters · Introduction · 0.95
Compares with 4 papers
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However, the joint EDE & sPNG simulation solving the original $S_8$ tension inferred from weak-lensing would likely not explain the recent results of the eROSITA collaboration [ref] .
The SRG/eROSITA all-sky survey: Cosmology constraints from cluster abundances in the western Galactic hemisphere · Conclusions and perspectives · 0.96
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The EDE & sPNG simulation bringing back the non-linear PS at the $Λ$CDM level would on the other hand be closer to these eROSITA results, as well as to the latest results from KiDS [ref] .
KiDS-Legacy: Cosmological constraints from cosmic shear with the complete Kilo-Degree Survey · Conclusions and perspectives · 0.97
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The EDE & sPNG simulation bringing back the non-linear PS at the $Λ$CDM level would on the other hand be closer to these eROSITA results, as well as to the latest results from KiDS [ref] .
2503.19442 · Conclusions and perspectives · 0.97
Cites as background 32 papers
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Simulations of EDE were already carried out in Refs. [ref] while simulations of sPNG were presented in Refs. [ref] .
Early dark energy resolution to the Hubble tension in light of weak lensing surveys and lensing anomalies · Results · 0.85
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Simulations of EDE were already carried out in Refs. [ref] while simulations of sPNG were presented in Refs. [ref] .
Cosmological simulations of scale-dependent primordial non-Gaussianity · Results · 0.85
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Simulations of EDE were already carried out in Refs. [ref] while simulations of sPNG were presented in Refs. [ref] .
Clustering and Halo Abundances in Early Dark Energy Cosmological Models · Results · 0.85
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