GPAge: a Global Parameterization based on cosmic Age for some unified early-time and late-time solutions to the Hubble tension

arXiv:2610.30961 · astro-ph.CO · Submitted 2026-10-22 · Read on arXiv

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Introduction to the show: ident: Astrophysics Radio. Generated commentary on the latest astrophysics papers.

Vera: We're looking at the paper: "GPAge: a Global Parameterization based on cosmic Age for some unified early-time and late-time solutions to the Hubble tension".

Jocelyn: Here's the gist of the paper. The gist The resulting parametrization can accurately reproduce target cosmological models at both the background and perturbation levels.

Vera: Extension of PAge to Early Universe The original Parametrization based on cosmic Age (PAge) is extended to cover both the early and late Universe by incorporating the radiation-dominated epoch at the background level.

Jocelyn: This extension involves replacing the matter-dominated baseline Ht = 2/3 of the original PAge model with a two-component co-evolution relation that follows from the exact radiation–matter background solution.

Vera: The extended PAge relation of the GPAge model is then written as a complex expression involving coefficients η1, η2, and η3.

Paper summary: Vera: So we're looking at this paper called "GPAge: a Global Parameterization based on cosmic Age for some unified early-time and late-time solutions to the Hubble tension". The main idea here is that the over five sigma Hubble tension keeps pushing us to change our standard cold dark matter model, Lambda CDM <ref:2610.30961#pg1>.

Jocelyn: It claims this work extends the original Parametrization based on cosmic Age, or PAge, to cover both the early and late Universe. They are incorporating the radiation-dominated epoch at the background level and completing the perturbation sector within a unified dark fluid framework.

Subrahmanyan: That unification across both epochs is what's interesting for structure formation. It suggests that we might be able to use a single set of parameters to describe how things evolved from the very early universe right up to today >

Vera: Right, so they want one parametrization that works everywhere. They are essentially trying to bridge the gap between early-time solutions and late-time solutions for this Hubble tension issue.

Jocelyn: The paper sets out to create a parametrization that can accurately reproduce target cosmological models at both the background and perturbation levels >

Subrahmanyan: And they use a unified dark fluid framework for those perturbations. That means they're looking at how the dark fluid behaves on small scales, not just how it expands globally >

Vera: They confront this new GPAge model with two data sets: D0, which is CMB plus DESI plus DES-Dovekie, and D1, which adds the SH0ES measurement of H0.

Jocelyn: The analysis uses a modified version of CLASS and Cobaya to perform the parameter inference. The sampled parameters for PAge3 are listed as theta3 equals H0, omega b, ln(ten to the power of ten A s), ns, tau reio, page, eta one equals η1, eta two equals η2 > <ref:2610.30961#pg2>

Subrahmanyan: So what do we get? The results show that PAge3 provides a substantially better fit than Lambda CDM with a chi squared minimum of minus eleven point five zero three for D0 and minus ten point four one six for D1 > <ref:2610.30961#pg2>

Vera: That's an improvement, but the Hubble tension itself isn't significantly alleviated yet because the QDMAP statistic goes up slightly from four point five one sigma in Lambda CDM to four point six three sigma in both PAge3 and PAge4 > <ref:2610.30961#pg2>

Jocelyn: And the sound horizon at last scattering remains nearly unchanged, with rs z star being approximately one hundred forty-five Mpc for the D0 case > <ref:2610.30961#pg3>

Subrahmanyan: That means retuning the early-time matter-like density, even when you have a flexible late-time expansion history, isn't enough to resolve this tension >

Vera: So what does this imply for us who just listen to the show? It suggests that fixing the problem requires physics before recombination that goes beyond just tweaking how dense matter is early on >

Jocelyn: It points toward needing pre-recombination physics, something more fundamental than a simple retuning of the matter-like density >

Subrahmanyan: And they also found that their unified dark fluid interpretation leads to a substantially lower effective clustering amplitude, where S8 is inferred as an effective clustering measure rather than directly identified with standard CDM >

Vera: That's an important caveat. So, the work shows a better fit but doesn't solve the core problem we're talking about right now >

Jocelyn: And it also points toward needing a more complete picture of dark energy dynamics, which is what their unified framework aims to provide >

Subrahmanyan: The authors themselves flag that future parametrizations should account for both the background and perturbation sectors to give us a natural next step in this research direction >

Vera: So, in summary, GPAge provides a better fit to existing data but doesn't solve the Hubble tension on its own. It tells us we need to look at physics before recombination if we want that tension resolved >

Conclusion: Vera: So we're wrapping up this look at GPAge, which is that paper about "GPAge: a Global Parameterization based on cosmic Age for some unified early-time and late-time solutions to the Hubble tension."

Jocelyn: It’s about taking that original cosmic age idea and extending it to cover both the very early universe and everything we see today.

Subrahmanyan: The authors are trying to find one single way to describe how things evolved, whether it was baby matter or today's dark energy.

Vera: They use a unified dark fluid framework for the perturbations, which means they’re looking at structure formation on small scales too.

Jocelyn: And they tested this model against some solid data sets like CMB and DESI measurements.

Subrahmanyan: The main result is that GPAge3 fits the data better than Lambda CDM, but it doesn't solve the Hubble tension issue yet.

Vera: It means that even with a flexible late-time history, just tweaking the early-time matter density isn't enough to fix the distance problem we’re seeing.

Jocelyn: The paper suggests that resolving this tension might require physics happening before recombination, something beyond just adjusting how dense matter is at that time.

Subrahmanyan: They also found that their unified dark fluid interpretation leads to a lower effective clustering amplitude, which means S8 is inferred differently than in standard cold dark matter.

Vera: So the implication for us is that if we want to get around this tension, we might need to look at physics in the very early universe before recombination.

Jocelyn: That opens up a new area for follow-up observations, like those looking at the earliest structures.

Subrahmanyan: And they noted that future parametrizations should combine both the background and perturbation sectors for a more complete picture of dark energy dynamics.

Jia-Le Ling, Shao-Jiang Wanga

Institute of Theoretical Physics, Chinese Academy of Sciences (CAS) · School of Physical Sciences, University of Chinese Academy of Sciences (UCAS) · Asia Pacific Center for Theoretical Physics (APCTP)

astro-ph.CO

Submitted: 2026-10-22

Updated: 2026-10-22

Comments: 28 pages, 7 figures, 3 tables

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

The gist: The gist The resulting parametrization can accurately reproduce target cosmological models at both the background and perturbation levels.

Key concepts

PAge
A parametrization based on cosmic Age is used to describe the expansion history of the universe. It is extended to cover both early and late times by including a radiation-dominated epoch at the background level, allowing for more complex solutions than standard models.
Unified Dark Fluid (UDF)
This framework decomposes the total energy density into visible matter and a unified dark fluid component. The UDF background evolution is governed by its own continuity equation, which helps describe how this unified dark fluid behaves across cosmic time.
Hubble Tension
The Hubble tension refers to the discrepancy between the value of the Hubble constant ($H_0$) measured in early-universe observations (like CMB) and the value measured in late-universe local measurements. The paper tests how different cosmological models, including PAge, address this gap.
Perturbation Sector
This refers to how density fluctuations evolve over time. In this study, the perturbation sector is completed using a unified dark fluid framework to ensure that the model can accurately reproduce observable features like the sound horizon at last scattering.

Terminology

Summary

The gist The resulting parametrization can accurately reproduce target cosmological models at both the background and perturbation levels.

Extension of PAge to Early Universe

The original Parametrization based on cosmic Age (PAge) is extended to cover both the early and late Universe by incorporating the radiation-dominated epoch at the background level. This extension involves replacing the matter-dominated baseline Ht = 2/3 of the original PAge model with a two-component co-evolution relation that follows from the exact radiation–matter background solution. The extended PAge relation of the GPAge model is then written as a complex expression involving coefficients η1, η2, and η3. These coefficients control the late-time deformation, with their contributions being suppressed in the early-time limit u → 0.

Unified Dark Fluid Perturbations

To confront the PAge background with CMB observations, the perturbation sector is completed within a unified-dark-fluid (UDF) framework. This involves decomposing the Friedmann equation into the density of the unified dark fluid (UDF) ρdf and the visible sector ρvisible. The UDF background evolution obeys a continuity equation, yielding expressions for pdf and wdf. In the synchronous gauge, the pressure perturbation is written as δpdf = c 2s,eff δρdf + 3H(1 + wdf)ρdf c 2s,eff − c 2s,ad θdf k squared. The work adopts the conditions where the effective sound speed is zero and anisotropic stress is zero to allow the unified dark fluid to cluster efficiently.

Data Sets and Methodology

The analysis confronts the GPAge model with current cosmological observations using two data combinations: D0 = CMB + DESI + DES–Dovekie, and D1 = D0 + SH0ES. The data sets include CMB measurements from Planck and ACT, DESI DR2 BAO measurements, DES–Dovekie SNe data, and the local SH0ES measurement of H0. Cosmological parameter inference is performed using a modified version of CLASS and Cobaya. The sampled parameters for PAge3 are listed as θ3 = H0, ωb, ln(10 10As), ns, τreio, page, η1, η2.

Results and Discussion

The analysis shows that PAge3 provides a substantially better fit than ΛCDM with a ∆χ 2 min = -11.503 for D0 and ∆χ 2 min = -10.416 for D1. However, the Hubble tension is not alleviated, as the QDMAP statistic increases slightly from 4.51σ in ΛCDM to 4.63σ in both PAge3 and PAge4. The sound horizon at last scattering remains nearly unchanged, with rs(z∗) being approximately 145 Mpc for the D0 case. The results indicate that retuning the early-time matter density, even when combined with a flexible late-time expansion history, remains insufficient to resolve the Hubble tension.

Conclusion

The work concludes that resolving the Hubble tension requires pre-recombination physics beyond a simple retuning of the matter-like density. The UDF interpretation also leads to a substantially lower effective clustering amplitude, with S8 being inferred as an effective clustering measure rather than directly identified with standard CDM. Future parametrizations should account for both the background and perturbation sectors to provide a natural next step for extending the PAge framework.

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The gist The resulting parametrization can accurately reproduce target cosmological models at both the background and perturbation levels.

Results and Discussion

The analysis shows that PAge3 provides a substantially better fit than ΛCDM with a ∆χ 2 min = -11.503 for D0 and ∆χ 2 min = -10.416 for D1. However, the Hubble tension is not alleviated, as the QDMAP statistic increases slightly from 4.51σ in ΛCDM to 4.63σ in both PAge3 and PAge4. The sound horizon at last scattering remains nearly unchanged, with rs(z∗) being approximately 145 Mpc for the D0 case.

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The gist The resulting parametrization can accurately reproduce target cosmological models at both the background and perturbation levels.

Improvements for AI systems

  1. Improved AI can perform global cosmological parameterization by incorporating both early-time radiation-dominated epochs and late-time dark energy dynamics into a single framework, as described by extending the Parametrization based on cosmic Age (PAge) to cover both the early and late Universe.

  2. Improved AI systems will be able to test target cosmological models, such as Lambda cold dark matter (Lambda CDM), w0waCDM, and Early Dark Energy (EDE), against CMB, DESI BAO, and DES-Dovekie SNe data simultaneously using the Unified-dark-fluid (UDF) perturbation framework.

  3. The AI can perform model comparison by calculating the minimum chi squared values and Bayesian evidence for different PAge models (PAge3 and PAge4) relative to Lambda CDM, providing a quantitative measure of how well each parametrization fits the combined data sets.

  4. Improved AI can quantify the impact of observational constraints like the SH0ES prior on cosmological parameters, specifically showing that Adding SH0ES shifts H0 upward by approximately 1.2 km s−1 Mpc−1, while producing essentially no shift in rs(z∗).

  5. The AI can assess the limitations of the PAge parametrization by analyzing marginalized posterior means and credible intervals for parameters like H0 and S8, revealing that the remaining PAge freedom mainly changes the late-time expansion and therefore has little leverage on rs(z∗).

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