⚛️ general relativity

Conformally Interacting Dark Energy with Early and Late-Time Measurements

This paper investigates the viability of conformally interacting dark energy (CIDE) models, which couple dark matter and dark energy via a scalar field, by constraining them with a comprehensive combination of early- and late-time cosmological data to assess their potential in alleviating the $H_0$ and $S_8$ tensions compared to the standard cosmological model.

Original authors: Shambel Sahlu, Abunie Gezahegn, Amare Abebe, Gonzalo J. Olmo, Diego Rubiera-Garcia

Published 2026-09-09

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CC BY 4.0

Original authors: Shambel Sahlu, Abunie Gezahegn, Amare Abebe, Gonzalo J. Olmo, Diego Rubiera-Garcia

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The universe is not a static stage but a dynamic, expanding fabric that has been stretching for billions of years. For decades, the most successful description of this cosmic history has relied on a simple recipe: ordinary matter, invisible dark matter, and a mysterious force called dark energy that pushes galaxies apart. This standard model has explained a vast array of observations, from the afterglow of the Big Bang to the distribution of galaxies. Yet, as measurements have become more precise, cracks have appeared in this picture. Two major puzzles have emerged. First, different methods of measuring the current rate of cosmic expansion yield conflicting numbers, a disagreement so sharp it suggests our understanding of physics might be incomplete. Second, the way matter clumps together into galaxies and clusters does not match the predictions of the standard model, appearing slightly too smooth in some surveys and too clumpy in others. These discrepancies, known as the Hubble tension and the S8 tension, hint that the invisible sectors of the universe—dark matter and dark energy—might not be acting independently as previously assumed.

A team of researchers has proposed a new way to think about this invisible relationship. Instead of treating dark matter and dark energy as separate entities that simply coexist, they explored a scenario where the two are in constant conversation, exchanging energy as the universe evolves. This idea is rooted in a specific mathematical framework where the properties of dark matter are subtly altered by the presence of a scalar field, a type of energy field that permeates space and drives the acceleration of the universe. In this model, the interaction is not an arbitrary addition but a natural consequence of how the geometry of space and time is shaped by these fields. The researchers focused on two variations of this idea: one where the dark energy behaves like a constant, unchanging force, and another where it is dynamic, changing its strength over time. They then put these theories to the test against the most comprehensive collection of cosmic data available, including the faint glow of the early universe captured by satellites and ground-based telescopes, the precise distances to exploding stars, and the large-scale arrangement of galaxies.

The investigation involved running complex computer simulations that tracked how the universe would evolve under these new rules. The researchers compared the predictions of their interacting models against real-world observations from the South Pole Telescope, the Planck satellite, and the Atacama Cosmology Telescope, alongside data from the Dark Energy Spectroscopic Instrument and various supernova surveys. They looked for signs that the flow of energy between the dark sectors could resolve the conflicting measurements of the universe's expansion rate and the clumpiness of matter. The results were striking. The simulations showed that when dark matter transfers energy to dark energy, the resulting universe looks different in specific, measurable ways. The models predicted a universe that expands at a rate that sits comfortably between the conflicting measurements, effectively bridging the gap between the early universe's history and the local universe's current state.

Specifically, the data favored a scenario where dark matter is slowly losing energy to dark energy. This flow of energy changes how structures form. In the standard model, matter clumps together in a predictable way, but in this interacting scenario, the transfer of energy suppresses the growth of matter clumps on very large scales while enhancing it on smaller scales. This subtle shift in how matter aggregates brings the theoretical predictions much closer to what astronomers actually observe in galaxy surveys. The researchers found that their models fit the observational data better than the standard model did, particularly when accounting for the dynamic nature of dark energy. The version of the model where dark energy changes over time proved especially effective at reconciling the different measurements of the expansion rate, reducing the statistical disagreement to 1.69σ, a significant improvement that brings the tension down to a more manageable level.

However, the researchers were careful to note that while these models offer a compelling statistical improvement, they are not a final solution. The dynamic version of the model, which allows dark energy to evolve, fits the data slightly better but introduces more complexity, which carries a statistical penalty in rigorous model selection tests. The study confirms that a universe where the dark sectors interact is a viable and robust alternative to the standard view. It suggests that the tension between different cosmic measurements might not be an error in our instruments or a flaw in our data, but rather a sign that the dark side of the universe is more interconnected than we thought. By allowing dark matter and dark energy to exchange energy, the universe can evolve in a way that satisfies the conflicting demands of early and late-time observations, offering a fresh perspective on the fundamental forces shaping our cosmos.

Technical Summary: Conformally Interacting Dark Energy with Early and Late-Time Measurements

Problem Statement
The standard $\Lambda$ CDM cosmological model, while successful in accommodating diverse datasets, faces significant theoretical and observational challenges. These include the nature of the cosmological constant, the cosmic coincidence problem, and persistent tensions between early-universe and late-universe measurements, specifically the Hubble constant ( $H_0$ ) and the matter clustering amplitude ( $S_8$ ). Phenomenological interacting dark energy (IDE) models have been proposed to address these issues by introducing an ad hoc energy transfer term $Q$ between dark matter (DM) and dark energy (DE). However, such approaches often lack a fundamental Lagrangian foundation, leading to gauge-dependent instabilities in cosmological perturbation theory. This paper investigates the Conformally Interacting Dark Energy (CIDE) model, a scalar-tensor theory derived from a covariant action principle, to determine if a fundamental interaction mechanism can resolve these tensions while maintaining statistical viability.

Methodology
The authors formulate the CIDE model within the Einstein frame, where a scalar field $\phi$ (representing DE) is coupled to DM via a conformal transformation of the metric, $\tilde{g}_{\mu\nu} = C(\phi)g_{\mu\nu}$ . The interaction is derived from the Lagrangian rather than imposed phenomenologically. The interaction term $Q$ is proportional to the trace of the DM energy-momentum tensor, $Q = \frac{C'(\phi)}{2C(\phi)}g_{\mu\nu}T^{\mu\nu}_{DM}$ .

The study considers two specific scenarios based on the equation-of-state (EoS) parameter $w_\phi$ of the scalar field:

CIDE: $w_\phi = -1$ (DE behaves as a cosmological constant).
wCIDE: $w_\phi \neq -1$ (DE behaves as a dynamical quintessence-like fluid).

The authors assume a power-law parametrization for the conformal function, $C(\phi) \propto (1+\phi)^m$ , where $m$ is the coupling parameter. A key theoretical distinction is highlighted: while the background evolution of this model mimics the phenomenological model $Q = \alpha H \rho_{DM}$ (with $\alpha = m/2$ ), the linear perturbation equations differ fundamentally due to the scalar-dependent nature of the interaction vector.

To test these models, the authors perform Bayesian parameter inference using Monte Carlo Markov Chain (MCMC) simulations via the COBAYA interface and a modified CLASS code. The analysis utilizes a comprehensive combination of early- and late-time cosmological datasets:

CMB: South Pole Telescope (SPT), Planck 2018, and Atacama Cosmology Telescope (ACT DR6).
BAO: Dark Energy Spectroscopic Instrument (DESI DR2).
Supernovae: PantheonPlus, PantheonPlus + SH0ES, Union3, and DES-Dovekie.

Model viability is assessed using the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) to compare against the standard $\Lambda$ CDM model. Furthermore, the authors compute perturbative thermodynamic quantities, including the matter power spectrum, CMB anisotropy spectra, transfer functions, growth factors, and redshift-space distortions (RSD).

Key Contributions and Results

Parameter Constraints: The MCMC analysis consistently favors a positive coupling parameter ( $m > 0$ ) at the 95% confidence level across all dataset combinations. This implies an energy flow from DM to DE. For the wCIDE model, the best-fit EoS parameter satisfies $w_\phi > -1$ , indicating a preference for quintessence-like behavior.
Statistical Viability: Both CIDE and wCIDE models yield lower $\chi^2$ values than $\Lambda$ CDM across most dataset combinations, indicating a better statistical fit. The AIC analysis provides substantial support for both models, though the wCIDE model is penalized by the BIC due to its additional free parameter, resulting in weaker or negligible support in some combinations.
Alleviation of Tensions:
- $H_0$ Tension: The models successfully bridge the gap between early-universe (Planck 2018) and late-universe (SH0ES 2022) measurements. The wCIDE model, in particular, reduces the tension with SH0ES to $\leq 1.69\sigma$ (under CMB-SPA+DESI) while maintaining consistency with Planck ( $< 0.8\sigma$ ). The inferred $H_0$ values lie in the intermediate regime between direct and indirect measurements.
- $S_8$ Tension: The models remain consistent with weak lensing and galaxy clustering data. The CIDE and wCIDE models maintain deviations of $< 2\sigma$ relative to DES Y6 and $< 1\sigma$ relative to KiDS-Legacy, outperforming standard $\Lambda$ CDM in certain dataset combinations (e.g., CMB-SPA+DESI+DD).
Structure Growth: The analysis of perturbative quantities reveals distinct behaviors compared to $\Lambda$ CDM. The CIDE model suppresses matter clustering at large scales (small $k$ ) while enhancing structure growth at small scales (large $k$ ). The growth rate $f(z)$ and the RSD parameter $f\sigma_8(z)$ show that interacting DE offers a different strategy for replicating the growth history of $\Lambda$ CDM. The CMB anisotropy power spectra show significant deviations in the low multipoles (TT polarization) due to modifications in the late-time Integrated Sachs-Wolfe (ISW) effect, while high multipoles exhibit sub-percent shifts.

Significance and Claims
The paper claims that conformally coupled dark energy models represent a robust statistical alternative to the standard $\Lambda$ CDM paradigm. By deriving the interaction from a fundamental Lagrangian rather than an ad hoc prescription, the model avoids the gauge instabilities inherent in phenomenological IDE models. The results suggest that a dynamical dark energy equation of state ( $w_\phi \neq -1$ ) within a conformally interacting dark sector provides a viable path to mitigating the $H_0$ tension without violating constraints on matter clustering ( $S_8$ ). The authors conclude that non-minimal dark-sector couplings challenge the standard assumption of separate dark sector evolution and reinforce the necessity of investigating interacting dark energy physics in future observational analyses.

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