⚛️ general relativity

A novel phenomenological parametrization of dynamical dark energy via matter-gravity coupling

This paper proposes a new phenomenological parametrization of dynamical dark energy derived from a Markov-Mukhanov action with non-minimal matter-gravity coupling, demonstrating how this framework naturally generates dynamical dark energy at low densities and offers a potential explanation for the DESI collaboration's tentative observations of phantom crossing.

Original authors: Hrishikesh Chakrabarty, Daniele Malafarina

Published 2026-09-22

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Hrishikesh Chakrabarty, Daniele Malafarina

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 expanding, and for decades, the leading explanation for this acceleration has been a simple, unchanging force known as the cosmological constant. In the standard model of cosmology, this force acts like a steady pressure pushing space apart, remaining exactly the same everywhere and at all times. This model has been remarkably successful, matching observations of the cosmic microwave background, the distribution of galaxies, and the light from distant exploding stars. However, a persistent mystery remains: why does this force exist at all, and why is its strength so specific? Furthermore, recent measurements from powerful new instruments have hinted that this force might not be constant after all. Instead of a steady push, the data suggests the force driving the universe's expansion might be changing over time, perhaps even shifting from one type of behavior to another in a way the standard model cannot explain.

A team of researchers has proposed a new way to understand this potential change, suggesting that the force driving the universe is not a fixed property of space, but a dynamic result of how matter and gravity interact. In their work, they explore a framework where the strength of gravity and the value of the cosmological constant are not fixed numbers, but variables that shift depending on the density of matter in the universe. Imagine the universe as a vast, thinning soup; as the soup becomes less dense over billions of years, the rules governing how gravity works within it might subtly change. The researchers argue that what we perceive as dark energy is actually the visible sign of these changing rules. By treating the interaction between matter and gravity as a flexible relationship rather than a rigid law, they can naturally generate a form of dark energy that evolves, offering a fresh perspective on why the universe's expansion might be behaving differently than the simplest models predict.

The researchers built their theory on a specific mathematical structure that modifies the standard equations of gravity. In this framework, the connection between matter and the fabric of spacetime is not fixed but depends on the energy scale of the environment. When the universe is dense, this connection behaves one way, but as the universe expands and matter becomes sparse, the connection shifts. This shift causes the effective strength of gravity and the value of the cosmological constant to run, or change, over time. The team showed that if you assume this connection is a simple, constant value, you get the standard model with a fixed cosmological constant. But if you allow for a more complex relationship that changes at low densities, you naturally get a dark energy component that evolves. This approach does not require inventing new, exotic particles or fields; instead, it suggests that the dynamical nature of dark energy is a consequence of the way gravity and matter couple to each other in the low-density environment of our current universe.

To test this idea, the researchers created two specific versions of their model and compared them against a vast collection of real-world data. They used observations from the Dark Energy Spectroscopic Instrument, which maps the positions of millions of galaxies and quasars, along with data from the Planck satellite, measurements of the ages of ancient galaxies, and surveys of supernovae. They analyzed whether their new models could fit this data better than the standard model or the popular alternative that assumes dark energy changes in a specific, simple way. The results showed that their new models could indeed describe the universe's expansion history just as well as the standard models, but with a crucial difference: they offered a physical mechanism for why dark energy might change. In one version of their model, the dark energy behaves consistently, never crossing a specific threshold that would indicate a dramatic shift in its nature. In a more complex version with two adjustable parameters, the model allowed for a "phantom crossing," a scenario where the dark energy shifts from one type of behavior to another, which aligns with some of the tentative hints seen in recent data.

The study found that while the data allows for these new, dynamic models, it does not yet force us to abandon the simpler, standard view. The researchers discovered that a version of their theory with just one extra parameter could explain the observations almost as well as the more complex versions, and it did so without requiring the dramatic "phantom crossing" that some other analyses have suggested. This finding is significant because it suggests that the apparent evidence for a changing dark energy might not be a sign of a fundamental shift in the universe's behavior, but rather a feature of how we choose to describe the data. The team's work indicates that the universe might be simpler than the most complex interpretations of recent data suggest, with the dynamical nature of dark energy potentially being a subtle, smooth evolution rather than a sudden crossover. Ultimately, the paper provides a compelling, physically grounded alternative to the standard model, showing that if gravity and matter interact in a slightly different way than Einstein originally described, the mysterious acceleration of the universe could be a natural consequence of that interaction, waiting to be confirmed by even more precise measurements in the future.

Technical Summary: A Novel Phenomenological Parametrization of Dynamical Dark Energy via Matter-Gravity Coupling

Problem Statement
The standard $\Lambda$ CDM cosmological model, while successful in describing the universe's geometry and matter content, faces theoretical and observational challenges. Theoretically, the nature of the cosmological constant ( $\Lambda$ ) remains unexplained. Observationally, recent data from the Dark Energy Spectroscopic Instrument (DESI) suggests that dark energy may be dynamical rather than constant. Specifically, DESI results hint at a redshift-dependent equation of state ( $w$ ) and a "phantom crossing" (where $w$ transitions from $w < -1$ to $w > -1$ ), deviating significantly from the constant $w = -1$ prediction of $\Lambda$ CDM at the $2\sigma$ to $4\sigma$ level. Existing phenomenological models, such as the $w_0w_a$ CDM (CPL) parametrization, attempt to capture this behavior but lack a fundamental theoretical underpinning linking these deviations to modifications of General Relativity (GR).

Methodology
The authors propose a phenomenological framework based on the Markov-Mukhanov (MM) action, which introduces a non-minimal matter-gravity coupling dependent on the energy scale. The action is given by:
$S = \int d^4x\sqrt{-g} \left( \frac{R}{8\pi G_N} + 2\chi(\varepsilon)L_m \right)$
where $\chi(\varepsilon)$ is a free function of the matter energy density $\varepsilon$ . In this framework, the Newtonian constant $G$ and the cosmological constant $\Lambda$ become dynamical quantities determined by the form of $\chi(\varepsilon)$ .

The authors interpret the standard $\Lambda$ CDM model as the lowest-order approximation of this coupling at low densities. To model dynamical dark energy, they expand $\chi(\varepsilon)$ in powers of $1/\varepsilon$ (low density expansion):
$\chi(\varepsilon) = 1 + \frac{\varepsilon_\Lambda}{\varepsilon} \left( 1 + \frac{\varepsilon_{\Lambda 1}}{\varepsilon} + \left(\frac{\varepsilon_{\Lambda 2}}{\varepsilon}\right)^2 + \dots \right)$
This expansion induces corrections to the Friedmann equations, effectively generating a dynamical dark energy component. The authors focus on two specific phenomenological models:

$\lambda_1$ CDM: Includes only the first-order correction term ( $\lambda_1$ ).
$\lambda_1\lambda_2$ CDM: Includes both first ( $\lambda_1$ ) and second-order ( $\lambda_2$ ) correction terms.

The models are tested against a combination of observational datasets:

DESI DR2: Baryon Acoustic Oscillations (BAO) from galaxies, quasars, and Lyman- $\alpha$ tracers.
Cosmic Chronometers (CC): Differential ages of passively evolving galaxies.
Supernovae: Pantheon+ (PP) and the DES-Dovekie (DD) samples.
CMB: Compressed likelihoods from Planck data.

Parameter inference is performed using Markov Chain Monte Carlo (MCMC) methods (emcee), and model selection is evaluated using the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC).

Key Contributions and Results

Theoretical Derivation: The paper demonstrates that the cosmological constant naturally emerges as the first-order term in the matter-gravity coupling expansion, while higher-order terms naturally induce a dynamical dark energy component without requiring ad-hoc scalar fields.
Phantom Crossing Mechanism: The analysis reveals that the $\lambda_1$ CDM model (single parameter) cannot exhibit phantom crossing; it remains either purely phantom or purely quintessence depending on the sign of $\lambda_1$ . In contrast, the $\lambda_1\lambda_2$ CDM model (two parameters) allows for phantom crossing when $\lambda_1$ and $\lambda_2$ have opposite signs, offering a theoretical mechanism to explain the tentative DESI observations.
Observational Constraints:
- The Hubble constant ( $H_0$ ) and matter density ( $\Omega_m$ ) are tightly constrained and consistent across all models ( $H_0 \approx 67.3-67.7$ km/s/Mpc, $\Omega_m \approx 0.306-0.311$ ).
- For the $\lambda_1$ CDM model, the parameter $\lambda_1$ is constrained to be negative at the $2-3\sigma$ level, indicating a mild tension with $\Lambda$ CDM but no evidence for phantom behavior.
- For the $\lambda_1\lambda_2$ CDM model, the parameters $\lambda_1$ and $\lambda_2$ are consistent with zero within uncertainties. A strong degeneracy exists between these two parameters, meaning current data cannot independently constrain them.
Model Comparison:
- The $\lambda_1$ CDM model performs comparably to the standard $w_0w_a$ CDM model in terms of AIC, despite having fewer free parameters.
- The BIC strongly favors the simpler $\lambda_1$ CDM model over both the two-parameter $\lambda_1\lambda_2$ CDM and the reference $w_0w_a$ CDM models, penalizing the complexity of the latter.
- The reconstructed equation of state $w_{de}(z)$ for $\lambda_1$ CDM approaches $-1$ at high redshifts and does not cross the phantom divide. The $\lambda_1\lambda_2$ CDM model shows a phantom crossing behavior in the best-fit, but this is not statistically robust given the parameter degeneracy.

Significance and Claims
The authors claim that their framework provides a "model-agnostic" way to describe classical departures from GR, where dynamical dark energy is a consequence of matter-gravity coupling at low densities. They argue that the phantom crossing tentatively observed by DESI can be naturally explained by including the next-to-leading order terms in the coupling expansion ( $\lambda_1\lambda_2$ CDM).

However, the paper maintains a modest stance regarding the necessity of this phantom behavior. The authors note that the single-parameter $\lambda_1$ CDM model, which forbids phantom crossing by construction, fits the data nearly as well as the more complex models. Consequently, they suggest that the preference for phantom crossing found in CPL parametrizations and non-parametric reconstructions of DESI data may not constitute robust evidence for the existence of phantom crossing itself, but rather an artifact of the specific parametrization used. The authors conclude that more precise data is required to determine whether the observed deviations are due to the nature of the parametrization or the existence of additional physical terms in the gravity-matter coupling.

Technical Summary: A Novel Phenomenological Parametrization of Dynamical Dark Energy via Matter-Gravity Coupling

More like this