⚛️ phenomenology

Testing cosmic acceleration from thermogravity without vacuum energy

This paper presents a background-level observational test of a thermogravity theory where cosmic acceleration arises from energy non-conservation rather than a cosmological constant, finding that while a model restricting non-conservation to cold dark matter improves the fit to distance data compared to $\Lambda$ CDM, it exacerbates the Hubble tension by lowering the inferred value of $H_0$ .

Original authors: Dong Ha Lee, João Magueijo, Carsten van de Bruck, Eleonora Di Valentino

Published 2026-09-25

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CC BY 4.0

Original authors: Dong Ha Lee, João Magueijo, Carsten van de Bruck, Eleonora Di Valentino

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 mysterious force called dark energy, often modeled as a cosmological constant. This concept suggests that empty space itself possesses an inherent energy that pushes galaxies apart. However, this idea faces a profound theoretical problem: calculations of the energy expected from empty space predict a value vastly larger than what we actually observe. Furthermore, recent measurements of the universe's expansion rate have revealed persistent disagreements between what we see in the early cosmos and what we measure in the nearby universe. These tensions have led physicists to wonder if the standard model of cosmology is missing something fundamental, perhaps a flaw in how we understand gravity itself or how energy behaves on the largest scales.

A new study by researchers at the University of Sheffield and Imperial College London explores a radical alternative to the standard model. Instead of assuming that empty space pushes the universe apart, they investigate a theory where gravity and thermodynamics are deeply linked. In this framework, the equations that describe gravity are modified so that the vacuum energy of empty space does not contribute to gravity at all. More importantly, the theory allows for a controlled violation of the law of energy conservation. In the standard view, energy cannot be created or destroyed, but in this thermogravity model, the universe can generate energy density over time without creating momentum. The researchers asked a simple question: if the universe can create energy on its own, could that process alone drive the observed acceleration, eliminating the need for a cosmological constant entirely?

To answer this, the team tested two versions of this theory against real astronomical data. The first version, called the universal model, assumed that this energy creation happens for all forms of matter and light equally. When they compared this model to observations of distant supernovae and the large-scale structure of the universe, the results were stark. The universal model failed to fit the data. It created a rigid trade-off: to match the expansion rate seen in the middle of the universe's history, the model had to predict a current acceleration that was too weak to match what we see today. The data strongly disfavored this idea, showing that a simple, universal creation of energy cannot explain the cosmos as we observe it.

The researchers then turned to a more nuanced version of the theory, where this energy creation is restricted only to cold dark matter, the invisible substance that holds galaxies together. In this scenario, ordinary matter, light, and neutrinos behave exactly as they do in the standard model, while only the dark matter sector gains energy over time. This approach proved much more successful. When tested against the same astronomical data, this model provided a better fit than the standard cosmological constant model. The improvement was statistically significant, with the data favoring this new explanation over the old one by a margin that suggests a genuine preference for the theory. The model works by slightly slowing down the expansion rate in the past relative to the standard model, which aligns better with the distances measured to faraway galaxies.

However, the story does not end with a simple victory for the new theory. While the dark-matter-only version fits the expansion history better, it does not solve the other major puzzle plaguing cosmology: the Hubble tension. This tension arises because measurements of the universe's expansion rate from the early universe disagree with measurements from the nearby universe. When the researchers used data from the early universe to calibrate their model, the result was that the predicted expansion rate for today dropped even lower, making the disagreement with nearby measurements worse rather than better. The new theory successfully describes how the universe expands, but it does not yet resolve the conflict between different ways of measuring that expansion.

The study concludes that while a universal creation of energy is likely not the answer, a version where only dark matter participates in this process remains a viable and compelling possibility. It offers a concrete, testable alternative to the standard model that improves our description of cosmic history without adding extra parameters. The researchers emphasize that this is only a first step, focusing on the smooth, large-scale background of the universe. The true test will come when scientists can apply this theory to the clumpy, fluctuating structures of the cosmos, such as the cosmic microwave background and the growth of galaxy clusters. Until then, the idea that dark matter might be slowly gaining energy from the fabric of spacetime itself stands as a serious contender in the quest to understand why the universe is accelerating.

Technical Summary: Testing Cosmic Acceleration from Thermogravity without Vacuum Energy

Problem Statement
The standard $\Lambda$ CDM model successfully describes the observed Universe but relies on the cosmological constant $\Lambda$ , whose physical origin remains obscure (the old cosmological constant problem) and which is not observed to gravitate with its natural quantum field magnitude. Furthermore, persistent tensions exist between early- and late-Universe probes, particularly regarding the Hubble parameter $H_0$ and the amplitude of late-time structure. This paper investigates an alternative framework where late-time acceleration is generated not by a dark energy sector or vacuum energy, but by controlled violations of energy-momentum conservation arising from a "thermogravity" theory. In this framework, the Einstein equations are restricted to their trace-free form, rendering vacuum energy gravitationally inactive, while energy non-conservation prevents the reinstatement of $\Lambda$ as an integration constant. The central question is whether such non-conservation can solely drive cosmic acceleration without introducing extra background parameters relative to flat $\Lambda$ CDM.

Methodology
The authors analyze two specific implementations of the thermogravity theory derived in Ref. [18], focusing exclusively on the homogeneous background level to avoid the complexities of perturbations in a theory with broken local Lorentz and diffeomorphism invariance.

Universal Model: In this minimal benchmark, all matter species (baryons, photons, CDM) participate in the energy non-conservation. The violation is governed by a length scale $L^2$ . The authors note that a universal violation modifies the "observational dictionary" itself (e.g., definitions of redshift, luminosity distance, and standard rulers), making a self-consistent background analysis difficult. Consequently, they test this model using standard Type Ia supernova (SNe) distances and uncalibrated Baryon Acoustic Oscillation (BAO) measurements, acknowledging that the exclusion of this model under standard assumptions may not rule out the broader theory.
CDM-Only Model ( $\xi$ CDM): To achieve a self-contained analysis, the authors restrict the non-conservation violation to the Cold Dark Matter (CDM) sector only. Baryons, photons, and neutrinos follow standard conservation laws. This preserves the standard operational meaning of SNe redshifts, luminosities, Big Bang Nucleosynthesis (BBN) constraints, and the BAO ruler at the background level. The model is treated as a one-parameter extension of $\Lambda$ CDM, where the parameter $\xi_c \equiv 1/(H_0 L^2)$ quantifies the strength of CDM energy creation.

The analysis employs Markov Chain Monte Carlo (MCMC) methods using the Cobaya sampler. Datasets include:

SNe Ia: DES Year 5 (DD) and Pantheon+ (PP) samples.
BAO: DESI DR2 measurements (uncalibrated and calibrated).
Early-Universe Anchors: BBN constraints on baryon density ( $\omega_b$ ) and compressed CMB likelihoods (Planck 2018) for the sound horizon angle $\theta_s$ .
Distance Ladder: $H_0$ constraints from SH0ES and $H_0$ DN.

For the $\xi$ CDM model, the authors introduce an "effective" CDM density ( $\omega_c^{\text{eff}}$ ) to correctly calibrate the sound horizon ( $r_{\text{drag}}$ ) and recombination epoch, accounting for the fact that CDM density in the past differs from the standard $a^{-3}$ evolution.

Key Contributions and Results

Universal Model: The universal implementation is strongly disfavoured by background data. While SNe data alone can be accommodated, the inclusion of DESI BAO measurements drastically worsens the fit ( $\Delta\chi^2 \simeq 51$ relative to $\Lambda$ CDM). The model exhibits an intrinsic rigidity: increasing the matter density $\Omega_m$ to match intermediate-redshift BAO normalization simultaneously increases the present deceleration parameter ( $q_0 = -1 + 3\Omega_m/2$ ), thereby weakening the current acceleration required by low-redshift SNe. The authors caution that this exclusion applies to the standard application of the observational dictionary to a universal theory, not necessarily to the thermogravity framework itself, as the dictionary would require rederivation in a fully universal scenario.
$\xi$ CDM Model: The CDM-only model provides a systematically improved fit to the background datasets considered.
- Fit Quality: It achieves a reduction in $\chi^2$ of $\Delta\chi^2 = -4.85$ (approx. $2.2\sigma$ ) relative to $\Lambda$ CDM for certain dataset combinations (e.g., DD+DESI).
- Bayesian Evidence: The model shows positive Bayesian preference, with a maximum $\ln B = 2.77$ (approx. $2.9\sigma$ ) for the DD+DESI combination.
- Mechanism: The improvement arises because the non-conservation suppresses the expansion rate $H(z)$ in the past relative to $\Lambda$ CDM, allowing for a better fit to the observed distance-redshift relation.
- Hubble Tension: Crucially, the model does not resolve the Hubble tension. When the BAO ruler is calibrated using early-Universe information (BBN or CMB), the reduced effective early-time CDM density increases the sound horizon ( $r_{\text{drag}}$ ). Since uncalibrated distances tightly constrain the product $r_{\text{drag}}h$ , this forces $H_0$ to lower values, thereby increasing the tension with distance-ladder calibrations (e.g., SH0ES).

Significance and Claims
The paper claims to present the first background-level observational test of the thermogravity scenario proposed in Ref. [18]. Its primary significance lies in distinguishing between the viability of different implementations of the theory:

Formal Benchmark: The universal model serves as a formal benchmark. Its strong disfavor under standard assumptions highlights the tension between universal matter creation and the observed expansion history, but the authors emphasize this is not a complete physical exclusion of universal thermogravity, as the theory would fundamentally alter the observables used to test it.
Viable Alternative: The CDM-only implementation ( $\xi$ CDM) is identified as a viable, self-contained, and competitive target for future analysis. It offers a concrete mechanism to improve the fit to background expansion data without adding extra parameters beyond $\Lambda$ CDM.
Limitations: The authors explicitly state that these results are provisional. The analysis is restricted to the homogeneous background because the breaking of local Lorentz invariance makes the choice of frame physically relevant for perturbations. A definitive assessment requires a dedicated perturbative treatment of the CMB, weak lensing, and structure growth, which is deferred to future work.

In conclusion, the paper demonstrates that while a standard application of thermogravity is inconsistent with current background data, restricting energy non-conservation to the dark sector provides a phenomenologically successful extension of $\Lambda$ CDM that improves the fit to expansion history data, though it fails to alleviate the $H_0$ tension.

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