Could cosmic acceleration end? A dark energy preprint explores the possibility

What is being tested?

The standard cosmological model, called flat ΛCDM, combines a cosmological constant, Λ, with cold dark matter and other cosmic ingredients. The cosmological constant has an unchanging energy density and leads to continuing accelerated expansion in the distant future.

The researchers instead allow dark energy’s equation of state to evolve. This quantity, written as w, describes the ratio of pressure to energy density in the units used by the paper. A cosmological constant has w = −1. The authors call values below −1 the “phantom” regime and values above −1 the “quintessence” regime. These labels describe behavior in the model, not a detection of a particular substance or field.

The proposed sourced oscillatory model, abbreviated SO, allows w to oscillate around −1 while an additional mathematical term gradually shifts its behavior. That term depends on the cube of N = ln(a), where a is the scale factor—a measure of the Universe’s relative size, set to one today. Negative N describes the past; positive N describes the future. An increase of one in N is called an e-fold and represents a multiplication of the scale factor by approximately 2.72, not a fixed interval of time.

How temporary acceleration arises

In the SO equations, the cubic term eventually pushes w upward in the future. Dark energy then becomes increasingly dilute, and the model evolves from accelerated to decelerated expansion.

Under this extrapolation, the Hubble parameter, H, which measures the expansion rate relative to the Universe’s size, approaches zero. Expansion nevertheless continues without contraction, and the scale factor grows without bound.

The paper describes this limiting behavior as an “asymptotically static” Universe. This should not be read as a prediction that the Universe freezes at a finite size on a specified date. The result concerns the distant limit of the assumed equations, rather than an observed slowdown or a measured countdown to the end of acceleration.

Which observations were used?

The analysis combines Planck 2018 measurements of the cosmic microwave background—the relic radiation from the early Universe—with baryon acoustic oscillation measurements from DESI Data Release 2. Baryon acoustic oscillations are a characteristic distance pattern in cosmic structure that can be used as a ruler for studying expansion.

The researchers separately add three compilations of Type Ia supernova observations: Pantheon+, Union3 and DES-Dovekie. Supernova brightness measurements help constrain cosmic distances. Because these compilations overlap and use different calibration procedures, the authors do not treat them as three independent datasets to combine together.

They compare SO with flat ΛCDM and two other evolving-dark-energy descriptions. BellDE allows a bell-shaped excursion in w as a function of redshift. CPL, named after Chevallier, Polarski and Linder, uses two parameters to describe changes in w with scale factor. Redshift measures how much cosmic expansion has stretched light; higher redshift generally corresponds to earlier epochs.

What the statistical comparison found

The authors calculate Bayesian evidence, which assesses a model’s fit across its allowed parameter ranges rather than considering only its single best-fitting case. Their reported differences in natural-log evidence relative to ΛCDM are:

Positive values favor the evolving-dark-energy model; negative values favor ΛCDM. On the paper’s adopted interpretation scale, SO has inconclusive evidence for Pantheon+ and Union3, and weak support for DES-Dovekie.

BellDE receives the strongest support among the alternatives tested: weak support with Pantheon+ and moderate support with the other two compilations. None reaches the paper’s threshold for strong evidence. These comparisons apply to the specified models, parameter ranges and combined datasets; they are not a DESI-only determination of cosmic destiny.

The oscillation is not securely measured

The SO model’s inferred behavior depends on the supernova compilation. With Union3, its present-day equation of state is w = −0.778 ± 0.069, with a central 68% credible interval. With Pantheon+ and DES-Dovekie, the corresponding intervals include −1.

The oscillation frequency is also uncertain. For Pantheon+ and DES-Dovekie, its probability distribution is broad and has two peaks, meaning that substantially different frequencies remain compatible with the analysis. The authors caution that the observations constrain the oscillation amplitude more effectively than its period.

Across the evolving-dark-energy models, central estimates of today’s Hubble parameter range from about 66.0 to 67.84 kilometres per second per megaparsec. The ΛCDM fits give about 68.3 in the same units. The authors report that none of these alternatives alleviates the Hubble tension—the disagreement with the higher expansion rate inferred by SH0ES.

Assumptions limit the prediction

The calculation assumes a spatially flat Universe that is homogeneous and isotropic on large scales: statistically uniform, with no preferred direction. Matter, radiation and dark energy are assumed to obey separate energy-conservation equations.

For the statistical fits, the researchers fix the SO model’s mean equation of state at −1, its present-day slope with respect to N at zero, and the source coefficient to the present-day matter density parameter. They then vary two additional dark energy parameters: today’s w and the oscillation frequency. These are modeling choices, not independently established properties of dark energy.

The authors also acknowledge that the model lacks a fundamental microscopic explanation. Its treatment of small disturbances uses a numerical prescription designed to handle crossings of w = −1; that prescription does not itself identify the underlying physics.

The preprint therefore presents a conditional possibility: a changing dark energy model can fit current observations while predicting temporary acceleration. The reported evidence does not establish that oscillations exist or that cosmic acceleration must end.