One Field to Rule the Dark Sector: New Gravity Model Takes Aim at the Hubble Tension

Cosmology’s most stubborn problem may have just met its most ambitious challenger. In a paper published in The European Physical Journal C, a team of theoretical physicists led by Kimet Jusufi, with Amir A. Khodahami, Ahmad Sheykhi, Jackson Levi Said and Emmanuel N. Saridakis, has constructed a unified framework in which a single scalar field simultaneously drives dark energy, modifies the observed expansion rate of the universe, and eases the long-standing disagreement over the value of the Hubble constant. The work, which also weaves a massive vector field into the gravitational sector to play the role of dark matter, offers one of the most complete attempts yet to solve several cosmic mysteries with one set of equations.

The problem the authors set out to address is the so-called Hubble tension. When the Planck satellite measures the cosmic microwave background, the afterglow of the Big Bang, and interprets the data through the standard Lambda-CDM model, it infers a present-day expansion rate of about 67.4 kilometers per second per megaparsec. When astronomers in the SH0ES collaboration measure the same quantity directly using Cepheid variable stars and Type Ia supernovae in the local universe, they obtain roughly 73.0 in the same units. The two numbers disagree by far more than their combined uncertainties, and after a decade of increasingly precise measurements, the discrepancy can no longer be dismissed as a statistical fluke. Something, somewhere, is missing from our picture of the cosmos.

The new framework belongs to a class of theories known as scalar-vector-tensor gravity. In addition to the familiar spin-two graviton of general relativity, the gravitational sector contains a scalar degree of freedom, denoted by a dimensionless field Xi, and a massive vector field. The crucial ingredient is a conformal coupling: ordinary matter does not respond to the bare Einstein-frame metric but to a rescaled version of it, multiplied by the factor one plus Xi. Because atoms, rulers and clocks all live in this rescaled Jordan frame, the expansion rate that matter observers actually measure differs from the Einstein-frame rate. In the small-field regime relevant to the model, the observed Hubble rate receives an additive correction proportional to the scalar field’s velocity, meaning a slowly rolling scalar can systematically boost the expansion rate inferred at low redshift without touching the early universe.

Here the authors make a subtle but decisive observation that elevates the paper above many previous attempts. The Hubble constant itself is not a conformal invariant: it depends on which metric you quote it in. However, the acoustic angular scale measured by the cosmic microwave background, the ratio of the sound horizon at recombination to the comoving distance to the last-scattering surface, is exactly invariant under conformal transformations, because the conformal factor cancels between time and distance. This means the Hubble tension is a genuine physical discrepancy between invariants, not an artifact of bookkeeping, and it imposes a strict integral condition that any viable modification of the expansion history must satisfy. The team proves that a scalar field whose velocity keeps a single sign throughout cosmic history necessarily violates this condition, shifting the acoustic angle by about 2.5 percent, roughly eighty times the observational uncertainty.

The escape route is a two-epoch scalar evolution in which the field’s velocity changes sign. In the late universe, a positive scalar velocity enhances the observed Hubble rate toward the locally measured value of 73. Before recombination, an earlier component with the opposite sign drives the scalar field to a small positive value that freezes in, effectively rescaling the gravitational constant by about 2.4 percent during the acoustic era. This shrinks the sound horizon by just the right amount to compensate for the late-time enhancement, allowing the model to match the observed acoustic scale exactly while still delivering a present-day Hubble rate of 73 kilometers per second per megaparsec. Crucially, the microphysics of recombination is untouched: because particle masses are constant in the Jordan frame, hydrogen recombines at exactly the same temperature as in the standard model, and only the expansion rate at that epoch is altered.

The framework also enforces a constraint that simpler treatments would miss. Because the conformal coupling exchanges energy between matter and the scalar sector, the scalar is not separately conserved; its continuity equation carries a source term proportional to the baryon density. Where the early scalar velocity is negative, this term drains the scalar’s energy density as one looks back in time. Requiring the scalar energy density to remain positive at all epochs bounds the transition redshift of the early component to values below roughly 13, carving a well-defined window in the model’s parameter space. Even within that window, the authors are candid about costs: the total matter density emerges as an output rather than an input and lands slightly above the Planck-preferred value, and residual deviations of a few percent remain in baryon acoustic oscillation observables at intermediate redshifts, larger than current DESI uncertainties.

Perhaps the most striking feature is that the same scalar field doubles as a dynamical dark-energy sector. Its self-interaction potential, reconstructed self-consistently from the expansion history rather than assumed in advance, reproduces the late-time accelerated expansion, with a characteristic energy scale of about one millielectronvolt to the fourth power. The model predicts a present-day dark-energy equation-of-state parameter that deviates from minus one at the level of roughly one percent, with the deviation tied directly to the same quantity that controls the Hubble enhancement. This is a falsifiable correlation: future measurements of the time evolution of dark energy, of the kind now being pursued by the Dark Energy Spectroscopic Instrument, whose latest results already mildly favor evolving dark energy, will directly test whether this link holds.

The vector sector completes the unified dark sector with two distinct contributions. The temporal component of the massive vector field is not a propagating particle at all but an auxiliary variable fixed algebraically by the conserved baryon number current. Its energy is an apparent, matter-like contribution to the background expansion, a manifestation of interaction energy rather than a true fluid, locked to the baryons and unable to cluster independently. The propagating spatial modes, by contrast, can form a coherent condensate that, when the vector mass greatly exceeds the Hubble rate, oscillates rapidly and time-averages into a collisionless, pressureless component scaling exactly like cold dark matter. Unlike the baryon-locked interaction energy, this condensate clusters on its own and can supply the non-oscillating gravitational wells that the observed acoustic peak structure demands, its abundance set by primordial initial conditions.

One formidable obstacle remains: local gravity tests. An unscreened scalar with the order-unity coupling adopted in the numerical analysis would renormalize Newton’s constant by fifty percent in the Solar System, grossly violating the Cassini constraint on light deflection. The authors show that a chameleon-type screening mechanism, in which the scalar acquires a large effective mass in dense environments and becomes short-ranged, is essential rather than optional, and that for the chosen normalization it requires the scalar potential to contain a runaway piece. Alternatively, the coupling can be weakened by pushing the mass scale two hundred times beyond the Planck mass, a rescaling the background cosmology accommodates without changing its predictions. Either way, the survival of the model hinges on screening physics that must be verified in realistic astrophysical settings.

The authors are appropriately measured about what they have achieved. Matching the acoustic scale exactly is by construction, not prediction; what is nontrivial is that a consistent solution exists at a fixed high Hubble constant with only a modest pre-recombination gravitational shift. A full statistical confrontation with cosmic microwave background priors, baryon acoustic oscillations, supernovae and growth-of-structure data, together with a complete perturbation analysis in a Boltzmann code, is the necessary next step. But if the framework survives that scrutiny, cosmology may have gained something remarkable: a single gravitational extension in which dark energy, dark matter and the Hubble tension are not three separate puzzles, but three faces of one underlying field.

Subject of Research: A scalar-vector-tensor gravity model that unifies the dark sector and alleviates the Hubble tension through conformal scalar coupling and a vector condensate acting as cold dark matter.

Article Title: Unified dark sector and Hubble-tension alleviation in scalar–vector–tensor gravity

Article References: Jusufi, K., Khodahami, A. A., Sheykhi, A., Said, J. L., & Saridakis, E. N. (2026). Unified dark sector and Hubble-tension alleviation in scalar–vector–tensor gravity. The European Physical Journal C, 86(10), Article 1149. https://doi.org/10.1140/epjc/s10052-026-16406-4

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-16406-4

Keywords: Hubble tension, dark energy, dark matter, scalar-tensor gravity, vector field, cosmology, conformal coupling, cosmic microwave background, Lambda-CDM, modified gravity, recombination, DESI