Nonlocal MOND Model Interpolates Between Cosmology and Gravitationally Bound Systems, Reproducing Dark Matter Phenomena

Modifications to gravity offer potential explanations for both the missing mass inferred from galactic rotation curves and the accelerated expansion of the universe, yet reconciling these observations remains a significant challenge. C. Deffayet and R. P. Woodard demonstrate a novel theoretical model that successfully bridges the gap between these seemingly disparate phenomena, offering a single framework to explain both cosmological observations and the behaviour of gravitationally bound systems. The researchers achieve this by constructing a nonlocal modification of gravity, where corrections to the gravitational stress tensor evolve nonperturbatively, potentially persisting from the early universe to the present day. This work represents a substantial step forward, providing a unified approach to understanding dark matter and dark energy without invoking exotic, unseen particles.

The study establishes a timelike vector field, derived from a scalar field, governed by a first-order equation with specific initial conditions, linking it to the energy density of a dark matter-like component. Solving for the scalar field’s time derivative yields an equation that uniquely determines its value at any given time and location, dependent on the underlying spacetime geometry. To model the energy density of this dark matter component, researchers employed the principle of energy conservation, leading to a first-order equation that governs its evolution.

This equation is coupled with the scalar field equation and initialized with a nearly homogeneous energy density, reflecting the conditions present in the early universe. Perturbations in this initial density are driven by primordial fluctuations, mirroring the seeds of structure formation. The initial energy density is set to a value consistent with replacing cold dark matter, providing a natural explanation for the observed abundance of dark matter in the universe.

Nonlocal Gravity Explains Galaxy Dynamics and Cosmology

Scientists have developed a model that successfully accounts for both cosmological observations traditionally explained by dark matter and the dynamics of gravitationally bound systems, such as galaxies, without invoking the existence of dark matter particles. This work establishes a single framework that unifies these two regimes, previously addressed by separate models, and delivers a nonlocal modification of gravity. The core of this achievement lies in constructing a timelike vector field, defined by a scalar field, which obeys a first-order equation with specific initial conditions, and linking it to the energy density of a dark matter-like component. The team demonstrated that the energy density is uniquely determined as a function of the spacetime geometry through a first-order equation derived from the conservation of energy.

Initial conditions were set to produce a nearly homogeneous energy density, with perturbations mirroring primordial density fluctuations, and a magnitude consistent with replacing cold dark matter. This model automatically recovers the observed spectrum of anisotropies in the cosmic microwave background radiation, baryon acoustic oscillations, and the formation of large-scale structure. Measurements confirm that the model’s success stems from a numerical coincidence between the Hubble constant and Milgrom’s constant, a key parameter in Modified Newtonian Dynamics.

Unified Gravity Model Explains Cosmic Observations

This research presents a novel model of gravity that successfully addresses both cosmological observations and the dynamics of gravitationally bound systems, such as galaxies, without invoking dark matter. Scientists developed a framework where modifications to gravity arise from corrections to the gravitational stress tensor, becoming significant during the early universe’s inflationary period and potentially persisting to the present day. The model achieves a unified description, seamlessly transitioning between regimes that previously required separate explanations for cosmological phenomena and galactic behavior. This approach offers a compelling alternative to the standard cosmological model.

The core achievement lies in formulating a single set of equations that accurately reproduces the observed cosmic microwave background radiation, baryon acoustic oscillations, and the large-scale structure of the universe, while simultaneously accounting for the observed rotation curves of galaxies. This is accomplished through a nonlocal modification of gravity, where the energy density is determined as a unique function of the spacetime geometry, governed by a first-order equation. Notably, the model incorporates a numerical coincidence between the Hubble constant and Milgrom’s constant, a key parameter in Modified Newtonian Dynamics, further strengthening its explanatory power. The authors acknowledge that the model relies on the persistence of effects originating in the early universe and that further investigation is needed to fully understand its implications for structure formation.

Future research will likely focus on refining the model’s predictions and testing them against increasingly precise observational data. The team intends to explore the model’s behavior in more complex scenarios and investigate potential connections to other modified gravity theories. However, the current work represents a significant step towards a more complete and self-consistent understanding of gravity and its role in shaping the universe.