Unimodular Gravity and Cosmological Theories

Unimodular gravity is a variant of Einstein’s general theory of relativity in which the determinant of the spacetime metric is fixed, decoupling the cosmological constant from vacuum energy. At the classical level it reproduces the same field equations as general relativity except that the cosmological term appears as an integration constant. This feature offers a new angle on the long-standing cosmological constant problem, suggesting mechanisms that shield vacuum fluctuations from gravitating. Extensions of unimodular ideas appear in formulations based on trace-free field equations, transverse diffeomorphism invariance and teleparallel geometries, each preserving local energy–momentum conservation while altering the symmetry structure of the theory. In parallel, cosmological applications explore how these modifications influence the early universe, dark energy and dark matter: models with extra scalar degrees of freedom can mimic a perfect fluid with time-dependent equation of state or induce nonsingular bounces that avert the big bang singularity. Advances in Hamiltonian methods, quantum path integral treatments and phenomenological perturbations further connect unimodular frameworks to broader scalar-tensor and Horndeski theories, underscoring their role in the quest for a consistent quantum theory of gravity and a deeper understanding of cosmic acceleration.

Research from Nature Portfolio

No recent Nature Portfolio content available.

Unimodular Gravity and Cosmological Theories publication trend

The graph below shows the total number of articles in unimodular gravity and cosmological theories across all publications each year (not limited to Nature Index journals).

Technical terms

Unimodular gravity: A theory of gravitation fixing the determinant of the metric tensor, yielding Einstein’s equations with the cosmological constant as an integration constant.

Cosmological constant: A term in the gravitational field equations representing uniform energy density of empty space, often associated with dark energy.

Diffeomorphism invariance: Symmetry under smooth coordinate transformations, a foundational property of general relativity and its variants.

Symmetric teleparallelism: A geometric framework in which gravity is described by a flat, torsionless connection, offering alternative formulations to curved spacetime.

Horndeski interactions: The most general class of scalar–tensor couplings leading to second-order field equations, widely studied in modified gravity and cosmology.

Raychaudhuri equation: A fundamental relation in cosmology governing the evolution of the expansion rate of a congruence of worldlines, instrumental in singularity theorems.

Cosmic bounce: A scenario in which the early universe undergoes a contraction phase followed by a non-singular rebound, circumventing the initial singularity of standard cosmology.

References

1. Multi-field TDiff theories for cosmology. Physics of the Dark Universe (2025).
2. Introduction to Hamiltonian formulation of general relativity and homogeneous cosmologies. SciPost Physics Lecture Notes (2023).
3. A class of ghost-free theories in symmetric teleparallel geometry. Journal of High Energy Physics (2024).
4. Cosmological constant as an integration constant. European Physical Journal C (2024).
5. Friedmann equations and cosmic bounce in a modified cosmological scenario. Physics Letters B (2023).
6. A note on classical and quantum unimodular gravity. European Physical Journal C (2015).
7. Classical Weyl transverse gravity. European Physical Journal C (2017).