Effective Field Theories of Dark Energy and Modified Gravity

Effective Field Theory (EFT) has emerged as a unifying framework to describe the accelerated expansion of the universe and possible deviations from general relativity on cosmic scales. By organising physical effects according to their relevance at different energy or curvature scales, EFT allows cosmologists to parametrise a broad class of scalar-tensor, vector-tensor and more exotic models in terms of a handful of time-dependent operators and coupling functions. In this approach, cosmic acceleration is attributed to a dynamical field or a modification of the gravitational sector, whose low-energy behaviour is captured by an effective Lagrangian expanded around a homogeneous background. This formalism naturally incorporates screening mechanisms that reconcile long-range modifications with stringent tests of gravity in the Solar System, and it provides a systematic way to compute linear perturbations, determine stability criteria and identify observational signatures in the cosmic microwave background, large-scale structure and gravitational waves. The observation of the coincident electromagnetic counterpart to a neutron-star merger has, for example, placed tight bounds on the speed of tensor modes, ruling out large classes of models. Current theoretical efforts focus on mapping EFT parameters to covariant actions—such as Horndeski and beyond-Horndeski theories—while refining predictions for forthcoming surveys. By bridging model building and observation, EFT of dark energy and modified gravity offers a coherent language to probe the physics driving cosmic acceleration and to test Einstein’s theory in novel regimes.

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Effective Field Theories of Dark Energy and Modified Gravity publication trend

The graph below shows the total number of articles in effective field theories of dark energy and modified gravity across all publications each year (not limited to Nature Index journals).

Technical terms

Effective Field Theory: A framework that organises physical phenomena by energy scale, capturing low-energy effects of a theory through an expansion of relevant operators.

Scalar-tensor theory: A class of gravity theories that introduce one or more scalar fields coupled to the metric tensor to drive cosmic acceleration or modify gravitational interactions.

Horndeski Lagrangian: The most general four-dimensional scalar-tensor action with second-order field equations, avoiding Ostrogradski instabilities.

Kinetic Gravity Braiding: A mechanism in scalar-tensor theories where kinetic terms mix scalar and metric derivatives, affecting the propagation of perturbations.

Screening mechanism: A process by which modifications of gravity are suppressed in high-density environments, ensuring agreement with local tests.

Line Intensity Mapping: An observational technique that measures the integrated emission of spectral lines across large volumes, tracing matter distribution over wide redshifts.

References

1. Dark energy with a shift-symmetric scalar field: Obstacles, loophole hunting and dead ends. Physics of the Dark Universe (2024).
2. Probing Dark Energy and Modifications of Gravity with Ground-based millimeter-wavelength Line Intensity Mapping. The Astrophysical Journal (2024).
3. Testing the speed of gravity with black hole ringdowns. Physical Review D (2023).
4. Cosmological constraints on Horndeski gravity in light of GW170817. Journal of Cosmology and Astroparticle Physics (2018).