Gauss-Bonnet Gravity and Dark Energy Cosmology

Gauss–Bonnet gravity introduces a curvature-squared invariant into the gravitational action, extending Einstein’s theory while preserving second-order field equations when coupled to a scalar field. In four dimensions this term becomes dynamically relevant through non-minimal scalar couplings, offering rich phenomenology across cosmic epochs. Within dark energy cosmology, scalar–Gauss–Bonnet models can emulate a cosmological constant, generate effective phantom behaviour without pathological instabilities and moderate future singularities. The additional curvature coupling also interacts with higher-dimensional scenarios, potentially stabilising extra dimensions and influencing the late-time acceleration rate. Observational bounds on the speed of gravitational waves and precision measurements of cosmic expansion impose stringent conditions on the form and strength of the coupling function and scalar potential, yet viable regions of parameter space remain that can accommodate both early inflationary dynamics and present-day accelerated expansion. The interplay between curvature corrections and scalar dynamics thus provides a globally significant framework for testing gravity beyond general relativity and for unravelling the nature of dark energy.

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Gauss-Bonnet Gravity and Dark Energy Cosmology publication trend

The graph below shows the total number of articles in gauss-bonnet gravity and dark energy cosmology across all publications each year (not limited to Nature Index journals).

Technical terms

Gauss–Bonnet term: A combination of quadratic curvature invariants (R² – 4RₘₙRᵐⁿ + RₘₙᵣₛRᵐⁿᵣˢ) that modifies gravitational dynamics when coupled to a scalar field.

Dark energy: A form of energy with negative pressure responsible for the observed accelerated expansion of the Universe.

Phantom fluid: A hypothetical dark energy component whose equation-of-state parameter w < –1, leading to super-accelerated cosmic expansion and potential future singularities.

Gravitational-wave speed: The propagation speed of tensor perturbations in spacetime, observationally constrained to equal the speed of light within extremely tight bounds.

Horndeski theory: The most general scalar–tensor theory with second-order field equations, encompassing Gauss–Bonnet couplings as a special case.

References

1. Isotropic compact stars in four-dimensional Einstein–Gauss–Bonnet gravity coupled with scalar field: reconstruction of model. European Physical Journal C (2023).
2. Revisiting Einstein-Gauss-Bonnet theories after GW170817. Physics Letters B (2024).
3. Einstein-Gauss-Bonnet Gravity with Extra Dimensions. Galaxies (2019).
4. The fate of (phantom) dark energy universe with string curvature corrections. Physics Letters B (2005).