A systematic approach to generalisations of General Relativity and their cosmological implications

By Lavinia Heisenberg. Physics reports, 2018

446 citations recorded by the source corpus.

A century ago, Einstein formulated his elegant and elaborate theory of General Relativity, which has so far withstood a multitude of empirical tests with remarkable success. Notwithstanding the triumphs of Einstein's theory, the tenacious challenges of modern cosmology and of particle physics have motivated the exploration of further generalised theories of spacetime. Even though Einstein's interpretation of gravity in terms of the curvature of spacetime is commonly adopted, the assignment of geometrical concepts to gravity is ambiguous because General Relativity allows three entirely different, but equivalent approaches of which Einstein's interpretation is only one. From a field-theoretical perspective, however, the construction of a consistent theory for a Lorentz-invariant massless spin-2 particle uniquely leads to General Relativity. Keeping Lorentz invariance then implies that any modification of General Relativity will inevitably introduce additional propagating degrees of freedom into the gravity sector. Adopting this perspective, we will review the recent progress in constructing consistent field theories of gravity based on additional scalar, vector and tensor fields. Within this conceptual framework, we will discuss theories with Galileons, with Lagrange densities as constructed by Horndeski and beyond, extended to DHOST interactions, or containing generalized Proca fields and extensions thereof, or several Proca fields, as well as bigravity theories and scalar-vector-tensor theories. We will review the motivation of their inception, different formulations, and essential results obtained within these classes of theories together with their empirical viability.

Subfields: Astronomy and Astrophysics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/b6609a35bc5fc40ce44b9b5be860b0c2e9163267

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Citations in the corpus

Horndeski theory and beyond: a review (2019, background): “For a more comprehensive review including other types of modified gravity, see [13, 14].”
The Geometrical Trinity of Gravity (2019, background): “It is then convenient to recall at this point that a spacetime can be endowed with a metric and an affine structure [1] determined by a metric tensor gμν and a connection Γμν , respectively.”
Teleparallel theories of gravity: illuminating a fully invariant approach (2018, background): “Although Einstein’s General Theory of Relativity (GR) is well studied and tested in many settings [1], alternative theories of gravity continue to be of considerable interest [2– 6].”
Stellar structure models in modified theories of gravity: Lessons and challenges (2019, background): “for Born-Infeld inspired modifications of gravity [63], and Heisenberg for theories based on additional scalar, vector, and tensor fields and their cosmological implications [64].”