A systematic approach to generalisations of General Relativity and their cosmological implications (1807.01725v1)

Abstract: 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.

• The paper presents a systematic evaluation of modified gravity theories that extend General Relativity to resolve cosmological challenges.
• It details methodologies including scalar-tensor, massive gravity, and vector field frameworks, emphasizing their theoretical consistency and empirical tests.
• The research outlines future directions such as using AI to explore vast parameter spaces and improve analyses of cosmological datasets.

A Systematic Approach to Modifications of General Relativity

The paper "A systematic approach to generalisations of General Relativity and their cosmological implications" by Lavinia Heisenberg presents a comprehensive review of various attempts to modify General Relativity (GR) in response to theoretical and empirical challenges in modern cosmology. Notwithstanding GR's successes since its inception, the need to address issues like the cosmological constant problem, the nature of dark energy, and quantum gravity has driven the exploration of alternative gravitational theories. This paper evaluates several extensions of GR, focusing on their theoretical consistency and empirical viability.

Overview of General Relativity and Its Limitations

General Relativity, formulated by Einstein, interprets gravity as the curvature of spacetime due to energy and momentum. Despite its empirical triumphs, GR faces significant theoretical challenges: it cannot naturally accommodate the small observed value of the cosmological constant and its classical framework cannot be straightforwardly reconciled with quantum mechanics. Additionally, the standard model of cosmology, which combines GR with the cosmological principle, relies on several poorly understood components like dark energy, dark matter, and inflation.

Modified Gravity Theories

The paper examines several frameworks that extend GR by introducing additional fields or modifying the underlying geometrical structure:

1. Scalar-Tensor Theories: These involve additional scalar fields besides the tensor field of GR. Notably, Horndeski theories, which are the most general scalar-tensor theories with second-order field equations, are explored. They naturally extend the idea of scalar fields being responsible for dark energy and inflation.
2. Massive Gravity: This involves giving the graviton a mass, which alters gravitational interactions on large scales and could potentially address the cosmological constant problem. The dRGT (de Rham-Gabadadze-Tolley) model constructs a ghost-free massive graviton theory with a specific structure to avoid instabilities.
3. Generalized Proca and Multi-Proca Theories: By introducing vector fields, these theories extend Proca's massive vector field theory. The generalized Proca theories relax gauge invariance to construct higher-order derivative interactions free from ghost instabilities, while multi-Proca theories generalize this to multiple interacting vector fields.
4. DHOST and Beyond Horndeski Theories: These push beyond the restrictions of Horndeski theories, allowing for higher-order derivatives in field equations while maintaining the absence of Ostrogradsky ghost instabilities.
5. Bigravity: A theory in which two interacting metric tensors are considered, allowing for novel interactions between them, which can lead to a richer phenomenology, particularly in cosmological contexts.

Empirical Viability and Future Directions

The paper underscores the importance of empirical viability for modified gravity theories. Constraints from laboratory tests, solar system experiments, gravitational wave observations, and cosmological data (such as the Cosmic Microwave Background and large-scale structure) place stringent limits on deviations from GR.

Heisenberg speculates that future developments in AI might further optimize the exploration of vast parameter spaces in modified gravity models or improve the analysis of complex datasets crucial for testing these theories.

In conclusion, while GR remains the cornerstone of our understanding of gravity, a myriad of theoretical developments continues to refine or potentially supplement its framework in pursuit of resolving its limitations. This paper manages to encapsulate a detailed landscape of such theories, providing clarity on their theoretical and empirical aspects, and setting the stage for future advancements in understanding gravity's role in the cosmos.