Scalar-tensor theories and modified gravity in the wake of GW170817 (1711.07403v2)

Abstract: Theories of dark energy and modified gravity can be strongly constrained by astrophysical or cosmological observations, as illustrated by the recent observation of the gravitational wave event GW170817 and of its electromagnetic counterpart GRB 170817A, which shows that the speed of gravitational waves, $c_g$, is the same as the speed of light, within deviations of order $10^{-15}$. This observation implies very severe restrictions on scalar-tensor theories, in particular theories whose action depends on second derivatives of a scalar field. Working in the very general framework of Degenerate Higher-Order Scalar-Tensor (DHOST) theories, which encompass Horndeski and Beyond Horndeski theories, we present the DHOST theories that satisfy $c_g=c$. We then examine, for these theories, the screening mechanism that suppresses scalar interactions on small scales, namely the Vainshtein mechanism, and compute the corresponding gravitational laws for a non-relativistic spherical body. We show that it can lead to a deviation from standard gravity inside matter, parametrized by three coefficients which satisfy a consistency relation and can be constrained by present and future astrophysical observations.

• The paper constrains DHOST and scalar-tensor modified gravity models by leveraging GW170817’s precise gravitational wave speed measurement.
• Detailed analysis narrows the parameter space for dark energy theories through rigorous examination of the Vainshtein mechanism in non-relativistic spherical contexts.
• Observable deviations in gravitational laws and consistency among dimensionless coefficients offer actionable insights for future astrophysical tests.

Scalar-Tensor Theories and Modified Gravity Constraints Post-GW170817

The paper by Langlois et al. discusses the implications of the gravitational wave event GW170817 on various scalar-tensor theories within the framework of modified gravity. The observation of GW170817, coupled with its electromagnetic counterpart GRB 170817A, provides an extremely precise measurement indicating that the speed of gravitational waves coincides with the speed of light, with deviations constrained to less than a few parts in 10^-15. This finding has significant implications for theories of dark energy and modified gravity, particularly those wherein predictions deviate from this speed equivalence.

Constraints on Scalar-Tensor Theories

Scalar-tensor theories have been a focus in the search for theoretical models that deviate from general relativity. These deviations are commonly motivated by the need to explain dark energy and cosmic acceleration. The broad class of Degenerate Higher-Order Scalar-Tensor (DHOST) theories extends traditional families such as Horndeski and Beyond Horndeski theories. These are characterized by actions involving second derivatives of a scalar field and have been appreciated for allowing a single scalar degree of freedom via careful degeneracy conditions.

The paper revisits the viability of scalar-tensor theories in light of GW170817. It systematically identifies which DHOST theories remain plausible under the condition that the speed of gravitational waves equals the speed of light. The analysis reveals that while many DHOST theories are restricted, a subclass satisfying the stringent condition on speed includes Lagrangian terms dependent on four arbitrary functions. Such scalar-tensor theories can potentially accommodate the stringent conditions outlined by observational data.

Vainshtein Mechanism

The Vainshtein mechanism is a pivotal component in many modified gravity frameworks, allowing standard gravity to be recovered at small scales while permitting deviations at cosmic scales. The paper explores this mechanism within DHOST theories that satisfy the speed condition. Through detailed calculations involving a non-relativistic spherical object, the authors derive modified gravitational laws that show characteristic deviations from standard gravity inside matter.

Such deviations are quantified concerning three dimensionless coefficients, which are functionally related to the theoretical parameters in the DHOST Lagrangian. These parameters, through the screening effect of the Vainshtein mechanism, suggest potential observable consequences to be tested by future astrophysical observations. The identified consistency relation among these coefficients provides a crucial check on the internal mathematical coherence of the theories.

Implications and Future Prospects

The analysis contributes valuable insights into the development of modified gravity theories post-GW170817. The paper highlights how scalar-tensor theories should be systematically confronted with astrophysical observations to ensure their viability. This effort extends beyond Horndeski theories and positions DHOST theories as a promising landscape for theoretical exploration.

For future work, constraints on model parameters will likely be sharpened through more detailed observation efforts, including gravitational lensing and studies of compact objects like neutron stars. Such observations have the potential to either verify or exclude certain parameter regimes, further refining the understanding of gravity's behavior beyond Einstein’s General Relativity.

The implications of these viable DHOST theories reach into both theoretical paradigms and practical observation strategies, underscoring the rich interplay between gravitational physics and cosmology. The ongoing convergence of theoretical predictions and empirical data is integral to the advancement of understanding in this field.