k-Mouflage gravity

Abstract: We introduce a large class of scalar-tensor theories where gravity becomes stronger at large distances via the exchange of a scalar that mixes with the graviton. At small distances, i.e. large curvature, the scalar is screened via an analog of the Vainshtein mechanism of massive gravity. The crossover distance between the two regimes can be made cosmological by an appropriate choice of the parameters.

• The paper introduces a novel scalar-tensor framework that modifies gravitational interactions on cosmological scales.
• It employs a screening mechanism similar to the Vainshtein approach to ensure that General Relativity is recovered in high-curvature regions.
• Numerical analyses reveal a clear transition at the Vainshtein radius, offering a potential explanation for cosmic acceleration without dark energy.

An Examination of k-Mouflage Gravity

The paper under discussion presents a novel class of scalar-tensor theories designated as k-Mouflage gravity. This framework introduces modifications to gravity at cosmological scales by employing a scalar field that interacts with the graviton, thereby enhancing gravitational interactions at large distances. The methodological approach involves screening the scalar field at small distances through a mechanism akin to Vainshtein's approach in massive gravity models. Consequently, the transition between these behavioral regimes occurs at a distance that can be tailored to coincide with cosmological scales.

Theoretical Context and Framework

k-Mouflage gravity is contextualized within a broader spectrum of modified gravity theories that aim to address phenomena such as the Universe's accelerating expansion without invoking dark energy. Among these theories are the Dvali-Gabadadze-Porrati (DGP) model and various extensions like the Chameleon and $f(R)$ models. In modifying General Relativity (GR) at large scales, one of the primary challenges is preserving empirical concordance with GR predictions in the solar system and other high-curvature environments.

The foundation of k-Mouflage gravity lies in scalar-tensor frameworks that naturally extend the derivative interactions seen in the decoupling limit of massive gravity. This approach allows the scalar field to decouple in strong gravitational fields, thereby mitigating deviations from GR in dense regions, akin to the Vainshtein mechanism. The specific action proposed incorporates these derivative interactions to enable large distance gravitational modification while ensuring conventional GR results in smaller scale, strong-field regimes.

Model Specification and Dynamics

In constructing this class of theories, the paper details a scalar-tensor action that parallels the decoupling limit formulation in nonlinear massive gravity. It explores various viable forms for scalar field self-interactions (denoted $H(\phi)$), encoding different specific models such as Chameleon gravity, K-essence, and the Galileon model, among others. The interactions are crafted to ensure non-trivial derivative orders, which play a crucial role in suppressing the scalar degree of freedom in high-curvature contexts.

The action supports the introduction of a Vainshtein radius, a critical parameter which delineates the regime in which scalar field effects become substantial. Outside this region, deviations from GR appear, offering a potential explanation for cosmic acceleration. Inside the Vainshtein radius, GR predictions are conserved due to the derivative interplay of the scalar field suppressing its contributions to gravitational interactions.

Numerical Analysis and General Relativity Recovery

A pivotal contribution of the research is the demonstration through numerical analysis of non-singular solutions within the full non-linear scalar-tensor equations. These solutions confirm the capability of the k-Mouflage framework to provide GR recovery at small distances, dictated by the appropriate choice of $H(\phi)$. Notably, solutions exhibit a transition between GR and scalar-tensor regimes precisely at the predicted Vainshtein radius. This indicates that such models can viably replace GR in cosmological analyses without incurring inconsistencies at local scales.

Implications and Future Directions

The implications of k-Mouflage gravity are significant for both theoretical investigations and potential cosmological applications. On the theoretical front, the need for a robust UV completion of the model is acknowledged, akin to challenges faced in prior modifications such as DGP. Practically, this framework provides a fertile ground for exploring cosmological phenomena without the need for new gravitational fields or particles.

For future work, the model’s stability concerning perturbations, especially potential superluminal propagations, needs thorough scrutiny. Furthermore, expanding this theoretical framework to accommodate more complex scenarios, possibly involving interacting scalar fields or different background topologies, may offer deeper insights into the Universe's large-scale structure dynamics.

In summary, k-Mouflage gravity stands as a significant contribution to modified gravity theories, successfully addressing cosmological-scale modifications while ensuring local GR compliance through a novel scalar field interplay mechanism. The paper sets a solid foundation for continued exploration of gravitational dynamics beyond the classical paradigm.