Cosmological solutions with massive gravitons in the bigravity theory

Abstract: We present solutions describing homogeneous and isotropic cosmologies in the massive gravity theory with two dynamical metrics recently proposed in arXiv:1109.3515 and claimed to be ghost free. These solutions can be spatially open, closed, or flat, and at early times they are sourced by the perfect fluid, while the graviton mass typically manifests itself at late times by giving rise to a cosmological term. In addition, there are also exotic solutions, for which already at early times, when the matter density is high, the contribution of the graviton mass to the energy density is negative and large enough to screen that of the matter contribution. The total energy can then be negative, which may result in removing the initial singularity. For special parameter values there are also solutions for which the two metrics effectively decouple and evolve independently of each other. In the limit where one of the gravitational coupling constant vanishes, such special solutions reduce to those found in arXiv:1107.5504 within the theory where one of the metrics is flat.

• The paper presents ghost-free massive gravity cosmological solutions that shift from matter-dominated expansion to graviton mass-driven acceleration.
• The paper demonstrates special decoupled metric regimes where the physical and auxiliary metrics evolve independently, linking to RGT models.
• The paper explores conditions under which a large negative graviton mass screens matter density, potentially preventing the initial singularity.

Cosmological Solutions with Massive Gravitons in Bigravity Theory

The paper explores cosmological solutions within the framework of bigravity theory, focusing on scenarios with massive gravitons. Bigravity theory extends the notion of general relativity by incorporating two dynamical metrics—namely, a physical metric $g_{\mu\nu}$ and an auxiliary metric $f_{\mu\nu}$. This setup facilitates the formulation of a theory where gravitons can acquire mass, leading to novel cosmological phenomena.

Key Contributions and Results

1. Homogeneous and Isotropic Cosmologies: The paper presents solutions describing homogeneous and isotropic cosmologies that can be spatially closed, open, or flat. The solutions consider scenarios where universe expansion is initially governed by typical matter but later dominated by the structure attributed to graviton mass.
2. Ghost-free Massive Gravity: Integral to this discussion is the claim of a ghost-free massive gravity model, crucial for the theoretical consistency of the framework. The paper builds upon the parameters and conditions established for maintaining ghost-freedom in this dual metric setting.
3. Influence of Graviton Mass: At early times, the graviton mass is typically negligible, but at late times it contributes significantly, manifesting as a cosmological term similar to the cosmological constant that drives acceleration in universal expansion. Moreover, certain "exotic" solutions demonstrate a remarkable property: a large negative graviton mass contribution can screen matter density, resulting in a total negative energy density that potentially evades the initial singularity.
4. Special Solutions and Decoupled Metrics: There exist special solutions where the metrics decouple, evolving independently. In the limit of vanishing gravitational coupling for the auxiliary metric, these solutions align with those in the simpler RGT theory where one metric remains flat.
5. Relation to the RGT Model: The study acknowledges solutions in the limit that reduces to known RGT (de Rham–Gabadadze–Tolley) models. However, the generic solutions within the bigravity theory do not universally reduce to any single-metric formulation, revealing the complexity added by the dynamical second metric.
6. Energy-momentum Conservation: The tensors associated with each metric satisfy conservation conditions aligned with Bianchi identities, ensuring physical robustness against perturbations.

Implications and Future Research Directions

The research broadens the scope of massive gravity models, with potential implications for understanding late-time acceleration in the universe without invoking a cosmological constant. Practically, this framework could guide the formulation of alternative models of dark energy and cosmic inflation, providing theoretical underpinnings that differ from the standard $\Lambda$CDM model.

The paper speculates on the future extraction of gravitational wave data, emphasizing prospects for directly probing graviton mass. Additionally, the potential resolution of singularity issues opens paths for consistent theories of early universe behavior, wherein initial singularities are replaced by more physically viable scenarios.

The discussion on stability and ghost presence remains open, hinting at prospects for more comprehensive analysis through perturbative or non-perturbative means. Future work in this area might explore more complex interactions between metrics, potential coupling constants, or propose experimental tests capable of distinguishing between bigravity theories and standard general relativity or RGT gravity.