Massive Cosmologies (1108.5231v1)

Abstract: We explore the cosmological solutions of a recently proposed extension of General Relativity with a Lorentz-invariant mass term. We show that the same constraint that removes the Boulware-Deser ghost in this theory also prohibits the existence of homogeneous and isotropic cosmological solutions. Nevertheless, within domains of the size of inverse graviton mass we find approximately homogeneous and isotropic solutions that can well describe the past and present of the Universe. At energy densities above a certain crossover value, these solutions approximate the standard FRW evolution with great accuracy. As the Universe evolves and density drops below the crossover value the inhomogeneities become more and more pronounced. In the low density regime each domain of the size of the inverse graviton mass has essentially non-FRW cosmology. This scenario imposes an upper bound on the graviton mass, which we roughly estimate to be an order of magnitude below the present-day value of the Hubble parameter. The bound becomes especially restrictive if one utilizes an exact self-accelerated solution that this theory offers. Although the above are robust predictions of massive gravity with an explicit mass term, we point out that if the mass parameter emerges from some additional scalar field condensation, the constraint no longer forbids the homogeneous and isotropic cosmologies. In the latter case, there will exist an extra light scalar field at cosmological scales, which is screened by the Vainshtein mechanism at shorter distances.

• The paper presents a ghost-free massive gravity model that eliminates the Boulware-Deser ghost using a carefully constructed action.
• The paper demonstrates that homogeneous and isotropic solutions are generally absent, with only Minkowski space emerging under strict symmetry conditions.
• The paper establishes graviton mass constraints and shows how the Vainshtein mechanism recovers General Relativity in high-density regimes.

Overview of "Massive Cosmologies" by D’Amico et al.

The paper "Massive Cosmologies" by D’Amico et al. presents a detailed examination of the ramifications of introducing a Lorentz-invariant mass term to General Relativity (GR), resulting in a theory of so-called massive gravity. The investigation centers around the cosmological implications of this theoretical extension, particularly focusing on its potential to reconcile certain cosmological phenomena with the standard Friedmann-Robertson-Walker (FRW) cosmologies derived from GR in specific regimes.

Key Insights and Results

1. Ghost-free Massive Gravity: The authors explore a theory of massive gravity that is free from the Boulware-Deser ghost, a problematic additional degree of freedom that typically plagues such theories. This ghost is eliminated through careful construction of the action, consistent with constraints identified in the ADM/Hamiltonian framework.
2. Nonexistence of Homogeneous and Isotropic Solutions: A pivotal result is the demonstration that, under general conditions, this ghost-free theory does not admit solutions that are both homogeneous and isotropic, contrary to standard GR. Only Minkowski space arises as a vacuum solution under these symmetries.
3. Regime Transitions: The analysis reveals that approximately homogeneous and isotropic solutions can exist within domains scaled by the inverse of the graviton mass. These solutions closely mimic the FRW evolution at high energy densities but diverge as the density decreases below a critical crossover value. This divergence establishes a distinct cosmological signature for theories of massive gravity and places an upper bound on the graviton mass.
4. Graviton Mass Constraints: Using a parameterized scenario where the graviton mass is tied to an additional scalar field, the authors note the potential for regaining homogeneous and isotropic cosmological signatures at astronomical scales. However, they underscore an inherent constraint on the graviton mass, estimating it to be less than an order of magnitude smaller than the current Hubble parameter.
5. Vainshtein Mechanism: The authors rely on the Vainshtein mechanism as a critical process allowing massive gravity to reproduce GR outcomes in the massless limit. They demonstrate the mechanism's functioning in spherically symmetric domains, ensuring massive gravity's capability to recover known gravitational physics within specific limits.
6. Cosmology Across Density Scales: The paper explores the cosmological landscape of the high-density regime, approximating FRW dynamics up to densities significantly greater than the crossover threshold. Conversely, in low-density regimes, the deviations from GR become pronounced, manifested through the vDVZ discontinuity. This demands careful examination of cosmological behavior on domain scales larger than the inverse graviton mass.

Implications and Future Work

The exploration of massive gravity and its cosmological implications entails profound potential for expanding our understanding of universal expansion phenomena, such as cosmic acceleration. The paper establishes a foundational framework for further rigorous investigations into massive gravity models, advocating for additional studies into their predictive power regarding observable cosmological parameters.

The findings demand refined scrutiny of the graviton mass parameter in light of current empirical data and future experiments aimed at probing the nature of gravity on both large and small scales. Additionally, the potential matching between self-accelerated solutions and regimes dominated by the Vainshtein mechanism suggests rich avenues for future theoretical work. This includes addressing the interplay between traditional cosmological observations and deviations introduced by massive gravity at various energy densities.

By dissecting the structure and predictions of a ghost-free massive gravity theory, D’Amico et al. provide significant contributions to the ongoing quest for unifying GR with aspects of quantum field theory and explaining cosmic dynamics beyond the standard model of cosmology.