Abstract
The exact non-linear theory of massive gravity has a very complex structure and therefore in this section we will take an alternative approach of covariantizing the Lagrangian in the decoupling limit, and use the resulting theory as a proxy and study the cosmology in this proxy theory.
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Notes
- 1.
It is an attractor solution as long as \(\mathrm {H}{\uppi }\ll \dot{\uppi }\).
- 2.
At early times the densities are large and the Vainshtein mechanism freezes out the helicity-0 mode.
- 3.
Notice the factor \(\mathrm {b}_2\) in this definition of the matter density parameter that does not appear in the usual definition.
- 4.
The Bianchi identity for an arbitrary p-form \(\mathrm {d}{\upomega }=0\), where \({\upomega }\) is the strength of the p-form, guaranties that the Lagrangian \(\epsilon ^{{\upmu }{\upnu }\ldots }\epsilon ^{\mathrm {ab}\ldots }{\upomega }_{{\upmu }{\upnu }\ldots }{\upomega }_{\mathrm {ab}\ldots }\cdots (\partial _{\uprho }{\upomega }_{\mathrm {cd}\ldots })\cdots (\partial _{\mathrm {e}}{\upomega }_{\sigma \tau \ldots })\) for the p-form will only give rise to second-order equations of motion (Deffayet et al. 2010).
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Heisenberg, L. (2015). Proxy Theory. In: Theoretical and Observational Consistency of Massive Gravity. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-18935-2_3
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DOI: https://doi.org/10.1007/978-3-319-18935-2_3
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