Abstract
We investigate the cosmology of interacting spin-2 particles, formulatingthe multi-gravitational theory in terms of vierbeins and without imposingany Deser-van Nieuwen-huizen-like constraint. The resultingmulti-vierbein theory represents a wider class of gravitational theories ifcompared to the corresponding multi-metric models. Moreover, as opposed toits metric counterpart which in general seems to contain ghosts, it hasalready been proved to be ghost-free. We outline a discussion about thepossible matter couplings and we focus on the study of cosmological scenariosin the caseof three and four interacting vierbeins. We find rich behavior, including deSitter solutions with an effective cosmological constant arising from the multi-vierbein interaction,dark-energy solutions and nonsingular bouncing behavior.
Highlights
We investigate the cosmology of interacting spin-2 particles, formulating the multi-gravitational theory in terms of vierbeins and without imposing any Deser-van Nieuwenhuizen-like constraint
In the case of massive gravity [40], or at the perturbative level of multi-metric gravity [37], this condition arises from the field equations, in the general case of more than two interacting gravitational sectors it is not clear whether this is still true [41, 42], or if it has to be imposed as a separate assumption
As we mentioned in the Introduction, in the case of massive gravity [40], or at the perturbative level of multi-metric gravity [37], this condition arises from the field equations themselves, in the general non-perturbative case of more than two interacting gravitational sectors it is not clear whether this is still true [41, 42], or if it has to be imposed as a separate assumption
Summary
We briefly present the formulation of multi-gravitational theories describing N interacting spin-2 fields in 4 dimensions [37]. In the present work we prefer not to impose the Deser-van Nieuwenhuizen condition or any other constraint on the tetrad fields This leads to a much wider class of multi-gravitational theories, and to formulations of multi-vierbein theories with no known corresponding metric formulation, 3This is because the isotropic and homogeneous background would not allow nontrivial contributions from the parity-odd terms. In passing we note that the possible role of those terms could be interesting to explore in view of the parity-odd anomalies observed in the cosmic microwave background [52] They have been attempted to be generated by extended gravity by assuming (metric) Chern-Simons modifications [53] or noncommutativity of space-time [54]. The details of the derivation of the field equations can be found in Appendix A
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