Abstract
Effective Field Theory methods are employed to investigate the leading order quantum corrections to the backreaction of gravitational waves. The effective energy-momentum tensor is computed and we show that it has a non-zero trace that contributes to the cosmological constant. By confronting our result with LIGO’s data, the first constraint on the amplitude of the massive mode is obtained: \(\epsilon < 1.4\times 10^{-33}\).
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Notes
- 1.
Observe that \(\bar{R}_{\mu \nu }\sim \frac{1}{L^2}\), \(R_{\mu \nu }^{(n)}\sim \frac{h^{n}}{\lambda ^2}\) and the contribution of GWs to the curvature is negligible compared to the contribution of matter sources.
- 2.
When performing the scalar-vector-tensor decomposition to second order in perturbation theory, one has to take into account the contributions from the coupling between scalar and tensor perturbations [16]. These contributions are automatically being taken into account here as we are not decomposing the metric perturbation and everything is given in terms of the entire perturbation \(h_{\mu \nu }\).
- 3.
This conservative bound, and consequently the bound on \(\epsilon \), was found assuming all the energy of a merger goes into the complex mode. Naturally, this does not represent the real situation as the classical mode should also be excited. In a more detailed analysis, we expect to obtain a better bound.
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Kuntz, I. (2019). Backreaction of Quantum Gravitational Modes. In: Gravitational Theories Beyond General Relativity. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-030-21197-4_4
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DOI: https://doi.org/10.1007/978-3-030-21197-4_4
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