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# Title: Gravitational waves from bubble collisions: analytic derivation

Abstract: We consider gravitational wave production by bubble collisions during a cosmological first-order phase transition. In the literature, such spectra have been estimated by simulating the bubble dynamics, under so-called thin-wall and envelope approximations in a flat background metric. However, we show that, within these assumptions, the gravitational wave spectrum can be estimated in an analytic way. Our estimation is based on the observation that the two-point correlator of the energy-momentum tensor $\langle T(x)T(y)\rangle$ can be expressed analytically under these assumptions. Though the final expressions for the spectrum contain a few integrations that cannot be calculated explicitly, we can easily estimate it numerically. As a result, it is found that the most of the contributions to the spectrum come from single-bubble contribution to the correlator, and in addition the fall-off of the spectrum at high frequencies is found to be proportional to $f^{-1}$. We also provide fitting formulae for the spectrum.
 Comments: 14 pages, 11 figures Subjects: Cosmology and Nongalactic Astrophysics (astro-ph.CO); General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Phenomenology (hep-ph) Journal reference: Phys. Rev. D 95, 024009 (2017) DOI: 10.1103/PhysRevD.95.024009 Report number: KEK-TH-1900 Cite as: arXiv:1605.01403 [astro-ph.CO] (or arXiv:1605.01403v2 [astro-ph.CO] for this version)

## Submission history

From: Ryusuke Jinno [view email]
[v1] Wed, 4 May 2016 20:00:00 GMT (640kb)
[v2] Tue, 18 Oct 2016 16:29:21 GMT (1146kb)