Abstract
Stochastic gravitational wave background (SGWB) is a promising tool to probe the very early universe where the standard model of particle physics and cosmology are connected closely. As a possible component of SGWB, gravitational waves (GW) from bubble collisions during the first order cosmological phase transitions deserve comprehensive analyses. In 2017, Ryusuke Jinno and Masahiro Takimoto proposed an elegant analysis approach to derive the analytical expressions of energy spectra of GW from bubble collisions in Minkowski spacetime avoiding large-scale numerical simulations for the first time [26]. However, they neglect the expansion of the universe and regard the duration of phase transitions as infinity in their derivation which could deviate their estimations from true values. For these two reasons, we give a new expression of GW spectra by adopting their method, switching spacetime background to FLRW spacetime, and considering a finite duration of phase transitions. By denoting σ as the fraction of the speed of phase transitions to the expansion speed of the universe, we find when σ is around mathcal{O} (10), the maxima of estimated GW energy spectra drop by around 1 order of magnitude than the results given by their previous work. Even when σ = 100, the maximum of GW energy spectrum is only 65% of their previous estimation. Such a significant decrease may bring about new challenges for the detectability of GW from bubble collisions. Luckily, by comparing new spectra with PLI (power-law integrated) sensitivity curves of GW detectors, we find that the detection prospect for GW from bubble collisions is still promising for DECIGO, BBO, LISA, and TianQin in the foreseeable future.
Highlights
To the thermal history of the universe, the oldest photons we can receive are CMB (Cosmic Micro Background) photons which were free from the Thomson scattering and propagated in the universe without restriction when the redshift was around 1100
By comparing new spectra with PLI sensitivity curves of gravitational waves (GW) detectors, we find that the detection prospect for GW from bubble collisions is still promising for DECIGO, BBO, LISA, and TianQin in the foreseeable future
After the generation of GW, it has nearly no interaction with the contents of the universe [38], so GW contains a huge amount of precious information from the very early universe compelling us to explore the cosmology and particle physics by studying the properties of GW generated at that epoch
Summary
Because our analyses and calculations are all based on their model, we summarize the assumptions and approximations adopted by them at here and directly list the result they’ve obtained. [26] to get a more in-depth understanding. The calculation details won’t be shown so for those readers who are interested in those details can read ref. Their calculations are based on Minkowski spacetime, including tensor perturbation the metric can be written as: ds2 = −dt2 + (δij + 2hij)dxidxj (2.1). The speed of light c has been set to 1, we’ll adopt this convention as well in our own derivation. As for the convention of indices, the Greek indices run over 0, 1, 2, 3 and the Latin indices run over 1, 2, 3 throughout our paper
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