Abstract
We perform direct numerical simulations to compute the net circular polarization of gravitational waves from helical (chiral) turbulent sources in the early Universe for a variety of initial conditions, including driven (stationary) and decaying turbulence. We investigate the resulting gravitational wave signal assuming different turbulent geneses such as magnetically or kinetically driven cases. Under realistic physical conditions in the early Universe we compute numerically the wave number-dependent polarization degree of the gravitational waves. We find that the spectral polarization degree strongly depends on the initial conditions. The peak of the spectral polarization degree occurs at twice the typical wavenumber of the source, as expected, and for fully helical decaying turbulence, it reaches its maximum of nearly 100\% {\it only} at the peak. We determine the temporal evolution of the turbulent sources as well as the resulting gravitational waves, showing that the dominant contribution to their spectral energy density happens shortly after the activation of the source. Only through an artificially prolonged decay of the turbulence can further increase of the gravitational wave amplitude be achieved. We estimate the detection prospects for the net polarization, arguing that its detection contains {\it clean} information (including the generation mechanisms, time, and strength) about the sources of possible parity violations in the early Universe.
Highlights
A remarkable possible source of stochastic gravitational waves (GWs) from the early Universe is turbulence in the primordial plasma induced either from cosmological first-order phase transitions [1,2,3], or from the primordial magnetic fields that are coupled to the cosmological plasma [4,5,6,7]
The universal form of the GW spectrum does not allow us to discriminate between helical and nonhelical sources and limits our ability to determine the parity violation in the early Universe. This leads us to the present study with its main focus on GW circular polarization estimates and the question whether the detection of polarization can help in the identification of distinct properties of the source
In this paper we present numerical simulations of the circular polarization degree of GWs generated through parity violating turbulent sources in the early Universe
Summary
A remarkable possible source of stochastic gravitational waves (GWs) from the early Universe is turbulence in the primordial plasma induced either from cosmological first-order (electroweak or QCD) phase transitions [1,2,3], or from the primordial magnetic fields that are coupled to the cosmological plasma [4,5,6,7]. The dipolar anisotropy induced by our proper motion with respect to the cosmic reference frame makes it possible to measure the net circular polarization of the stochastic GW background [38,39], and recently it has been shown that the net polarization of GWs could be detected with a signal-to-noise ratio of order one by LISA if the strength of the signal achieves h02 GW ∼ 10−11 (with GW the fraction between the GW energy with dHe0ns=ity10a0nhd0thkemcsr−it1icMalpdce−n1sitthyetoHduabybElecrp=ara3mHe02t/e(r8tπodGa)y, and G is the gravitational constant) [40] These findings make it extremely important to properly compute all characteristics (such as the amplitude, the spectral shape, and the polarization degree) of the GW signal from primordial helical (chiral) sources. We apply hydrodynamic and magnetic forcing terms that have a realistic representation of the time dependent generation of turbulence
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