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Register a new userA plausible model of inflation driven by strong gravitational wave turbulence
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Sebastien Galtier
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It is widely accepted that the primordial universe experienced a brief period of accelerated expansion called inflation. This scenario provides a plausible solution to the horizon and flatness problems. However, the particle physics mechanism responsible for inflation remains speculative with, in particular , the assumption of a scalar field called inflaton. Furthermore, the comparison with the most recent data raises new questions that encourage the consideration of alternative hypotheses. Here, we propose a completely different scenario based on a mechanism whose origins lie in the nonlin-earities of the Einstein field equations. We use the analytical results of weak gravitational wave turbulence to develop a phenomenological theory of strong gravitational wave turbulence where the inverse cascade of wave action plays a key role. In this scenario, the space-time metric excitation triggers an explosive inverse cascade followed by the formation of a condensate in Fourier space whose growth is interpreted as an expansion of the universe. Contrary to the idea that gravitation can only produce a decelerating expansion, our study reveals that gravitational wave turbulence could be a source of inflation. The fossil spectrum that emerges from this scenario is shown to be in agreement with the cosmic microwave background radiation measured by the Planck mission.
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We present the first direct numerical simulation of gravitational wave turbulence. General relativity equations are solved numerically in a periodic box with a diagonal metric tensor depending on two space coordinates only, $g_{ij} equiv g_{ii}(x,y,t) delta_{ij}$, and with an additional small-scale dissipative term. We limit ourselves to weak gravitational waves and to a freely decaying turbulence. We find that an initial metric excitation at intermediate wavenumber leads to a dual cascade of energy and wave action. When the direct energy cascade reaches the dissipative scales, a transition is observed in the temporal evolution of energy from a plateau to a power-law decay, while the inverse cascade front continues to propagate toward low wavenumbers. The wavenumber and frequency-wavenumber spectra are found to be compatible with the theory of weak wave turbulence and the characteristic time-scale of the dual cascade is that expected for four-wave resonant interactions. The simulation reveals that an initially weak gravitational wave turbulence tends to become strong as the inverse cascade of wave action progresses with a selective amplification of the fluctuations $g_{11}$ and $g_{22}$.
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A fourth-order and a second-order nonlinear diffusion models in spectral space are proposed to describe gravitational wave turbulence in the approximation of strongly local interactions. We show analytically that the model equations satisfy the conservation of energy and wave action, and reproduce the power law solutions previously derived from the kinetic equations with a direct cascade of energy and an explosive inverse cascade of wave action. In the latter case, we show numerically by computing the second-order diffusion model that the non-stationary regime exhibits an anomalous scaling which is understood as a self-similar solution of the second kind with a front propagation following the law $k_f sim (t_*-t)^{3.296}$, with $t<t_*$. These results are relevant to better understand the dynamics of the primordial universe where potent sources of gravitational waves may produce space-time turbulence.
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