Gravitational Waves from Oscillon Preheating

TL;DR

The paper investigates the stochastic gravitational wave background arising from oscillon preheating after inflation, focusing on an oscillon-dominated phase and using an axion monodromy-type potential as a representative model. It shows that isolated, spherically symmetric oscillons do not radiate efficiently, and that GW production during the fully formed oscillon era is suppressed, while violent preheating during oscillon formation can generate a significant background with a spectrum featuring multiple peaks corresponding to oscillon scales. The authors support these conclusions with semi-analytic arguments and detailed lattice simulations, revealing a characteristic four-stage evolution of the GW spectrum and highlighting the high frequencies and low amplitudes expected in such scenarios. The results have implications for the phenomenology of monodromy inflation and offer spectral signatures that, while difficult to detect with current technology, could serve as a diagnostic for post-inflationary dynamics in high-scale inflation models.

Abstract

Oscillons are long-lived, localized excitations of nonlinear scalar fields which may be copiously produced during preheating after inflation, leading to a possible oscillon-dominated phase in the early Universe. For example, this can happen after axion monodromy inflation, on which we run our simulations. We investigate the stochastic gravitational wave background associated with an oscillon-dominated phase. An isolated oscillon is spherically symmetric and does not radiate gravitational waves, and we show that the flux of gravitational radiation generated between oscillons is also small. However, a significant stochastic gravitational wave background may be generated during preheating itself (i.e, when oscillons are forming), and in this case the characteristic size of the oscillons is imprinted on the gravitational wave power spectrum, which has multiple, distinct peaks.

Figures (5)

• Figure 1: A late time snap shot of the energy density in oscillon preheating. The model is that of Eq. (\ref{['modelpot']}) with $\alpha=1/2$ and $M=0.01M_P$. The box size is $L=50/m$ and the energy density isosurface is taken at a value 5 times the average energy density.
• Figure 2: Evolution of the gravitational wave power spectrum. The lattice is $256^3$, the box size is $L=50/m$ and the evolution time shown is from $t=80/m$ to $t=240/m$. There are (at least) four distinct stages: (top-left) - steady "pumping" (linear parametric resonance) in low momentum modes; (top-right) - rapid growth (nonlinear "re-scattering"), oscillons forming; (bottom-left) - oscillons stabilizing, peaks and troughs becoming significant; (bottom-right) - long stable stage, very slow growth.
• Figure 3: The energy densities of the same slice of the box at two different times. The model is that of Eq. (\ref{['modelpot']}) with $\alpha=1/2$ and $M=0.01M_P$. The lattice is $256^3$ and the box size is $L=50/m$. The top is taken at the late time of the rapid growth stage and the bottom is taken at the early time of the stabilizing stage. We can see that at the onset of the stabilizing stage oscillons become very massive, dominating the energy density of the Universe.
• Figure 4: Peaks and troughs of the gravitational wave power spectrum. The model is that of Eq. (\ref{['modelpot']}) with $\alpha=1/2$ (the axion monodromy model) and $M=0.01M_P$. The lattice is $256^3$, plotted at $t=240/m$. The box size is $L=25/m$, instead of $L=50/m$, so as to resolve more high momentum modes. The vertical lines correspond to the gravitational wave frequencies associated with the different harmonics of the oscillon, which are twice the frequencies of the oscillon harmonics. Note that the values indicated for the vertical lines ($m/\pi,3m/\pi,5m/\pi,...$) should be understood as being multiplied by a redshift factor ($\sim 10^{-30}$). Even order oscillon harmonics ($2m/\pi, 4m/\pi,$ ..., in terms of the gravitational wave frequency; the dotted lines) are absent in our model, because of the symmetry $\phi\to -\phi$. The matches of the vertical lines with the troughs indicate that oscillons are suppressing the gravitational wave production at those frequencies.
• Figure 5: The function $F(\sigma)/\sigma^2$. $m_x = m_y =\mu, m_z=\sigma \mu$, where $\sigma$ encodes the extent of the ellipse of the oscillating oscillon. For $\sigma=1$, we have $F(1)=0$, which means the oscillon is spherically symmetric and around which the gravitational energy emission is suppressed.