Invisible dilaton
- Brax, Philippe et al
- arXiv:2303.14469IPARCOS-UCM-23-021CERN-TH-2023-049
| \small The normalised potential $V(y)$ where $y=\frac{\pi\phi}{2f}$ for $\epsilon=0.05$. The oscillations of the dark matter field take place on the flat part of the potential close to the first minimum on the positive real axis. The field is first stabilised during inflation and then released in the post-inflationary era when the Hubble rate drops below the mass of the scalar field. The oscillatory behaviour is guaranteed as long as the potential is not too flat. The mass on the steep part of the potential is typically $1/\sqrt \epsilon$ larger than close to the minimum. |
| \small Scalar field trajectories $y(\tau)=\frac{\pi\phi}{2f} $ as a function of $\tau$ for the initial conditions $y_0 = 1$, $0$, $-1$, and the smallest associated values of $\epsilon$ that ensure the field remains trapped in the first local minimum. |
| \small The normalised $y=\pi\phi/2f$ field as a function of $\tau$ for $\epsilon=0.01$. The blue curve is the numerical solution. The red one the approximate solution. One can see that the slow roll approximation is valid for a few Hubble times. |