Two-field inflation from one complex scalar with symmetry breaking

TL;DR

This work analyzes two-field inflation arising from a single complex scalar with spontaneous symmetry breaking and a soft-breaking mass, producing a radial mode and a pseudo-Nambu-Goldstone boson that jointly drive inflation. By incorporating a non-minimal coupling to gravity and solving the full two-field dynamics, the authors classify trajectories into Higgs-like, Mixed, and Natural-type inflation and map regions consistent with Planck data, highlighting how the pNGB can alter standard single-field predictions. They develop a transfer-function formalism for isocurvature and curvature perturbations, obtaining constraints on the potential parameters, especially the non-minimal coupling $\xi$, symmetry-breaking scale $v_\phi$, and $m_\chi$. The paper further explores reheating and leptogenesis via inflaton decays to right-handed neutrinos, estimating reheating temperatures and identifying viable regions where the observed matter–antimatter asymmetry can be generated, thereby connecting early-universe dynamics to beyond-Standard-Model physics such as the Majoron and RH-neutrino sectors.

Abstract

We study two-field inflation derived from a single complex scalar field with a nonzero vacuum expectation value. The dynamics of inflation are governed by two parameters, the vacuum expectation value and the mass parameter of the phase mode, which together give rise to a rich variety of inflationary structures. We classify the possible trajectories of the two inflaton fields and identify the parameter regions consistent with current cosmological observations. Furthermore, we investigate the reheating process through the inflaton decay to right-handed neutrinos and the subsequent generation of lepton number within these regions. Our findings suggest that the presence of multiple scalar degrees of freedom can significantly alter the conditions for successful reheating and leptogenesis.

Figures (9)

• Figure 1: Typical inflation trajectories in the present two-field model with various e-folding ratios $N_\phi /N$. The model parameters are chosen as $v_\phi =10^{-4}$, $m_\chi = 10^{-4.5}$, $\xi=10^{-2}$, $\lambda = 10^{-12.6}$ (Left), and $v_\phi = 20$, $m_\chi = 10^{-6}$, $\xi = 10^{-3}$, $\lambda=10^{-14.6}$ (Right). The total e-folding number is fixed to $N=60$. The color density shows the value of $d N_\phi / dN$, which is the integrand in \ref{['eq:def-N_phi']}. The gray and shaded regions are excluded by the inflationary conditions $\varepsilon < 1$ and $\eta_\parallel < 1$, respectively.
• Figure 2: Typical predictions for the spectral index and the tensor-to-scalar ratio for a fixed value $\chi_* = \pi / 3$. The red and blue lines correspond to $N = 50$ and $N=60$, respectively. The dashed, solid, and dotted lines in the left panel correspond to $\xi=1$, $10^{-2}$, and $10^{-3}$. The dashed (solid) lines in the right panel represent $\xi=10^{-3}$ ($\xi=10^{-6}$). The soft-breaking mass ranges are $0\leq m_\chi \leq 1.4\times 10^{-5}$ ($\xi=10^{-3}$), $0\leq m_\chi \leq 2.3\times 10^{-5}$ ($\xi=10^{-2}$), and $0\leq m_\chi \leq 1.1\times 10^{-4}$ ($\xi=1$) in the left panel, and $0\leq m_\chi \leq 7.0 \times 10^{-6}$ in the right panel. The arrows indicate the direction of increasing $m_\chi$. The markers show fixed values of $m_\chi$: $m_\chi =0$ (circle), $6\times 10^{-6}$ (square), $7.6 \times 10^{-6}$ (diamond), $5.9 \times 10^{-6}$ (blue star), $7.0 \times 10^{-6}$ (red star), $6.2\times 10^{-6}$ (blue triangle), and $7.0 \times 10^{-6}$ (red triangle). The contours indicate the $1\sigma$ and $2\sigma$ confidence regions from Planck observations.
• Figure 3: Higgs
• Figure 4: Mixed
• Figure 5: Natural