Toward a magnetic warm inflation scenario

In this work we explore the effects that a possible primordial magnetic field can have on the inflaton effective potential, taking as the underlying model a warm inflation scenario, based on global supersymmetry with a new-inflation-type potential. The decay scheme for the inflaton field is a two-step process of radiation production, where the inflaton couples to heavy intermediate superfields, which in turn interact with light particles. In this context, we consider that both sectors, heavy and light, are charged and work in the strong magnetic field approximation for the light fields. We find an analytical expression for the one-loop effective potential, for an arbitrary magnetic field strength, and show that the trend of the magnetic contribution is to make the potential flatter in the origin’s vicinity, preserving the conditions for a successful inflationary process. This result is backed up by the behavior of slow-roll parameter $\epsilon$. The viability of this magnetic warm inflation scenario is also supported by the estimation of the effect of the magnetic field on the heavy particles decay width.

Figure 1

Feynman diagrams that account for the interaction between heavy and light fields at one-loop, where double lines indicate that the charged particles are dressed with the magnetic field effects. Continuous lines indicate fermionic fields, ${\psi }_{\chi }$ and ${\psi }_{y_i}$, and dashed lines indicate bosonic fields, $\chi$ and $y_i$.

Figure 2

Decay width ratio ${\mathrm{\Gamma }}^B/\mathrm{\Gamma }$, Eqs. (70)–(71), of a heavy charged scalar into two light charged fermions, for different magnetic field strengths, for $M_s/{\varphi }_0=0.05$, $m_1/{\varphi }_0={10}^{-3}$, $m_2/{\varphi }_0=5\times {10}^{-3}$, $g=0.1$. The magnetic field enhances this process.

Figure 3

Effective potential normalized by $\mathcal{V}(0,0)$, Eq. (74), for different magnetic field strengths for $M_s/{\varphi }_0=0.05$, $m_1/{\varphi }_0={10}^{-3}$, $m_2/{\varphi }_0=5\times {10}^{-3}$, $g=0.1$ and $h=0.1$.

Figure 4

(a) Slow-roll parameter $\epsilon$ for different magnetic field strengths and (b) ${\varphi }_{\epsilon =1}/{\varphi }_0$ as a function of the magnetic field, both with $M_s/{\varphi }_0=0.05$, $m_1/{\varphi }_0={10}^{-3}$, $m_2/{\varphi }_0=5\times {10}^{-3}$, $g=0.1$, and $h=0.1$.

Figure 5

$\eta$ as a function of $\varphi /{\varphi }_0$ for three values of the magnetic field strength, (a) in the neighborhood of $\varphi /{\varphi }_0$ for which $\epsilon =1$ and (b) for an earlier inflationary stage. In both cases, $M_s/{\varphi }_0=0.05$, $m_1/{\varphi }_0={10}^{-3}$, $m_2/{\varphi }_0=5\times {10}^{-3}$, $g=0.1$, and $h=0.1$.