Supergravity and two-field inflation effects in right-handed sneutrino-modified D-term inflation

We extend previous work on the minimal D-term inflation model modified by right-handed (RH) sneutrino fields to include additional inflaton-sector supergravity corrections and two-field inflation effects. We show that supergravity corrections simultaneously allow $n_s$ to be within 3-year Wilkinson Microwave Anisotropy Probe limits and the cosmic string contribution to the cosmic microwave background (CMB) power spectrum to be less than 5%. For gauge coupling $g\le 1$, the CMB contribution from cosmic strings is predicted to be at least 1% while the spectral index is predicted to be less than 0.968 for a CMB string contribution less than 5%. Treating the inflaton-RH sneutrino system as a two-field inflation model, we show that the time-dependence of the RH sneutrino field strongly modifies the single-field results for values of RH sneutrino mass $m_{\Phi }>0.1H$. The running spectral index is $\alpha \approx -0.0002$ when $m_{\Phi }<0.1H$ but increases to positive values as $m_{\Phi }/H$ increases, with $\alpha >0.008$ for $m_{\Phi }>1.0H$.

Figure 1

${\xi }^{1/2}$ as a function of $n_s$ in the original RHSM D-term inflation model. The $1\mathrm{\text{−}}\sigma$ and $2\mathrm{\text{−}}\sigma$ bounds on $n_s$ are shown for the case of (a) “WMAP only” data and (b) “$\mathrm{WMAP}+\mathrm{\text{ALL}}$” data. The cosmic string 10% and 5% upper bounds on ${\xi }^{1/2}$ are also shown.

Figure 2

Spectral index as a function of $\gamma$. The $2\mathrm{\text{−}}\sigma$ $\mathrm{WMAP}+\mathrm{\text{ALL}}$ lower bound and 5% cosmic string upper bound on $n_s$ are shown.

Figure 3

$c_{+}=c_{-}=3.0$, $g=0.6$ plot of ${\xi }^{1/2}$ versus $n_s$ for $b=0.0$, 1.0 and 3.0, for the case of (a) “WMAP only” data and (b) “$\mathrm{WMAP}+\mathrm{\text{ALL}}$” data.

Figure 4

$c_{+}=c_{-}=3.0$, $b=1.0$ plot of ${\xi }^{1/2}$ versus $n_s$ for $g=0.4$, 0.6 and 1.0, for the case of (a) “WMAP only” data and (b) “$\mathrm{WMAP}+\mathrm{\text{ALL}}$” data.

Figure 5

$c_{+}=c_{-}=3.0$, $b=1.0$ plot of $|S{|}^2/M^2$ at $N=60$ versus $g$ for $n_s=0.93$, 0.94 and 0.95.

Figure 6

$c_{+}=c_{-}=3.0$, $b=1.0$ plot of $\gamma$ as a function of $g$ for $n_s=0.93$, 0.94 and 0.95.

Figure 7

Two-field inflation trajectories for $m_{\Phi }/H=0.1$, 0.2, 0.4 and 0.6. Values of $N$ are shown on the trajectories.

Figure 8

Effect of $\varphi$ time evolution on (a) ${\xi }^{1/2}/{\xi }_o^{1/2}$ versus $m_{\Phi }/H$ and (b) $n_s$ versus $m_{\Phi }/H$.

Figure 9

Running spectral index $\alpha$ as a function of $m_{\Phi }/H$.