Observational constraints on an inflation model with a running mass

TL;DR

The paper tackles the eta-problem in supergravity by proposing a running-mass inflation model where the inflaton mass-squared $m^2(\phi)$ runs with scale due to coupling to a non-Abelian gauge field. Using one-loop renormalization group equations, the authors track the evolution of $\alpha(t)$, the gaugino mass $\tilde{m}(t)$, and $m^2(t)$ with the scale $Q=\phi$, derive the inflationary dynamics and slow-roll observables, and impose COBE normalization and bounds on the spectral index. They find an allowed region of parameter space where the model can reproduce the observed amplitude of perturbations and a spectral index with significant scale-dependence, for plausible ranges of $\mu_0^2$, $A_0$, and $\tilde{\alpha}_0$. A key prediction is the strong scale-dependence of $n(k)$ across cosmological scales, which could be tested by MAP and large-scale structure data, offering a direct probe of the running-mass mechanism.

Abstract

We explore a model of inflation where the inflaton mass-squared is generated at a high scale by gravity-mediated soft supersymmetry breaking, and runs at lower scales to the small value required for slow-roll inflation. The running is supposed to come from the coupling of the inflaton to a non-Abelian gauge field. In contrast with earlier work, we do not constrain the magnitude of the supersymmetry breaking scale, and we find that the model might work even if squark and slepton masses come from gauge-mediated supersymmetry breaking. With the inflaton and gaugino masses in the expected range, and $α= g^2/4π$ in the range $10^{-2}$ to $10^{-3}$ (all at the high scale) the model can give the observed cosmic microwave anisotropy, and a spectral index in the observed range. The latter has significant variation with scale, which can confirm or rule out the model in the forseeable future.

Figures (5)

• Figure 1: One loop potential $V/V_0-1$ for $\mu^2_0 =A_0 = 1$ and $\tilde{\alpha}_0 = 0.01$, as a function of the scale $Q=\phi$.
• Figure 2: The functions $\mu^2$, $\gamma$ and $\eta$ for $\mu^2_0 =A_0 = 1$ and $\tilde{\alpha}_0 = 0.01$, as a function of the scale $Q=\phi$.
• Figure 3: Contour levels of the spectral index and of $V_0$ in the $\mu^2_0-A$ plane for the different values of the coupling ($\tilde{\alpha}_0 = 0.1,0.05,0.01,0.001$). Notice that for $\tilde{\alpha}_0 = 0.1$ (upper left plot) a small strip of the parameter space is excluded by the consistency constraints (see Fig. 5): the unlabelled vertical line on the left indicates such constraint and is not a contour level. In the other cases the whole parameter region displayed here is contained in the allowed region of Fig. 5.
• Figure 4: The spectral index as a function of comoving wavenumber. The variable used is $N(\phi)\equiv \ln(k_{\rm end}/k)$, as described at the end of Section 4. Cosmological scales are assumed to correspond to $40\mathrel{\hbox{$\sim$} \hbox{$<$}} N(\phi) \mathrel{\hbox{$\sim$} \hbox{$<$}} 50$. Each plot corresponds to a representative point on the corresponding plot of Figure 3; (a) $\tilde{\alpha}_0 = 0.1, A_0 = 0.2, \mu^2_0 = 0.1$; (b) $\tilde{\alpha}_0 = 0.05, A_0 = 0.4, \mu^2_0 = 0.2$; (c) for $\tilde{\alpha}_0 = 0.01, A_0= 1.7, \mu^2_0 = 1$; (d) for $\tilde{\alpha}_0 = 0.001, A_0= 30, \mu^2_0 = 1.5$.
• Figure 5: The region in the $\mu^2_0-A_0$ plane allowed by the consistency checks for the different values of the coupling ($\tilde{\alpha}_0 = 0.1,0.05,0.01,0.001$) is below the curves down to the x-axis. They represent Eqs. (\ref{['bound-A-2']}) (dotted line), (\ref{['secondbound']}) (dashed line) and (\ref{['bound-A-1']}) (full line).