The running-mass inflation model and WMAP

TL;DR

The paper tests the running-mass inflation model, a SUSY-inspired single-field scenario with a radiatively generated inflaton mass, against precision CMB data from \textit{WMAP} and clustering data from SDSS and Ly-α forests. The authors parameterize the potential with RG-improved running mass via $c$ and $s$, yielding a scale-dependent spectrum with $n'(k)=2 s c\, e^{c\Delta N(k)}$ and constrain these via a likelihood analysis on a grid including $\omega_{cdm}h^2$, $\omega_b h^2$, and $h$, supplemented by Ly-α and SLOAN data. They find that large $|c|$ are disfavored by Ly-α, with $n'_0<0.024$ (95% CL) and $sc<0.0043$ (68% CL), while WMAP alone limits $n'_0<0.05$ (95% CL); nonetheless the running-mass model remains viable for a broad region of $(c,s)$, including small $|c|$ where the running is subtle. The results demonstrate that current data can tightly bound the scale dependence of the spectrum but do not rule out a running mass, linking inflationary dynamics to SUSY-breaking parameters and guiding future observations toward detecting or further constraining running.

Abstract

We consider the observational constraints on the running-mass inflationary model, and in particular on the scale-dependence of the spectral index, from the new Cosmic Microwave Background (CMB) anisotropy measurements performed by WMAP and from new clustering data from the SLOAN survey. We find that the data strongly constraints a significant positive scale-dependence of $n$, and we translate the analysis into bounds on the physical parameters of the inflaton potential. Looking deeper into specific types of interaction (gauge and Yukawa) we find that the parameter space is significantly constrained by the new data, but that the running mass model remains viable.

Figures (4)

• Figure 1: The theoretically expected region for the parameters $s$ and $c$ for a value of $N_{\rm 0} = 50$; the solid(red)-line-hatched region is strongly excluded, while the dashed(green)-line-hatched region is excluded only if the mass is supposed to run up to the end of inflation. The dotted (blue) line gives the prediction for the case when the end of inflation is triggered by $\eta = 1$. The circles correspond to the values in the explicit models discussed in section II.C: the upper ones (magenta) refer to the case of gauge coupling dominance, while the (blue) one at the origin to the case of Yukawa coupling dominance.
• Figure 2: Likelihood contour plot in the $c-s$ plane showing the $1$,$2$ and $3\sigma$ contours from the WMAP data (Top Panel), WMAP+SLOAN (Middle Panel) and WMAP+SLOAN+Ly-$\alpha$ (Bottom Panel).
• Figure 3: Likelihood contour plot in the $n_{\rm 0}-n'_{\rm 0}$ plane showing the $1$,$2$ and $3\sigma$ contours from the WMAP data (Top Panel), WMAP+SLOAN (Middle Panel) and WMAP+SLOAN+Ly-$\alpha$ (Bottom Panel).
• Figure 4: Likelihood contour plot in the plane $c-(s+c/2)$ showing the $1$,$2$ and $3\sigma$ contours from the WMAP+SLOAN+Ly-$\alpha$ data. We recall that these parameters are related to the physical inflaton potential parameters by $c = -\beta_m(\ln\phi_{0})/(3 H_I^2)$ and $s+c/2 = m^2(\ln\phi_{0})/(3 H_I^2)$.