Minimal Inflation

TL;DR

This work embeds inflation within the SUSY-breaking sector by using the universal $X$-superfield, identifying the inflaton with the imaginary component of $X$ and tracing its flow to the IR goldstino superfield $X_{NL}$. A key hurdle is the $\eta$-problem in supergravity, which is resolved by introducing explicit $R$-symmetry breaking, enabling flat slow-roll directions and a multifield (hybrid) inflation scenario. The model relates slow-roll parameters to the SUSY-breaking scale $\mu$ and the gravitino mass, yielding $\mu$ in the range $10^{11-13}$ GeV and an inflaton mass $m_\beta$ lighter than the gravitino by $\sqrt{\eta}$, with $\eta$ controlling the number of $e$-foldings and the spectrum tilt $n_S$. Cosmological predictions are consistent with current data (nearly scale-invariant spectrum, small tensor modes) and provide testable links between inflationary observables and high-energy SUSY-breaking physics, though explicit UV completions and reheating details remain for future work.

Abstract

Using the universal X superfield that measures in the UV the violation of conformal invariance we build up a model of multifield inflation. The underlying dynamics is the one controlling the natural flow of this field in the IR to the Goldstino superfield once SUSY is broken. We show that flat directions satisfying the slow roll conditions exist only if R-symmetry is broken. Naturalness of our model leads to scales of SUSY breaking of the order of 10^{11-13} Gev, a nearly scale-invariant spectrum of the initial perturbations and negligible gravitational waves. We obtain that the inflaton field is lighter than the gravitino by an amount determined by the slow roll parameter eta. The existence of slow-roll conditions is directly linked to the values of supersymmetry and R-symmetry breaking scales. We make cosmological predictions of our model and compare them to current data.

Figures (1)

• Figure 1: Left panel: The potential as a function of ($\alpha$) and ($\beta$) components of the field $X$. Note the nearly flat direction ($\beta$) that we use for our inflationary trajectories. Graceful exit and particle creation occurs in the non-linear part of the $X$ field. Right panel: WMAP5 cosmological constraints (yellow region) in the $r-n_S$ plane. For no-fine-tuned minimal inflation models the green and red area show our predictions for both cases of a stable (concave) potential and unstable (convex) potential. The Planck satellite will be able to provide significantly tigther constraints on $r$ and especially $n_S$ (at the $< 0.5\%$ level) thus further constraining our model. The dashed line is the limit in $r$ that can be achieved with an ideal CMB polarization experiment raulcmb