Dynamical supersymmetry breaking and late-time $R$ symmetry breaking as the origin of cosmic inflation

Spontaneously broken supersymmetry (SUSY) and a vanishingly small cosmological constant imply that $R$ symmetry must be spontaneously broken at low energies. Based on this observation, we suppose that, in the sector responsible for low-energy $R$ symmetry breaking, a discrete $R$ symmetry remains preserved at high energies and only becomes dynamically broken at relatively late times in the cosmological evolution, i.e., after the dynamical breaking of SUSY. Prior to $R$ symmetry breaking, the Universe is then bound to be in a quasi–de Sitter phase—which offers a dynamical explanation for the occurrence of cosmic inflation. This scenario yields a new perspective on the interplay between SUSY breaking and inflation, which neatly fits into the paradigm of high-scale SUSY: inflation is driven by the SUSY-breaking vacuum energy density, while the chiral field responsible for SUSY breaking, the Polonyi field, serves as the inflaton. Because $R$ symmetry is broken only after inflation, slow-roll inflation is not spoiled by otherwise dangerous gravitational corrections in supergravity. We illustrate our idea by means of a concrete example, in which both SUSY and $R$ symmetry are broken by strong gauge dynamics and in which late-time $R$ symmetry breaking is triggered by a small inflaton field value. In this model, the scales of inflation and SUSY breaking are unified, the inflationary predictions are similar to those of F-term hybrid inflation in supergravity, reheating proceeds via gravitino decay at temperatures consistent with thermal leptogenesis, and the sparticle mass spectrum follows from pure gravity mediation. Dark matter consists of thermally produced winos with a mass in the TeV range.

Figure 1

Effective CW potential for the Polonyi field, $V_{1-\mathrm{loop}}$, as a function of the order parameter $x$ for $\lambda =1$, see Eq. (45). The potential energy scales ${\mathrm{\Lambda }}_{\mathrm{LE}}$ and ${\mathrm{\Lambda }}_{\mathrm{HE}}$ are given in Eq. (44). For values $x\sim 1$, we can only have limited trust in our perturbative result because of potentially important strong-coupling effects at energies close to the dynamical scale $\mathrm{\Lambda }$.

Figure 2

Inflaton potential in the inflection-point regime ($\epsilon <{\epsilon }_0$). Here, the values for the free parameters in the inflaton sector have been chosen as in the benchmark scenario discussed in Sec. 4d: $\mathrm{\Lambda }\simeq 1.26\times 10^{16}\mathrm{GeV}$, $\lambda \simeq 1.66$, and $\epsilon \simeq 0.204$.

Figure 3

Viable region in the parameter space spanned by the Yukawa coupling $\lambda$ and the coefficient in the noncanonical Kähler potential, $\epsilon$. Here, the $\epsilon$ values on the vertical axis are normalized by the critical values ${\epsilon }_0$, see Eq. (137). For $\lambda \lesssim 1$, the VEV of the Polonyi field begins to exceed the critical field value ${\phi }_c$, see Eq. (127), whereas for $\lambda \gtrsim 3$, the Polonyi field begins to take super-Planckian values during inflation [this follows from Eq. (141)]. The black contours respectively indicate the values of $\mathrm{\Lambda }$ (left panel) and $m_{3/2}$ (right panel) required to obtain the correct scalar spectral amplitude, $A_s\simeq A_s^{\mathrm{obs}}$.