Dynamically Induced Topological Inflation

We propose an inflation model in which the inflationary era is driven by the strong dynamics of <math display="inline"><mi>S</mi><mi>p</mi><mo stretchy="false">(</mo><mn>2</mn><mo stretchy="false">)</mo></math> gauge theory. The quark condensation in the confined phase of <math display="inline"><mi>S</mi><mi>p</mi><mo stretchy="false">(</mo><mn>2</mn><mo stretchy="false">)</mo></math> gauge theory generates the inflaton potential comparable to the energy of the thermal bath at the time of phase transition. Afterwards, with a super-Planckian field value at the global minimum, the inflation commences at a false vacuum region lying between true vacuum regions and hence the name “topological inflation.” Featured by the huge separation between the scale of the false vacuum (<math display="inline"><mi>V</mi><mo stretchy="false">(</mo><mn>0</mn><msup><mo stretchy="false">)</mo><mrow><mn>1</mn><mo stretchy="false">/</mo><mn>4</mn></mrow></msup><mo>∼</mo><msup><mn>10</mn><mn>15</mn></msup><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>) and the field value at the global minimum (<math display="inline"><msub><mi>ϕ</mi><mi>min</mi></msub><mo>∼</mo><msub><mi>M</mi><mi>P</mi></msub></math>), the model can be consistent with cosmic microwave background (CMB) observables without suffering from the initial condition problems. Crucially, this is achieved only with some mild tuning of parameters in <math display="inline"><mi>V</mi><mo stretchy="false">(</mo><mi>ϕ</mi><mo stretchy="false">)</mo></math>. In addition to <math display="inline"><mi>S</mi><mi>p</mi><mo stretchy="false">(</mo><mn>2</mn><mo stretchy="false">)</mo></math>, this model is based on an anomaly free <math display="inline"><msub><mi>Z</mi><mrow><mn>6</mn><mi>R</mi></mrow></msub></math> discrete <math display="inline"><mi>R</mi></math> symmetry. Remarkably, while all parameters are fixed by CMB observations, the model predicts a hierarchy of energy scales including the inflation scale, supersymmetry-breaking scale, R-symmetry breaking scale, Higgsino mass and the right-handed neutrino mass given in terms of the dynamical scale of <math display="inline"><mi>S</mi><mi>p</mi><mo stretchy="false">(</mo><mn>2</mn><mo stretchy="false">)</mo></math>.