Search

Saddle-point configurations, such as the Euclidean bounce and sphalerons, are known to be difficult to find numerically. In this letter we study a new method, Quartic Gradient Flow, to search for such configurations. The central idea is to introduce a gradient-flow-like equation in such a way that all the fluctuations around the saddle-point have eigenvalues that are square of the eigenvalues of the original quadratic operator. We illustrate how the method works for the Euclidean bounce and sphalerons.

We discuss the unique phenomenology of first-order phase transitions catalyzed by primordial black holes (BHs). If the number of BHs within one Hubble volume is smaller than unity at the time of bubble nucleation, each bubble catalyzed around them can expand to the Hubble size, and the universe is eventually filled with true vacuum much after nucleation. This super-slow transition predicts enhanced gravitational wave signals from bubble collisions and can be tested in future observations. Moreover, the remaining rare false vacuum patches give birth to baby BHs, which can account for the abundance of dark matter in our universe.

It has been argued that the mixed Higgs-R2 model acts as the UV extension of the Higgs inflation, pushing up its cut-off scale in the vacuum close up to the Planck scale. In this letter, we study the inflaton oscillation stage after inflation, focusing on the effective mass of the phase direction of the Higgs field, which can cause a violent preheating process. We find that the “spikes” in the effective mass of the phase direction observed in the Higgs inflation still appear in the mixed Higgs-R2 model. While the spikes appear above the cut-off scale in the Higgs-only case, they appear below the cut-off scale when the model is extended with R2 term though reheating cannot be completed in the violent particle production regime since the spikes get milder. Keywords: Preheating, Higgs inflation, R2 inflation

A new setup of cosmic inflation with a periodic inflaton potential and conformal factor is discussed in the metric and Palatini formulations of gravity. As a concrete example, we focus on a natural-inflation-like inflaton potential, and show that the inflationary predictions fall into the allowed region of cosmic microwave background observations in both formulations.