Leonard E Parker Center for Gravitation, Cosmology and Astrophysics

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The Leonard E Parker Center for Gravitation, Cosmology and Astrophysics is supported by NASA, the National Science Foundation, UW-Milwaukee College of Letters and Science, and UW-Milwaukee Graduate School. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of these organizations.

The universe quickly expanded during inflation, leaving it cold and far from thermal equilibrium. Models of the next stage, 'reheating', suggest that standard model particle production resulted from an inflaton oscillating about the minimum of its potential. However, the reheating process can be preceded by a stage of 'preheating.' During preheating, the inflaton (φ) and matter fields interact (or couple), leading to exponential particle production as quantum fluctuations in the matter fields are amplified.

Preheating produces gravitational waves. There is general agreement about the predicted gravitational wave signal when preheating is modeled with one inflaton field and one matter field. However, the inflaton is expected to couple to many fields in the early universe. In this paper, the authors look at how the production of gravitational waves would change if the inflaton couples with multiple matter fields.

The preheating process evolves nonlinearly, so simulations were performed for an inflaton field interacting with 1, 2, 4, 8, 16 and 32 matter fields. Two cases studies for the inflationary potential, V(φ), were used: quartic (V(φ) ~ φ^{4}) and quadratic (V(φ) ~ φ^{2}) inflation.

Simulations of preheating can be described in three stages. In the first stage, the inflaton is oscillating coherently at the bottom of its potential. As the number of matter fields used in the simulation increases, so does the gravitational-wave production at all frequencies. After this initial period, the evolution is highly nonlinear. Inhomogeneities continue growing, and the matter fields are still resonating. In the simulations with more matter fields, the efficiency of the resonance decreases, causing the resonance to end sooner. In the final stage, thermal equilibrium is reached.

For quartic inflation, gravitational-wave production at low frequency is higher as an increasing number of matter fields is simulated. However, at high frequency, gravitational-wave production is strongest when few matter fields are simulated. This leads to a cross-over in the gravitational-wave spectrum for simulations involving varying numbers of matter fields. (See image below)

In quadratic inflation, the stages of preheating are the same as discussed for quartic inflation, however the overall effect of having multiple matter fields is small. The gravitational wave spectrum is virtually independent of the number of matter fields.