Abstract
In double-field inflation, which exploits two scalar fields, one of the fields rolls slowly during inflation whereas the other field is trapped in a meta-stable vacuum. The nucleation rate from the false vacuum to the true one becomes substantial enough that triggers a first order phase transition and ends inflation. We revisit the question of first order phase transition in an “extended” model of hybrid inflation, realizing the double-field inflationary scenario, and correctly identify the parameter space that leads to a first order phase transition at the end of inflation. We compute the gravitational wave profile which is generated during this first order phase transition. Assuming instant reheating, the peak frequency falls in the 1 GHz to 10 GHz frequency band and the amplitude varies in the range 10−11≲ΩGWh2≲10−8, depending on the value of the cosmological constant in the false vacuum. For a narrow band of vacuum energies, the first order phase transition can happen after the end of inflation via the violation of slow-roll, with a peak frequency that varies from 1 THz to 100 THz. For smaller values of cosmological constant, even though inflation can end via slow-roll violation, the universe gets trapped in a false vacuum whose energy drives a second phase of eternal inflation. This range of vacuum energies do not lead to viable inflationary models, unless the value of the cosmological constant is compatible with the observed value, M∼10−3 eV.
Highlights
The mechanism that ends inflation is still an open question in cosmology
We identify the parameter space for which inflation can end through a first order phase transition and calculate the power spectrum of gravitational waves produced during such phase transitions
Terminating inflation with a first order phase transition has the benefit of reheating the universe from the supercooling phase of inflation through the collisions of bubbles of true vacuum without invoking and fine-tuning of the couplings of the inflaton to the other fields. One can achieve this scenario, modifying the old inflation scenario, with time-dependent nucleation rate which is small in the beginning and becomes substantial at the end of inflation
Summary
The mechanism that ends inflation is still an open question in cosmology. it was the Achilles heel of the old inflation model [1], as the universe would never recover from inflation. [8] had tried to identify the parameter space which allows for exit from inflation with a first order phase transition In their calculation, they had assumed that the pre-exponential factor in the nucleation rate per unit four-volume, = A exp(−S E ), is given by the amplitude of the potential in the false vacuum, V 0. We investigate the gravitational profile from inflationary models that exit from inflationary phase through violation of slowroll but after the termination of inflation the nucleation rate from meta-stable vacuum to the true vacuum becomes large enough that first order phase transition occurs. We comment on the viability of such inflationary models and conclude our paper
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