Parametric resonance and cosmological gravitational waves

Abstract

We investigate the production of gravitational waves due to quantum fluctuations of the vacuum during the transition from the inflationary to the radiation-dominated eras of the universe, assuming this transition to be dominated by the phenomenon of parametric resonance. The energy spectrum of the gravitational waves is calculated using the method of continuous Bogoliubov coefficients, which avoids the problem of overproduction of gravitons at large frequencies. We found, on the sole basis of the mechanism of quantum fluctuations, that the resonance field leaves no explicit and distinctive imprint on the gravitational-wave energy spectrum, apart an overall upward or downward translation. Therefore, the main features in the spectrum are due to the inflaton field, which leaves a characteristic imprint at frequencies of the order of MHz/GHz.

Gravitational wave generation in power-law inflationary models

“…This method has been used by us in previous works to investigate the generation of gravitational waves in different cosmological models [19,22,34]. Upon the redefinition…”

“…Having determined the time evolution of a /a from Eqs. (16)- (19), we then solve Eqs. (26) and (27) (again with a Runge-Kutte method) for different values of ω(η 0 ) = k/a(η 0 ) and with initial conditions (32) and (33).…”

“…We use a Runge-Kutte method to solve the system of differential equations (16)- (19). Equations (15) and (20) are used as constraint equations to check the accuracy of the numerical solution.…”

Slow-roll inflation preceded by a topological defect phaseà laChaplygin gas

“…The gravitational waves energy density is given by [42] 1) where N k (τ ) is the number of gravitons created for a given mode k in a different vacuum state as the universe expands. Then the dimensionless relative logarithmic energy spectrum Ω GW at the present time τ 0 can be defined as [42] Ω…”

“…Then the dimensionless relative logarithmic energy spectrum Ω GW at the present time τ 0 can be defined as [42] Ω…”