Gravitational wave generation in power-law inflationary models

Abstract

We investigate the generation of gravitational waves in power-law inflationary models. The energy spectrum of the gravitational waves is calculated using the method of continuous Bogoliubov coefficients. We show that, by looking at the interval of frequencies between 10^(-5) and 10^5 Hz and also at the GHz range, important information can be obtained, both about the inflationary period itself and about the thermalization regime between the end of inflation and the beginning of the radiation-dominated era. We thus deem the development of gravitational wave detectors, covering the MHz/GHz range of frequencies, to be an important task for the future.Comment: 8 pages, 6 figures, added 3 references, text improve

Smoking guns of a bounce in modified theories of gravity through the spectrum of gravitational waves

“…The results obtained are within all the observational constraints considered except for the CMB radiation data as, for the higher energy scales even a contraction of two orders of magnitude before the bounce makes the spec-trum violate the limits imposed on the low frequencies of the spectrum [48,52]. An estimation on the maximum amount of the allowed contraction without violating the CMB constraints was determined by studying the dependence of the height of the most intense peak of the spectrum on the parameters of the model.…”

“…These coefficients, which carry the time dependence of the vacuum state, fulfill the initial conditions α(t ini ) = 1 and β(t ini ) = 0 at some time t ini . 4 Furthermore, |β(t)| 2 gives the density of gravitons of the universe at a time t. A second linear transformation is introduced to describe the evolution of the graviton density by the more practical X and Y variables, which obey [29][30][31]48]:…”

“…The graviton density, |β| 2 , at the present time, η 0 , defines the dimensionless relative logarithmic energy spectrum of GWs for the frequency ω as [28,48]:…”

“…The integration is divided in two parts with the first one, during the f (R) era, performed in terms of the cosmic time and the second one, during the mGCG and ΛCDM eras, performed in terms of the scale factor. Following previous works, [31,48,49], we stop the integration when k 2 ≫ z ′′ /z, i.e. when the mode is well inside the horizon, since in this regime X and Y have a highly oscillatory sinusoidal behaviour while |β| 2 is virtually constant.…”

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

“…4 and Fig. 5), and (ii) the analytical solutions for the power-law inflation [36] next. We first remind that the power law solutions for X and Y read [35] …”