GRAVITATIONAL WAVES IN HYBRID QUINTESSENTIAL INFLATION

1. GRAVITATIONAL WAVES IN HYBRID QUINTESSENTIAL INFLATION Paulo M. Sá Departamento de Física, Universidade do Algarve, Portugal Spanish Relativity Meeting – ERE 2010

2. Introduction Introduction Hybrid Quintessential Inflation Gravitational Wave Spectrum Conclusions Gravitational waves of cosmological origin are at present the object of an important research effort, as they will provide us with a unique telescope to the very early universe. In this talk, we analyse the gravitational-wave energy spectrum obtained within the recently-proposed hybrid quintessential inflationary model. • M. Bastero-Gil, A. Berera, B. M. Jackson and A. Taylor, • Phys. Lett. B 678, 157 (2009). • P. M. Sá and A. B. Henriques, • Phys. Rev. D 81, 124043 (2010).

3. Hybrid Quintessential Inflation Introduction Hybrid Quintessential Inflation Gravitational Wave Spectrum Conclusions Hybrid quintessential potential: One minimum at Two minima at

4. Hybrid Quintessential Inflation Second stage of evolution: The scalar field c rolls toward one of the new minima and starts to oscillate around it, thus acquiring kinetic energy. Third stage of evolution: The scalar field c oscillates around the miminum at c=0, transferring its kinetic energy to a radiation fluid, thus reheating the Universe. This field decays completely during this stage of evolution. Introduction Hybrid Quintessential Inflation Gravitational Wave Spectrum Conclusions First stage of evolution: The potential energy of the scalar f dominates the evolution, yielding a period of chaotic inflation. Fourth stage of evolution: Extends from the beginning of the radiation-dominated era to the present epoch. A matter component (dark and baryonic matter) is introduce into the equations of motion, giving rise to an intermediate matter-dominated period of evolution. The scalar field fbegins, at late times, to dominate the evolution of the Universe, behaving like quintessence.

5. Hybrid Quintessential Inflation Introduction Hybrid Quintessential Inflation Gravitational Wave Spectrum Conclusions Time evolution of the equation-of-state parameter, . Chaotic inflation Kination Radiation domination Matter domination Accelerated expansion The post-inflationary kination period, characteristic of quintessential inflationary models, leaves a clear signature on the gravitational-wave spectrum(a peak at high frequencies).

6. Gravitational Wave Spectrum Introduction Hybrid Quintessential Inflation Gravitational Wave Spectrum Conclusions The full gravitational-wave spectrum is calculated using the method of continuous Bogoliubov coefficients. Gravitational-wave spectral energy density parameter given by: where is the gravitational wave frequency and is the squared Bogoliubov coefficient determined from: The scale factor and its derivatives are determined from the evolutionary equations of the hybrid quintessential inflationary model.

7. Gravitational Wave Spectrum Introduction Hybrid Quintessential Inflation Gravitational Wave Spectrum Conclusions Gravitational-wave spectrum for different values of the parameters of the model The parameters of the potential are constrained by measurements of the cosmic microwave background radiation and dark energy, as well as certain restrictions imposed on the behaviour of the scalar field c.

8. Gravitational Wave Spectrum Agreement with measured value of today’s dark energy density requires M to be of the order of . The decay of the scalar field c into radiation is achieved by the introduction of a phenomenological dissipative coupling between the scalar field c and the radiation fluid, proportional to the mass of c: Introduction Hybrid Quintessential Inflation Gravitational Wave Spectrum Conclusions Gravitational-wave spectrum for different values of the parameters of the model

9. Conclusions The maximum of the peak is firmly located in the MHz-GHz region of the spectrum and can reach values of about . Introduction Hybrid Quintessential Inflation Gravitational Wave Spectrum Conclusions Within the hybrid quintessential inflationary model a unified description of inflation and dark energy is achieved with a single scalar field fplaying both roles of inflaton and quintessence. The scalar field c is responsible for reheating. The hybrid-like quintessential inflationary potential contains several parameters which are constrained by measurements of the cosmic microwave background radiation and dark energy, as well as certain restrictions imposed on the behaviour of the scalar field c. The gravitational-wave spectrum carries, at high frequencies, a clear signature of quintessential inflation, namely, a peak at high frequencies. The height of the peak depends crucially on the duration of the kination period, which in turn depends on the parameters of the potential, as well as on the dissipative parameter. A search for gravitational waves in this range of frequencies was initiated a few years ago, with both microwave-cavity detectors and interferometric detectors.