Gravitational waves from inflation

Abstract

The production of a stochastic background of gravitational waves is a fundamental prediction of any cosmological inflationary model. The features of such a signal encode unique information about the physics of the Early Universe and beyond, thus representing an exciting, powerful window on the origin and evolution of the Universe. We review the main mechanisms of gravitational-wave production, ranging from quantum fluctuations of the gravitational field to other mechanisms that can take place during or after inflation. These include e.g. gravitational waves generated as a consequence of extra particle production during inflation, or during the (p)reheating phase. Gravitational waves produced in inflation scenarios based on modified gravity theories and second-order gravitational waves are also considered. For each analyzed case, the expected power-spectrum is given. We discuss the discriminating power among different models, associated with the validity/violation of the standard consistency relation between tensor-to-scalar ratio $r$ and tensor spectral index $n_{\rm T}$. In light of the prospects for (directly/indirectly) detecting primordial gravitational waves, we give the expected present-day gravitational radiation spectral energy-density, highlighting the main characteristics imprinted by the cosmic thermal history, and we outline the signatures left by gravitational waves on the Cosmic Microwave Background and some imprints in the Large-Scale Structure of the Universe. Finally, current bounds and prospects of detection for inflationary gravitational waves are summarized.

Figures (9)

• Figure 1: Example of inflationary potential with a "flat" region. After the slow-roll of the inflaton field $\varphi$, the reheating phase starts, the field is supposed to oscillate around the minimum of the potential and to decay in other particles; see section \ref{['sezionere']}. $\Delta\varphi$ indicates the inflaton excursion between the horizon exit of a given comoving scale and the end of inflation; see section \ref{['escursione']}.
• Figure 2: Time evolution of the comoving Hubble horizon during inflation and the following epoch, compared to the evolution of a comoving scale $\lambda$Lucchin:1985wy. During the accelerated expansion the comoving Hubble horizon decreases in time, while it grows during the radiation and matter dominated epochs. At a certain time during inflation, the comoving scale $\lambda$ exits the comoving Hubble horizon and then re-enters after inflation is over. The behavior of the comoving Hubble horizon shown in this figure, provides a solution to the horizon problem.
• Figure 3: Example of large field inflationary potential. $\Delta\varphi$ indicates the inflaton excursion between the horizon exit of a given comoving scale and the end of inflation.
• Figure 4: Hybrid inflation potential. The field rolls down the potential up to the critical point $\varphi_{c}$, and then reaches the true minimum of the potential $\varphi=0$, $\sigma=v$.
• Figure 5: Gravitational waves spectral energy density from numerical simulations generated after hybrid inflation. On the left $\lambda_{\rm t} = 10^{-14}$, on the right $\lambda_{\rm t}=10^{-5}$. The spectra for $\lambda_{\rm t} = 10^{-5}$ are, from top to bottom, for $\lambda_{\rm t}/g^{2} = 20000,\, 5000,\, 500,\, 50,\, 0.5,\, 0.005,\, 0.0005$ respectively. The spectra for $\lambda_{\rm t} = 10^{-14}$ are for $\lambda_{\rm t}/g^{2} = 5000,\,500$ respectively. All the spectra are for $v = 10^{-3}M_{\rm pl}$, although for $g^{2}\ll \lambda_{\rm t}$ a lower value of $v$ may be necessary to consistently neglect expansion of the Universe. The figure is taken from Dufaux:2008dn (©$\,\,$IOP Publishing. Reproduced with permission. All rights reserved.).