Inflationary gravitational waves from unified spinor fields

Abstract

Recent observations of Gravitational Waves (GW) generated by black-hole collisions have opened a new window to explore the universe in diverse scales. Detection of primordial gravitational waves is expected to happen in the next years. However, the standard theory to describe these effects was developed for weak gravitational waves, when their dynamics can be linearized. In this work we develop a non-perturbative formalism to describe GW using the Unified Spinor Fields (USF) theory. The tensor index is calculated and we obtain that it must be $0.0283 <n_T < 0.0407$, in order for the $+$ and $\times$ polarisations modes to have the same spectrum. This imposes some restriction on the constant of self-interaction $3.0018\,<\,\xi^2\,< \,3.0025$ of the fermionic source. The most relevant result here obtained is that the intensity of energy density for GW during inflation is $1.25\times 10^{-4} \left(\frac{m}{H}\right)^2 \, < \,\Omega_{GW} \, < \,1.75\times 10^{-4} \left(\frac{m}{H}\right)^2$, where $m$ is the mass of the $1/2$-spin fermionic fields and $H$ the Hubble parameter during inflation. This cut imposes restrictions on the mass of these fields: $\left({m\over H}\right)^2\lesssim 1.1\,h_0^2\times 10^{-11}$.