Inflation as a spontaneous symmetry breaking of Weyl symmetry

Abstract

In this paper we study a novel realization of inflation, based on Weyl invariant gravity with torsion. We show that requiring the classical action for the scalar field to be Weyl invariant introduces a dilaton which induces a non trivial modification of the field space geometry of the scalar sector, which allows for inflationary phase that begins at the conformal point of the inflaton $\psi$, i.e. $\langle\psi\rangle=0$. Since the model is Weyl invariant, the inflaton condensation models a process of spontaneous Weyl symmetry breaking. For a wide range of parameters the spectral observables of the model are in good agreement with the CMB measurements, such that the scalar spectral index and the tensor-to-scalar ratio approximately agree with those of Starobinsky's inflation, i.e. $n_s\simeq 0.96-0.97$ and $r \approx 3\times 10^{-3}$. The simplest version of our model contains two scalar degrees of freedom, one of them being an exactly flat direction. If that degree is excited early on in inflation and if inflation lasts for about 60 e-foldings, we find that the Unverse undergoes a short period of kination that predates inflation. Such a period strongly suppresses the amplitude of large scale CMB temperature fluctuations providing thus an elegant explanation for the lack of power in the lowest CMB multipoles.