Abstract
Inflation driven by a generic self-gravitating medium is an interesting alternative to study the impact of spontaneous spacetime symmetry breaking during a quasi de-Sitter phase, in particular the 4-dimensional diffeomorphism invariance of GR is spontaneously broken down to I SO(3). The effective description is based on four scalar fields that describe the excitations of a supersolid. There are two phonon-like propagating scalar degrees of freedom that mix non-trivially both at early and late times and, after exiting the horizon, give rise to non-trivial correlations among the different scalar power spectra. The non-linear structure of the theory allows a secondary gravitational waves production during inflation, efficient enough to saturate the present experimental bound and with a blue-tilted spectral index.
Highlights
A matter of fact, φA can be interpreted as the coordinates of a self-gravitating nondissipative medium [10,11,12,13,14,15] that in our case is a supersolid
The secondary production can give a blue tilt to the spectral index, an important feature for the direct detection of the stochastic gravitational waves (GWs) background produced during inflation
A global spatial rotation Rijxj can be absorbed by a corresponding inverse internal transformation of φa and the same is true for a global translation xi → xi + ci thanks to the shift symmetry (2.2)
Summary
Several features of inflationary models can be traced back to the spontaneous symmetry breaking pattern: in single field inflation, the non-trivial time-dependent configuration of the inflaton breaks time reparametrization leaving unbroken the space diffeomorphisms of the t =const. hypersurface. The existence of a spatially homogeneous background is allowed by the presence of global symmetries of the scalar field action. That can be interpreted as the relativistic generalization of the low-energy effective Lagrangian describing homogeneous and isotropic supersolids at zero-temperature [17, 18] Such an action is the most general at leading order in a derivative expansion compatible with (2.2) and (2.3) and it is rather useful to study systematically the symmetry breaking pattern of spacetime symmetry during inflation. Notice that the space shift symmetry is crucial to have a homogeneous EMT even if the scalar fields have non-trivial background values. It is useful to summarize the main features associated with the presence or absence of some of the operators (and the related mass parameters) in the Lagrangian depending on a specific set of internal symmetries.
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