Improved DHOST Genesis

We improve the DHOST Genesis proposed in [1], such that the near scale invariant scalar power spectrum can be generated from the model itself, without invoking extra mechanism like a string gas. Besides, the superluminality problem of scalar perturbation plagued in [1] can be rescued by choosing proper DHOST action.

Nilpotent symmetries as a mechanism for Grand Unification

In the classic Coleman-Mandula no-go theorem which prohibits the unification of internal and spacetime symmetries, the assumption of the existence of a positive definite invariant scalar product on the Lie algebra of the internal group is essential. If one instead allows the scalar product to be positive semi-definite, this opens new possibilities for unification of gauge and spacetime symmetries. It follows from theorems on the structure of Lie algebras, that in the case of unified symmetries, the degenerate directions of the positive semi-definite invariant scalar product have to correspond to local symmetries with nilpotent generators. In this paper we construct a workable minimal toy model making use of this mechanism: it admits unified local symmetries having a compact (U(1)) component, a Lorentz (SL(2, ℂ)) component, and a nilpotent component gluing these together. The construction is such that the full unified symmetry group acts locally and faithfully on the matter field sector, whereas the gauge fields which would correspond to the nilpotent generators can be transformed out from the theory, leaving gauge fields only with compact charges. It is shown that already the ordinary Dirac equation admits an extremely simple prototype example for the above gauge field elimination mechanism: it has a local symmetry with corresponding eliminable gauge field, related to the dilatation group. The outlined symmetry unification mechanism can be used to by-pass the Coleman-Mandula and related no-go theorems in a way that is fundamentally different from supersymmetry. In particular, the mechanism avoids invocation of super-coordinates or extra dimensions for the underlying spacetime manifold.

Gravitoelectromagnetic inflation and seeds of cosmic magnetic fields from geometrical Weyl-invariant scalar–tensor theory of gravity

We investigate cosmological inflationary scenarios from a gravitoelectromagnetic theory. Our work is formulated in light of a recently introduced geometrical Weyl-invariant scalar–tensor theory of gravity, where the nature of both the electromagnetic potential and the inflaton field is attributed to the space–time geometry. We obtain a Harrison–Zeldovich power spectrum for quantum fluctuations of the inflaton field. In our model the electromagnetic fields also have a nearly scale-invariant power spectrum for a power-law inflation. We found that the seed magnetic fields have a nearly scale-invariant power spectrum and generate at the present time cosmic magnetic fields of the order ≲10−9 G, in good agreement with CMB observations.