Classical “no-hair theorems” state that stationary black holes in Einstein-Maxwell theory are characterised by their mass, angular momentum and electric charge. Hawking et al. have argued that these theorems could be evaded exploiting a loop-hole in their formulation.  According to their proposal, non-extremal black hole horizons are endowed with an infinite dimensional group of symmetries, i.e. horizon supertranslations, which act on the black hole transforming it into a physically inequivalent one.  As a result, the state of the black hole must be characterised specifying, in addition to the standard three parameters, the configuration of “supertranslation-hair”. This result would not violate the classical no-hair theorems since supertranslated black holes are related to each other by diffeomorphisms. In this talk I will present a classical analysis showing that supertranslations act trivially on the dynamical degrees of freedom of non-expanding horizons.  As these diffeomorphisms do not transform the physical state of the horizon we conclude that they can be regarded as pure gauge. I will also review the proposed mechanism to implant supertranslation- hair on horizons, and show that the construction is inconsistent.

I will introduce a class of inflationary models, where inflation is driven exclusively or in part by non-abelian gauge fields. I will describe how the spectrum of density fluctuations and gravitational waves is computed, and show that these models can produce observationally viable spectra, if the gauge symmetry is spontaneously broken by a Higgs sector. The background gauge field texture violates parity, resulting in a chiral gravitational wave spectrum. This arises due to an exponential enhancement of one polarization of the spin-2 fluctuation of the gauge field. Higgsed Gauge-flation and related models can produce observable gravitational waves at inflationary energy scales well below the GUT scale.