Bigravity with single graviton

I'll present a new model inspired by ghost-free bigravity. Despite involving two metrics as the usual bigravity models, it describes only one gravitational interaction. Expanded around a large class of backgrounds, the model propagates a single massless graviton. At non-linear level it has 6 additional degrees of freedom, but they contain neither massive graviton, nor the Boulware-Deser ghost. Thus, the model represents an interesting modification of general relativity which might be relevant for cosmology.