Fading Gravity and Self-Inflation

We study the cosmology of a toy modified theory of gravity in which gravity shuts off at short distances, as in the fat graviton scenario of Sundrum. In the weak-field limit, the theory is perturbatively local, ghost-free and unitary, although likely suffers from non-perturbative instabilities. We derive novel self-inflationary solutions from the vacuum equations of the theory, without invoking scalar fields or other forms of stress energy. The modified perturbation equation expressed in terms of the Newtonian potential closely resembles its counterpart for inflaton fluctuations. The resulting scalar spectrum is therefore slightly red, akin to the simplest scalar-driven inflationary models. A key difference, however, is that the gravitational wave spectrum is generically not scale invariant. In particular the tensor spectrum can have a blue tilt, a distinguishing feature from standard inflation.