Maximal momentum GUP leads to quadratic gravity
  Quantum theories of gravity predict interesting phenomenological features
such as a minimum measurable length and maximum momentum. We use the
Generalized Uncertainty Principle (GUP), which is an extension of the standard
Heisenberg Uncertainty Principle motivated by Quantum Gravity, to model the
above features. In particular, we use a GUP with modelling maximum momentum to
establish a correspondence between the GUP-modified dynamics of a massless
spin-2 field and quadratic (referred to as Stelle) gravity. In other words,
Stelle gravity can be regarded as the classical manifestation of a maximum
momentum and the related GUP. We explore the applications of Stelle gravity to
cosmology and specifically show that Stelle gravity applied to a homogeneous
and isotropic background leads to inflation with an exit. Using the above, we
obtain strong bounds on the GUP parameter from CMB observations. Unlike
previous works, which fixed only upper bounds for GUP parameters, we obtain
both \emph{lower and upper bounds} on the GUP parameter.
