Causal set theory is an approach to quantum gravity in which spacetime is fundamentally discrete at the Planck scale and takes the form of a irregular Lorentzian lattice, or "causal set", from which continuum spacetime emerges in a large-scale (low-energy) approximation.

After reviewing the formulation of free quantum field theory on causal sets, I will present new developments by adding interactions.

I will derive a manifestly causal diagrammatic expansion for in-in correlators in local scalar field theories with finite polynomial interactions. By the comparison with results in the continuum, I will highlight how the fundamental discreteness of the causal set acts as a natural cut-off, eliminating the UV divergences which characterise the continuum.

Moreover, I will propose a generating functional for in-out correlators and define a notion of scattering amplitudes on causal sets. I will conclude by describing how these formal developments can be implemented to compute early universe observables under the assumption that spacetime is fundamentally discrete.