Ordinary quantum field theories, which form the basis of standard model, are defined in flat Minkowski space, which is an excellent approximation when it comes to describing the behavior of microscopic particles in weak gravitational fields like those found on Earth.
For non-zero cosmological constants, on curved spacetimes quantum fields lose their interpretation as asymptotic particles.
[2] Only in certain situations, such as in asymptotically flat spacetimes (zero cosmological curvature), can the notion of incoming and outgoing particle be recovered, thus enabling one to define an S-matrix.
Another observation is that unless the background metric tensor has a global timelike Killing vector, there is no way to define a vacuum or ground state canonically.
Since the end of the 1980s, the local quantum field theory approach due to Rudolf Haag and Daniel Kastler has been implemented in order to include an algebraic version of quantum field theory in curved spacetime.
[13][14][15][16] This formalism is also used to predict the primordial density perturbation spectrum arising in different models of cosmic inflation.