Quantum field theory in curved spacetime provides many important insights into the interaction of matter and gravity. An unavoidable consequence of the theory is the amplification of field and metric fluctuations during inflation, which later become the seeds for the structure formation in the cosmos. These fluctuations get imprinted in the anisotropies of the Cosmic Microwave Background (CMB), which provide an excellent observational window to the physics of the early universe

In this work we consider a free scalar field ϕ propagating in a curved spacetime. A free floating scalar field is a function which associates a single number to every point in a space. In the simplest model realizations of inflation, the accelerated expansion of the universe is indeed generated by a scalar field. For (quasi-free) Gaussian states, the information about the state is encoded in the two-point correlation function.