Quantum initial conditions for inflation

In numerical simulations of the early universe, primordial perturbations are modelled and evolved from soon after the Big Bang until today. The simulations need to start the perturbations from some initial state (initial conditions), which depends on the way the quantum vacuum was defined. This definition is far from trivial on a time-dependent spacetime.

My work investigates different methods to define the ground state on non-static spacetimes. Some of the well-known methods yield different initial conditions for the perturbations under so-called canonical transformations. The transformations I looked at were either

  • a variable transform in the action associated with the system,

or

  • an integration by parts in the action.

Canonical transformations in classical mechanics are used to find the best parametrisation of the system, and to discover conserved quantities. They don’t change the equation of motion or anything physical - they are just coordinate transformations. In quantum field theory, they don’t change the dynamics of the system, and interestingly, if the vacuum is unchanged under canonical transformations then so will be the expectation values of quantum operators. The contrary is also true, the expectation values will shift with the vacuum if it isn’t canonically invariant. This has been accepted as a property of the transformations, but it also suggests that a vacuum formulation that is invariant under canonical transformations should be used preferentially. I found a physically well-motivated vacuum definition that is just like that, and it derives the vacuum via minimising the energy-density part of the renormalised stress-energy tensor.

More coming soon!