On the backreaction of quantum scalar fields on the de Sitter spacetime
The questions I wanted to address in my master thesis were: What effect do the particles, created during the expansion of our universe, have on the cosmological evolution?
In this work we analyse the behaviour of a quantised scalar field in a de Sitter background (a model of an exponentially expanding spacetime, which is often used as an approximation for the inflationary phase in the early universe) and the backreaction on the geometry. Due to the dynamic nature of the background no unique vacuum, diagonalising the Hamiltonian at all times, exists on the basis of which we can build a global Fock space. Imposing de Sitter invariance of our vacuum we find a two parameter class of vacua known in the literature as Mottola-Allen vacua, which are invariant under the time-preserving part of the de Sitter symmetry group. Furthermore, fixing one of the mentioned parameters results in a one parameter group of vacua, leaving argument-symmetric Green functions invariant under the full de Sitter group. Lastly, matching our result to the flat Minkowski solutions on very small scales where curvature is expected to be negligible, we can fix the last parameter and obtain what is referred to as the Bunch-Davies (BD) vacuum. We use our obtained insight to compute the expectation value of the regularised energy momentum tensor for a general choice of de Sitter invariant vacua. We conclude that as long as we respect de Sitter invariance, we do not get any dynamic backreaction and only obtain a constant shift in the cosmological constant. We then look for the breaking of this isometry in the loop corrections of a self interacting \( \lambda \phi^4 \) theory, but find that it is generally also respected in loops, as long we restrict to a certain coordinate patch of de Sitter spacetime. Finally, we break de Sitter isometry explicitly by introducing a scalar metric perturbation to the de Sitter geometry. We introduce a free massive scalar field to our spacetime and estimate the backreaction by solving for the perturbation. Our results show that in the short wavelength (UV) regime the largest contribution to the metric perturbation decays while oscillating in a similar way to gravitational wave modes. In the long wavelength (IR) regime we find that one part of the solution significantly grows and these perturbations can no longer be considered small.
