Cosmological Inflation and the Quantum Measurement Problem
  According to cosmological inflation, the inhomogeneities in our universe are
of quantum mechanical origin. This scenario is phenomenologically very
appealing as it solves the puzzles of the standard hot big bang model and
naturally explains why the spectrum of cosmological perturbations is almost
scale invariant. It is also an ideal playground to discuss deep questions among
which is the quantum measurement problem in a cosmological context. Although
the large squeezing of the quantum state of the perturbations and the
phenomenon of decoherence explain many aspects of the quantum to classical
transition, it remains to understand how a specific outcome can be produced in
the early universe, in the absence of any observer. The Continuous Spontaneous
Localization (CSL) approach to quantum mechanics attempts to solve the quantum
measurement question in a general context. In this framework, the wavefunction
collapse is caused by adding new non linear and stochastic terms to the
Schroedinger equation. In this paper, we apply this theory to inflation, which
amounts to solving the CSL parametric oscillator case. We choose the
wavefunction collapse to occur on an eigenstate of the Mukhanov-Sasaki variable
and discuss the corresponding modified Schroedinger equation. Then, we compute
the power spectrum of the perturbations and show that it acquires a universal
shape with two branches, one which remains scale invariant and one with nS=4, a
spectral index in obvious contradiction with the Cosmic Microwave Background
(CMB) anisotropy observations. The requirement that the non-scale invariant
part be outside the observational window puts stringent constraints on the
parameter controlling the deviations from ordinary quantum mechanics...
(Abridged).
