Decoherence and disentanglement of qubits detecting scalar fields in an expanded universe

We consider Unruh-Wald qubit detector model adopted for the far future region of an exactly solvable 1+1 dimensional scalar field theory in a Robertson-Walker expanding spacetime. It is shown that the expansion of the universe in its history enhances the decoherence of the qubit coupled with a scalar field. Moreover, we consider two entangled qubits, each locally coupled a scalar field. The expansion of the universe in its history degrades the entanglement between the qubits, and can lead to entanglement sudden death if the initial entanglement is small enough. The details depend on the parameters characterizing the expansion of the universe. This work, albeit on a toy model, suggests that the history of the universe might be probed through the coherent and entanglement behavior of future detectors of quantum fields.