  There are two kinds of quantum fluctuations relevant to cosmology that we
focus on in this article: those that form the seeds for structure formation in
the early universe and those giving rise to Boltzmann brains in the late
universe. First, structure formation requires slight inhomogeneities in the
density of matter in the early universe, which then get amplified by the effect
of gravity, leading to clumping of matter into stars and galaxies. According to
inflation theory, quantum fluctuations form the seeds of these inhomogeneities.
However, these quantum fluctuations are described by a quantum state which is
homogeneous and isotropic, and this raises a problem, connected to the
foundations of quantum theory, as the unitary evolution alone cannot break the
symmetry of the quantum state. Second, Boltzmann brains are random agglomerates
of particles that, by extreme coincidence, form functioning brains. Unlikely as
these coincidences are, they seem to be predicted to occur in a quantum
universe as vacuum fluctuations if the universe continues to exist for an
infinite (or just very long) time, in fact to occur over and over, even forming
the majority of all brains in the history of the universe. We provide a brief
introduction to the Bohmian version of quantum theory and explain why in this
version, Boltzmann brains, an undesirable kind of fluctuation, do not occur (or
at least not often), while inhomogeneous seeds for structure formation, a
desirable kind of fluctuation, do.

General Relativity and Quantum Cosmology;Quantum Physics