  The last decades have witnessed an unprecedented advancement in our knowledge
of the large scale universe. In particular, increasingly accurate cosmological
observations have allowed us to discover a form of "dark energy", which
presently dominates the expansion of the universe. On the other hand,
fundamental problems in the standard cosmological model point towards the
possibility of a primordial inflationary period. Both these expansion phases
have in common the fact that they should be governed by forms of energy with
properties much similar to those of vacuum energy of classical or quantum
fields. In the meanwhile, quantum field theory in curved spaces (QFTCS) has
proved a rich framework to analyze phenomena of a quantum nature in regimes
where spacetime curvature is relevant, but not too extreme; particularly, it
yields novel insights on the structure and dynamics of quantum vacuum. In this
dissertation, we make a thorough exposition of the fundamentals of QFTCS and
present some of its applications in cosmological spacetimes. Particular
attention is given to the construction of an empirical notion of particles
through an idealized model of particle detectors, and to the phenomenon of
particle creation in expanding FLRW spacetimes. Further, we develop the
procedure of adiabatic renormalization, and use it to compute the renormalized
stress tensor in these spacetimes. For a noninteracting scalar field in de
Sitter spaces, we find that it takes the form of a cosmological constant,
although a quantitatively self-consistent value with the background expansion
can only be found at Planckian densities. We also present a construction of a
simple inflationary model, driven by a self-interacting classical scalar field,
and show how the quantized fluctuations of this field could give rise to a
nearly scale-invariant power spectrum, like the one that is currently observed
in the CMB.
