Axions in Cold Dark Matter and Inflation Models
  The subjects of this thesis are the invisible axion and the more general
family of axion-like particles.
  The invisible axion is a hypothetical elementary particle and a cold dark
matter candidate. I present an improved computation of the constraints on the
parameter space of the cold dark matter axion in the standard cosmology, that
includes the contributions from anharmonicities in the axion potential and from
the decay of axionic strings. In this scenario, I update the value of the mass
of the cold dark matter axion, finding the value $(67\pm17){\rm \mu eV}$,
approximately one order of magnitude larger than previous computations.
  The effect of nonstandard cosmological scenarios on the parameter space of
axion cold dark matter is studied for the first time. In particular, I consider
the cases of low-temperature reheating and kination cosmologies, and I show
that the mass of the cold dark matter axion can differ from the value in the
standard cosmological scenario by orders of magnitude.
  Finally, I consider the family of axion-like particles, assuming that these
particles serve as the inflaton in the context of warm inflation. I find that
the axion energy scale $f$, which in the standard inflation scenario is of the
order of the Planck mass, can be lowered to the much safer Grand Unification
Theory scale $f \sim 10^{16}{\rm GeV}$. I also constrain the parameter space
and the amount of gravitational waves from this model, using results from the
Wilkinson Microwave Anisotropy Probe 7-year data.
