Constraining the physics of the early Universe
  The established cosmological theory which describes the history of the
Universe since shortly after the "Big Bang" until today is remarkably
successful. Thanks to the increasing precision of available observational data,
we are now able to considerably constrain the geometry and composition of the
Universe --- and to glimpse how these will evolve in the near future. However,
this success comes at a price: one must assume the Universe "started" in a
highly fine-tuned initial condition. Understanding what came before this is
therefore one of the main goals of modern cosmology.
  This thesis attempts to further our understanding of the epoch before this
initial condition in three different ways.
  Firstly, the concept of negative absolute temperatures (NAT) is introduced
and its potential relevance for cosmology is investigated. In particular, it is
shown that a Universe at a NAT should undergo a period of inflation ---
although it is unclear whether this would be consistent with current
observations.
  Secondly, work is done on the topic of the evolution of networks of cosmic
strings --- topological defects which are expected to form in a broad class of
phase transitions the Universe may have gone through. A model which takes into
account the presence of small-scale structure in strings is used to address
questions concerning the existence and stability of scaling regimes for these
networks.
  Finally, it is investigated how future experiments might try to falsify a
simple class of canonical single-field slow-roll inflation models by measuring
the running and the running of the running of the spectral index of scalar
perturbations.
