Nonlinear Field Space Cosmology
  We consider the FRW cosmological model in which the matter content of
universe (playing a role of inflaton or quintessence) is given by a novel
generalization of the massive scalar field. The latter is a scalar version of
the recently introduced Nonlinear Field Space Theory (NFST), where physical
phase space of a given field is assumed to be compactified at large energies.
For our analysis we choose the simple case of a field with the spherical phase
space and endow it with the generalized Hamiltonian analogous to the XXZ
Heisenberg model, normally describing a system of spins in condensed matter
physics. Subsequently, we study both the homogenous cosmological sector and
linear perturbations of such a test field. In the homogenous sector we find
that nonlinearity of the field phase space is becoming relevant for large
volumes of universe and then it can lead to a recollapse, and possibly also at
very high energies, leading to the phase of a bounce. Quantization of the field
is performed in the limit where nontrivial nature of its phase space can be
neglected, while there is a non-vanishing contribution from the Lorentz
symmetry breaking term of the Hamiltonian. As a result, in the leading order of
the XXZ anisotropy parameter, we find that the inflationary spectral index
remains unmodified with respect to the standard case but the total amplitude of
perturbations is subject to a correction. The Bunch-Davies vacuum state also
becomes appropriately corrected. The proposed new approach is bringing
cosmology and condensed matter physics closer together, which may turn out to
be beneficial for both disciplines.
