Applications of the Hawking Energy in Inhomogeneous Cosmology
  The past lightcone of an observer in a cosmological spacetime is the unique
geometric structure directly linked to observations. After general properties
of the Hawking energy along slices of the past lightcone have previously been
studied, the present work continues along this path by providing explicit
cosmological applications of the Hawking energy associated with a lightcone.
Firstly, it is shown that amongst all two-dimensional non-trapped spheres with
equal area and average matter density, a shear-free matter distribution
maximizes the Hawking energy for sufficiently high densities. Secondly, a
Robertson-Walker reference slice is constructed for every lightcone slice based
on area and energy. Thirdly, after a few pedagogical examples in concrete FLRW
spacetimes, the implications of monotonicity of the energy down the lightcone
are explored, arriving at two new bounds on the cosmic fluid's density and
equation-of-state parameter.
