Their calculations show that there is indeed a critical temperature at which an empty,
flat spacetime turns into an expanding universe with mass.
What causes this mismatch of the two
flat spacetime regions is the large spacetime curvature in the bubble wall that separates the regions.
However, it has been suspected for a while, that there may be a similar version of the «holographic principle» for
flat spacetimes.
Not exact matches
In the absence of mass,
spacetime is
flat and objects traveling through it move in a straight line.
Outside the bubble,
spacetime is also
flat and no particle can travel faster than light — relative to observers outside the bubble.
In curved
spacetimes, when we compare two observers at large separation, we can no longer use the «locally
flat» approximation.
When
spacetime is curved, the theory applies only «locally» — that is, over regions of
spacetime small enough to be considered
flat.
But special relativity applies when
spacetime is
flat.
In fact, we now know that
spacetime is
flat and that galaxies and radiation are evenly distributed throughout.