1. The universality of physical laws
2. The cosmological principle
3. The Copernican principle
When first developed, these ideas were simply taken as postulates,
but today there are efforts underway to test each of them. Tests
of the universality of physical laws have found that the largest
possible deviation of the fine structure constant over the age
of the universe is of order 10-5. The isotropy of the universe
that defines the Cosmological Principle has been tested to a level
of 10-5 and the universe has been measured to be homogenous on
the largest scales to the 10% level. There are efforts underway
to test the Copernican Principle by means of looking at the interaction
of galaxy clusters with the CMB through the Sunyaev-Zeldovich effect
to a level of 1% accuracy.
The Big Bang theory uses Weyl's postulate to unambiguously
measure time at any point as the "time since the Planck epoch".
Measurements in this system rely on conformal coordinates in which
so-called comoving distances and conformal times remove the expansion
of the universe, parameterized by the cosmological scale factor,
from consideration of spacetime measurements. The comoving distances
and conformal times are defined so that objects moving with the
cosmological flow are always the same comoving distance apart and
the particle horizon or observational limit of the local universe
is set by the conformal time.
Expansion of Spacetime
As the universe can be described by such coordinates, the Big Bang
is not an explosion of matter moving outward to fill an empty
universe; what is expanding is spacetime itself. It is this expansion
that causes the physical distance between any two fixed points
in our universe to increase. Objects that are bound together
(for example, by gravity) do not expand with spacetime's expansion
because the physical laws that govern them are assumed to be
uniform and independent of the metric expansion. Moreover, the
expansion of the universe on today's local scales is so small
that any dependence of physical laws on the expansion is unmeasurable
by current techniques.
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