Observations and horizons 145so there is no reason to think they are very different. Nevertheless, in the end this
argument rests on an unproved philosophical assumption (that other observers
see more or less what we do), and so is highly suggestive rather than a full
observational proof. In addition, there is a technical issue of substance, namely
what derivatives of the CBR temperature should be included in this formulation
(remembering here that there are Bianchi models where the matter shear remains
small but its time derivative can be large; these can have a large Weyl tensor but
small CBR anisotropy [99]).
3.8.5.4 Theoretical arguments
Given the observational difficulties, one can propose theoretical rather than
observational arguments for spatial homogeneity. Traditionally this was done by
appeal to acosmological principle[6,131]; however, this is no longer fashionable.
Still some kinds of theoretical argument remain in vogue.
One can try to argue for spatial homogeneity on the basis ofprobability:this
is more likely than the case of a spherically symmetric inhomogeneous universe,
where we are near the centre (see [43] for detailed development of such a model).
However, that argument is flawed [30], because spatially homogeneous universe
models are intrinsically less likely than spherically symmetric inhomogeneous
ones (as the latter have more degrees of freedom, and so are more general). In
additionally, it is unclear that any probability arguments at all can be applied to
the universe, because of its uniqueness [37].
Alternatively, one can argue thatinflation guarantees that the universe must
be spatially homogeneous. If we accept that argument, then the implication is that
we are giving preference to a theoretically based analysis over what can, in fact, be
established from observational data. In addition, it provides a partial rather than
complete solution to the issues it addresses (see the discussion in the next section).
Nevertheless it is an important argument that many find fully convincing.
Perhaps the most important argument in the end is that fromcumulative
evidence: none of these approaches by themselves proves spatial homogeneity,
but taken together they give a sound cumulative argument that this is indeed the
case—within the domain previously specified above.
3.8.5.5 Domains of plausibility
Accepting that argument, to what spacetime regions does it apply? We may take
it as applying to the observable region of the universeV,thatis,the region both
inside our visual horizon, and lying between the epoch of decoupling and the
present day. It will then also hold in some larger neigbourhood of this region, but
there is no reason to believe it will hold elsewhere; specifically, it need not hold
(i) very far out from us (say, 1000 Hubble radii away), hence chaotic inflation is
a possibility; nor (ii) at very early times (say, before nucleosynthesis), so Bianchi
anisotropic modes are possible at these early times; nor (iii) at very late times (say