Homogeny of the Universe far beyond the Observable Scale Thought experiment: Suppose we have complete knowledge of the observable universe (as of 2016) within some margin of error $\varepsilon$ for arbitrary but final $\varepsilon > 0$.  Call the radius of the observable universe $r$.  Suddenly, we have complete knowledge of the universe within a radius $mr$ where $m$ is a really large (but nameable) positive integer.
Would we learn anything new?  IE could there ultra-large scale force / phenomena undetectable at the "small" observable universe scale?  Are we agnostic that there may be supra-large scale or is it argued that everything possible that could be detected given accurate observation of our own observable universe?
I am thinking of the observable universe here as compared to a grain of sand and what is asserted about "everything else".  Is it assumed the beyond-observable-scale view is just more of the same: what we see in Hubble but in different variations... or is the possibility of large scale heterogeneity acknowledged but dismissed as a matter of philosophy?
 A: I attach a diagram below and reference a Phys.SE answer I gave a few months ago. I illustrate how the Friedman-Lemaitre-Robertson-Walker energy equation for the cosmological scale factor $a$
$$
\left(\frac{\dot a}{a}\right)^2 = H^2 = \frac{8\pi G\rho}{3}.
$$
can be derived from Newtonian mechanics. This has some subtle connections with the apparent nonrelativistic dynamics of a system approaching an event horizon, or the boundary of an anti-de Sitter spacetime. This gives the Hubble relationship $\dot a~=~Ha$ or $v~=~Hd$ for the expansion velocity of a galaxy at a distant $d$ with $H~=~70~{\rm km/s~Mpc}$. As a result a galaxy at a million parsecs away $1~{\rm pc}~=~3.26$ light years is receding away at $70~{\rm km/sec}$. The red shift factor $z~=~v/c$ for $z~=~1$ permits us to compute the distance $d~=~c/H$ that is then about $4000~{\rm Mpc}$ or about $13$ billion light years. Let us go more extreme. The optical photons released at the end of the radiation dominated phase is stretched by about $z~=~1100$ which gives a distance of $46$ billion light years. The distance to this region on the Hubble frame today is larger than the age of the universe multiplied by the speed of light. This is because space is being stretched by geometrodynamics or the dynamics of gravity or relativity.

I now refer to the diagram. The dark dashed line labelled the particle horizon is the CMB distance at the horizontal line corresponding to the current Hubble frame or spatial surface. This dashed line intersects the past light cone, a tear drop shaped curve at a time $380,000$ years. There are other dashed lines, and some of these will clearly intersect the Hubble surface region at a much larger spatial distance. These correspond to physical events that would have emitted light on the past light cone at a time previous to $380,000$ years. This does mean that data from events prior to the end of the radiation dominated phase are in principle observable.
We might in the future be able to observe this more ancient physics. The BICEP II data was meant to look for signatures of gravity waves produced by inflationary physics that induced B-modes on the CMB. This is a sort of indirect way of trying to observe more ancient data. After reporting a $6$ sigma data confirming this it was found that galactic dust which emulate B-modes reduced this data to about $3$ sigma. In the future it may be that neutrinos produced by the very early times of the universe. Maybe gravitons produced in the inflationary or quantum gravity time of the universe may also be observed. 
