World lines (blue dashes on left) show cosmic expansion for objects currently at
8, 16 & 46 Gly (the latter is the particle horizon). Black dotted lines on the
right show where the expansion speed is 2c, c, c/2 (expansion speed c is the Hubble
distance  currently c/H_{o} = 4.167 Gpc = 13.58 Gly). Black dotdashed line
on the left is the expanding particle horizon (approx 2c during the matter dominated
phase), which joins with the world line of our current particle horizon at time=now
(off the diagram).
Solid red line shows, on both sides, the trajectory of a light ray which starts at
the big bang from our current particle horizon. It is also the eventline which
we witness now as light comes to us, ie we see only those events lying on the red
line (light rays starting at other spacetime events have either already arrived or
will arrive in the future)  the light cone is for light arriving now.
Notice that for the first 4 Gyr, the light is actually getting further from
us, carried by cosmic expansion. At 4 Gly it crosses the Hubble distance at that
time (ie expanding at c) and finally begins to get closer. Other lines of constant
expansion speed are also shown (c/2 and 2c). Notice that the light cone finally
arrives at 45 degrees, since locally the expansion is essentially zero.
Redshift, z, and comoving (current) distance, r_{o}, scales are also indicated
on the right and left halves of the light cone (note that the r_{o} values
match the world line values at their intersection).

The equivalent spacetime diagram, but with space now in comoving (current) distance
(note that the scales are no longer 1:1, so the apex doesn't seem to be 45 degrees,
though in fact it is). World lines are now simple vertical lines. Notice also
that the Hubble distance (ie where v=c) reaches a maximum and begins to approach
us after acceleration has begun. The scales marked along the light cone are
redshift (right) and emission distance, r_{e} (left).
As before, the black dotdashed line shows the expanding particle horizon, meeting
the 46 Gly world line of our current particle horizon at time t=now. This distance,
in comoving coordinates, is also equal to c conformal time, which
will be used as the time axis in the third and final spacetime diagram.

The final spacetime diagram recovers the familiar 45 degree form, as long as we
use comoving distance and conformal time ((t) =
dt/a 0 to t), and plot these at the same scale.
As before, redshift and emission distance are marked along the cone. Notice how
rapid early expansion stretches conformal time near the big bang, so
that even the CMB is visibly offset from the y=0 axis (and would be impossible to
see with a normal time axis).
Notice that the Hubble distance is rapidly decreasing during acceleration, and in
fact becomes
zero at conformal time 65 Gly, which corresponds to the infinite future (we see
a smaller and smaller comoving part of the Universe as exponential expansion proceeds).
Figures made for this website.
