Question

What is the plot function: number of galaxy-clusters ( gravitationally bound objects) within the cosmic event horizon vs. time?

Answer 1

In a universe dominated by dark energy, the universe would expand forever. The equation for the comoving cosmological horizon in a universe that will expand forever is given by:

d(t)=∫∞tdt′a(t′)d(t)=∫t∞dt′a(t′)

Since we assume in the most accepted model that dark energy is due to a cosmological constant, the scale factor as a function of time in a universe with only dark energy would be approximately

a(t)∝eHta(t)∝eHt

where HH would be the Hubble parameter and constant.

Thus, we find that the cosmological at any time tt in a dark energy dominated universe is:

d(t)∝1a(t)H=1a˙(t)=e−HtHd(t)∝1a(t)H=1a˙(t)=e−HtH

In an expanding universe, this result is decidedly not constant (it definitely decreases), so the comoving distance is not unchanged and comoving objects do not remain in the observable universe (remember that at t→∞t→∞, the past light cone corresponding with what we can observe then would asymptotically overlap the event horizon, so comoving coordinates crossing outside the event horizon also cross outside of the observable universe).

The proper distance to the cosmological horizon in such a universe is constant. That means one could theoretically travel to the limits of it (limits here meaning arbitrarily close to but not at it) and then travel back in finite time, but the expansion would carry non-bound, comoving objects outside this limit eventually.

Answer 2

Timeline of the metric expansion of space, where space (including hypothetical non-observable portions of the universe) is represented at each time by the circular sections. On the left, the dramatic expansion occurs in the inflationary epoch; and at the center, the expansion accelerates (artist's concept; not to scale).

The Big Bang theory is the prevailing cosmological model for the universe from the earliest known periods through its subsequent large-scale evolution.The model describes how the universe expandedfrom a very high-density and high-temperature state, and offers a comprehensive explanation for a broad range of phenomena, including the abundance of light elements, the cosmic microwave background (CMB), large scale structure and Hubble's law. If the known laws of physics are extrapolated to the highest density regime, the result is a singularity which is typically associated with the Big Bang. Physicists are undecided whether this means the universe began from a singularity, or that current knowledge is insufficient to describe the universe at that time. Detailed measurements of the expansion rate of the universe place the Big Bang at around 13.8 billion years ago, which is thus considered the age of the universe.After the initial expansion, the universe cooled sufficiently to allow the formation of subatomic particles, and later simple atoms. Giant clouds of these primordial elements later coalesced through gravity in halos of dark matter, eventually forming the stars and galaxies visible today.