(Based on descriptions in ACP and PoI)
Technology and economy progresses until von Neumann probes becomes possible (Tipler equates this with at least human-level AI, but as seen in nature self-reproducing systems do not need more than instincts to spread change their environment). As the technology gets cheaper, they become available to more and more people and finally someone will launch one.
An intelligent civilisation (Tipler assumes it is us) begins to expand using von Neumann probes. Each probe can travel to another solar system, explore it, build a base out of native materials (where humans could be assembled from stored records), and finally build copies of itself which are then launched to the next system. These probes would most probably have human (or greater) intelligence, and during their gradual spread through space become more and more advanced. From the world of origin a biosphere (or at least a technosphere) will expand, engulfing stars and galaxies and spreading life (in some form) to them. The universe is becoming more and more diverse.
The initial probes would be rather non-relativistic, but as they spread they can become faster. Using self-replicating technology the resources of entire solar systems could be used in building probes or improving them (in addition to other uses such as colonisation), and while the original probes travel at only 10% of the speed of light, later versions might travel at 90% (Tipler points out that for short distances greater velocities are unnecessary since the savings in time are rather small and the energy requirements prohibitive).
To reach very distant destinations, such as remote galaxies or the "cosmic antipodes" the probes have to start with a very high velocity in order to get there, since the universe expands during flight. Tipler proposes antimatter reactions to fuel the probes; with the technology and energies available by now the manufacture of large amounts of matter-antimatter fuel would not be very expensive.
While the probes spread outward, building a network of civilisation behind them, the oldest parts around the core begins to suffer an energy shortage. The time at this happens depends on how fast the civilisation is using up available energy, but sooner or later it is going to run out. Inhabitants either move to neighbouring regions or "hibernate", waiting for the universe to start recollapsing again.
In 10^12 years, the creation of new stars will cease (unless intelligent life extends their lifetimes using stellar husbandry, which will give some extra time), and all massive stars will become neutron stars or black holes (which however are excellent sources of energy for advanced civilisations). In 10^14 years even the longest living stars will use up all their fuel, and become white dwarves. In 10^15 years even the white dwarves will cool off to black dwarves with a temperature of 5 K. And in 10^19 years even the neutron stars will cool off to 100 degrees K.
As the universe nears its maximum expansion (in 10^18 years or so), it grows colder and emptier. The stars have died long ago, and civilisation have used up most available energy. Energy is at a premium, and matter is gradually converted to meet the remaining demands.
As the universe begins to collapse, the civilisation begins to exploit the anisotropy of the universe. By moving around matter on immense scales the collapse can be made more anisotropic, and the shear energy exploited. The cosmic background radiation will slowly grow stronger, but not as fast in all directions. This could be used to drive a heat pump, but most probably the posthuman beings of this era have devised more elegant solutions.
As the collapse speeds up, the amount of available energy grows more and more, and life returns everywhere. Hibernating beings return to activity, and life spreads into regions where it had previously been absent.
As the universe heats up, the cold matter in it will come to life again, most probably in the form of structures devised by the beings of this era. As it grows smaller, the temperature rises more and more until it becomes so high that solids begin to melt and dissipate into plasma; intelligent life has to create new forms of itself able to live in the plasma if it is to survive. Exactly what forms this could be we do not know yet; Tipler proposes standing waves interacting nonlinearly, but this is just a guess.
In order to exploit the shear energy as much as possible, life manipulates the collapse in complex ways to make it shift from one direction to another, providing more and more energy and opening up more and more of the universe for communication as it gets smaller. Using the ever increasing energy available, information processing becomes faster and faster, and from a subjective view the collapse becomes slower as the inhabitants become proportionally faster.
It is in this remote era (10^-10^10 - 10^-10^123 seconds before the final singularity) Tipler suggests that the Universal Resurrection will occur; the relative amount of computation required to actually emulate the entire previous history of the universe (or all possible universes) has become so small even individual beings could have the means to do it. Essentially all beings who have ever lived, or could have lived can be resurrected and given a new existence as beings within the immense virtual worlds.
While the universe collapses into a true singularity within a finite time, life squeezes the last drops of energy from it to develop faster than the collapse, and experience an infinite subjective time before the singularity; life will become immortal in its own perspective. An infinite amount of information is stored and processed, life evolves to its conclusion (which Tipler thinks is a single godlike being, Omega) and the universe becomes a single point, the Omega Point.
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