Intelliverse is a Portmanteau combining the words intelligent and universe. The intelliverse is a hypothetical future state of the Universe, or portion of the Universe, in which intelligence saturates that volume of space by becoming embedded in all, or almost all, entities whether biological, physical or artificial.
To conform with customary usage of the words universe and Universe, the lower case "intelliverse" refers to a portion of the universe in which intelligence is embedded in all or almost all entities. The upper case "Intelliverse" refers to a future state of the entire Universe in which intelligence is embedded in all or almost all entities. The words intelliverse and Intelliverse having these definitions were coined by Robert Steven Kramarz. [✔]
The likelihood of an intelliverse or Intelliverse occurring is discussed in detail by Ray Kurzweil on the Edge site, in a post dated November 5, 2002, though he does not use the word intelliverse. According to Kurzweil, since there is no bona fide evidence that intelligence currently exists in any location except the planet Earth and on probes launched from the planet, the only known way, at the present time, that an intelliverse or the Intelliverse can come into existence is through the transportation of intelligent devices or biological beings (or some combination thereof) from the planet Earth to other planets and then later to other star systems and galaxies. Theoretically, this transportation can occur in a combination of ways: physical transport of intelligent devices and/or beings, and communication of information needed for the manufacture of intelligent devices and/or beings. Since the maximum rate of speed that physical devices, beings and information can travel is the speed of light, the theoretical maximum rate at which intelligence can spread out from the planet Earth is the speed of light. Therefore an intelliverse can expand at the maximum rate of the speed of light. Once a small portion of the universe becomes an intelliverse, this region can expand in all directions at the speed of life and at that rate eventually saturate the entire Universe, creating the Intelliverse. 
Ray Kurzweil stated the following in 2007 "The universe is made of stories, not atoms," and in Gardner's book, The Intelligent Universe, Kurzweil prefaces that "Gardner tells us the universe's own fascinating and unfinished story. Perhaps even more intriguing, Gardner relays in a clear and compelling manner the gripping stories of the rich, intellectual ferment from which our understanding of the universe is emerging."