Tenho certeza que esta é a Seqüência Eschaton, começando com O Outro Fim de Tempo de Frederick Pohl.
A descrição do Goodreads verifica o básico:
his latest novel features Dan Dannerman, a poorly paid government agent in the not-too-distant future. Dannerman discovers aliens on an abandoned space station and is drawn into a conflict that encompasses the universe. According to one of its protagonists, the war Dannerman blunders into centers on what "ordinary people have been used to calling 'Heaven.'"
Outras análises confirmam vários outros detalhes:
Not very thought provoking, aside from the annoyingly unrealistic paradox of what to do when you meet with your exact duplicate (not a clone, but a quantum-accurate copy of yourself). The plot worryingly revolves around a real astrophysical "heaven" where, after the big crunch, all living things are reborn and share eternal life together.
Incluindo inflação:
By necessity, everyone carries guns for their own protection. Inflation has become so devastating that every day it's necessary to convert unspent cash into commodities/collectibles. Florida has more or less seceded from the U.S., etc.