0. It must be a finite time period from the beginning of the Universe, (like 1 billion years)
1. It must have some relevance to the story or plot
2. It cannot be open ended, 'end of the Universe' as in The Last Question
3. Any Universe is allowed provided that it has a beginning (like a Big Bang)

closed as too broad by Wad Cheber, Rand al'Thor, Himarm, Jason Baker, Kyle Jones Dec 6 '15 at 2:56

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

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    Clicked wrong VTC reason. Duplicate of What is the latest date for the setting in a sci-fi text or movie? – Wad Cheber Dec 6 '15 at 2:34
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    Also, one billion years from the beginning of the universe is about 13 billion years ago. That is the opposite of the distant future. – Wad Cheber Dec 6 '15 at 2:42
  • @WadCheber You are right, I didn't see that. – Athena Widget Dec 6 '15 at 3:29
  • The Doctor, Jack Harkness, and Martha Jones travel to the year 100 trillion in the Doctor Who episode Utopia – Derek Dec 6 '15 at 5:10
  • Professor Farnsworth, Fry, and Bender travel to the very last moment of the universe 3 times in the Futurama episode The Late Philip J. Fry – Derek Dec 6 '15 at 5:11

I think it's in Stephen Baxter's Manifold: Time

Sheena – a genetically engineered squid, is traveling into the very deep future.
Paperback edition page 222

Malenfant said, "So the asteroid just evaporated."
"Yes, it got smaller and smaller, warmed gently by the annihilation of electrons and positrons in its interior, a thin smoke of neutrinos drifting out at light speed."
Emma asked, "How long this time?"
"The theories are sketchy, if you want me to put a number on it, I'd say ten to a power one hundred seventeen years." Even Cornelius looked bewildered now.

Bold added

Mr. Baxter's (an astrophysicist) idea is akin to Timeline of the far future

Far future

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