JAXA took a good long look at the Petrova line and they say it's getting brighter at the same rate that the sun is getting dimmer. Somehow or another, whatever it is, the Petrova line is stealing energy from the sun.
-- Marissa (chapter 2 paragraph 2)

Importance: In the novel's second flashback, Ryland recalls having dinner with his friend Marissa, who works for the U.S. government. She explains that the sun's output is decreasing because of whatever is causing the Petrova line (which turns out to be Astrophage), citing a discovery by the Japanese space program. This is a critical piece of information for Ryland to remember in the present-day timeline, and it also establishes the novel's central conflict for the reader.

I still don't remember my own name, but I remember random bits of information about the Petrova problem. They call it the Petrova problem. I just remembered that. My subconscious has priorities. And...
-- Ryland (chapter 2 paragraph 5-6)