Manifold Space

A young lunar scientist, Nemoto, invites Reid Malenfant, champion of space colonization and organizer of a failed attempt to launch an asteroid mining enterprise, to the moon to show him mysterious sources of infrared she's discovered in the asteroid belt--incontrovertible proof of aliens at last. After all manner of signals and even a probe fail to elicit a response from the aliens, who come to be called Gaijin, Malenfant sets off for the source of the wave of aliens, the solar focus of Alpha Centauri. This is only the start of a journey across the galaxy, as he and others struggle to understand why signs of intelligent life are appearing all over the galaxy now and what happened to all the previous waves of colonization soon apparent even in humanity's own solar system, while humanity itself struggles to survive against draining resources, war, and destructive waves of alien colonists.

Part of Stephen Baxter's Manifold series.

Tropes used in Manifold Space include:

Alternate Continuity - To the other books in the Manifold series.
Apocalypse How - X-3, with all complex life in the galaxy periodically sterilized by the massive bursts of radiation from colliding neutron stars.
Arc Words: "Where is everybody?"
Compound Interest Time Travel Gambit - Used by interstellar travelers, who are frozen in time while traveling through the portal network. It works at first, but laws are eventually passed and assets seized, leaving the travelers flat broke when they return.
Distant Finale: The epilogue, a billion years after the last chapter, seems to suggest that the plan worked, and the next iteration of the Reboot cycle was postponed or avoided entirely, allowing life to flourish. Madeleine Meacher wakes up in a Gaijin habitat orbiting a fucking Quasar, and realizes that if the Gaijin survived, maybe so did the humans. And even if they didn't life itself was free from the cycle and had spread to distant galaxies.
Dope Slap - Malenfant is repeatedly smacked on the head by superstrong Neanderthals for speaking at all. Turns out that nearly all of their language is sign, with a few super-special vocal words. The Neanderthals give him a sign-name that means "Stupid".
Fling a Light Into the Future - At the end of the book, a coalition of aliens (including the Gaijin) are working on a mammoth solar sail designed to prevent two neutron stars from colliding and sterilizing the galaxy... except there's another collision--too late to prevent--that's going to occur first, killing the current generation. And the sail they're working on is leftover from a previous cycle.
Heroic Sacrifice - At the end of the book, Malenfant sacrifices his very humanity--becoming some sort of pain-wracked hivemind program getting refreshed over and over again--in order to supervise the construction of the solar sail over millions of years.
Hive Mind - The Gaijin have little in the way of self and frequently temporarily merge together for debates.
Macross Missile Massacre - Nemoto seeds Mercury with re-engineered lunar flowers, which fire rocket-propelled seed pods. Once the entire Cracker fleet is in orbit around the planet, they simultaneously fire all pods into the sky, causing the obliteration of the entire fleet.
Mechanical Evolution - The Gaijin are subject to this, with errors creeping in with each replication. A visit to their homeworld confirms that they were never built by anyone else but really did naturally evolve from scratch in an exotic iron-based ecology.
Mechanical Lifeforms - The Gaijin
Merlin Sickness - The sentient lunar flowers. They even proliferate backwards, with seed pods converging until eventually there's only one plant left. It's... odd.
Numbered Homeworld - The Gaijin refer to their homeworld as Zero-zero-zero-zero and use a fluid, location-descriptive naming system for all other systems they expand to, which suits their mechanical nature.
Orion Drive - How Malenfant reaches the portal in our solar system.
Planet Looters - The galaxy has been picked over by all kinds of looters many times over. Venus, for instance, used to be a hospitable place until an acid-based species spun down the planet, triggered a runaway greenhouse reaction to generate acid to farm, and broke up Venus's moon to make more ships.
Planet of Hats - Humans are the only species able to devote themselves entirely to an idea (i.e. have faith), which becomes critical by the end of the book.
Portal Network - The Saddle Point network. Precursors scattered portals at solar focus points throughout the galaxy that use quantum teleportation, which limits travel speed (to lightspeed) and total number of uses.
Projected Man - See Virtual Ghost.
The Slow Path - While other characters travel into the far future through use of the portals, experiencing no time subjectively, Nemoto persists in real time through combination of advanced medical treatments and sheer force of will, building up influence and manipulating humanity from the shadows.
Vicious Cycle: the Reboot.
Virtual Ghost - The limited-sentience projection of Nemoto, which leads to a What Measure Is a Non-Human? moment.
What Measure Is a Non-Human? - Nemoto usually communicates with space travelers through holographic projections. One, however, is different--an advanced "limited-sentience projection", basically a copy of Nemoto's personality in a holographic "body". The characters, who have been away for subjective centuries due to relativity, have to ask what a "limited-sentience projection" is. Virtual Nemoto explains, bringing the concept into her awareness, then has just enough time to look horrified before her time expires and she evaporates into unbound light.
Who Wants to Live Forever? - Nemoto keeps herself alive with advanced medical treatments for well over a thousand years, so she can deal with the problem of the alien Gaijin (and whoever the Gaijin are fighting). She doesn't seem to enjoy it much, and becomes extremely crotchety — but she's too much of a control freak to leave things in anyone else's hands.
Xenofiction - The short segments from the perspective of a lunar flower.