Invisible Sun

Invisible Sun concludes Charles Stross's Empire Games trilogy, where two versions of America are locked in a cold war. This is a chillingly resonant dystopian vision.
Two twinned worlds are waiting for war ...
America is caught in a deadly arms race with the USA, its high-tech, parallel world. Yet it might just self-combust first. For its president-equivalent has died, leaving a crippling power vacuum. Without the First Man's support, Miriam Bernstein faces a paranoid government opponent. He suspects her of scheming to resurrect the American monarchy. And Miriam is indeed helping the exiled American princess. This is only to prevent her being used against them, but her rivals will twist anything to ruin her.
However, all factions will face a disaster bigger than anything they could imagine. In their drive to explore other timelines, hi-tech America has awakened an alien threat. This force destroyed humanity on one version of earth - and if they don't take action, it will do the same to both of their timelines.