Short answers, pulled from the story.
The Shiva hypothesis, also called coherent catastrophism, holds that global natural catastrophes including extinction events strike Earth at regular intervals, driven by the periodic motion of the Sun through the Milky Way galaxy. Each time the Solar System crosses the galactic plane, gravitational disturbances reach the Oort cloud, deflecting comets toward the inner Solar System and raising the risk of large impacts on Earth.
William Napier and Victor Clube first proposed the idea in a 1979 article in Nature titled "A Theory of Terrestrial Catastrophism." Michael R. Rampino began publishing followup research in 1984 and, in the 1990s, renamed the hypothesis after Shiva alongside Bruce Haggerty.
The Shiva hypothesis proposes that large impact events and associated extinction cycles repeat roughly every 30 million years. The Cretaceous-Paleogene extinction event is one of the catastrophes the hypothesis cites as evidence.
The hypothesis was renamed after Shiva, the Hindu god of destruction, by Michael R. Rampino and Bruce Haggerty in the 1990s. They replaced the original title, "A Theory of Terrestrial Catastrophism," which Napier and Clube had given it in 1979.
The Nemesis theory proposes that a brown dwarf companion to the Sun triggers extinctions every 26 million years. This differs slightly from the 30-million-year cycle the Shiva hypothesis proposes, and the Shiva hypothesis may have inspired the Nemesis idea.
The primary criticism is that the Shiva hypothesis assumes most or all extinction events share the same cause. Evidence from the geological record suggests extinctions more likely result from a variety of causes that are unlikely to be triggered by a single recurring astronomical cycle.