The fictional planet Lagash (Kalgash in the novel adaptation) is located in a stellar system containing six suns (Alpha, Beta, Gamma, and Delta are the only ones named in the short story; Onos, Dovim, Trey, Patru, Tano, and Sitha are named in the novel), which keep the whole planet continuously illuminated; total darkness is unknown, and as a result, so are all the stars outside the planet's stellar system.
A group of scientists from Saro University begin to make a series of related discoveries: Sheerin 501, a psychologist, researches the effects of prolonged exposure to darkness; Siferra 89, an archaeologist, finds evidence of multiple cyclical collapses of civilization which have occurred regularly about every 2000 years, and Beenay 25 is an astronomer who has discovered irregularities in the orbit of Lagash around its primary sun Alpha. Beenay takes his findings to his superior at the university, Aton, who formulated the Theory of Universal Gravitation (the in-story discussion of this makes light of an article once written about Einstein's theory of relativity, referencing the false notion that "only twelve men" could understand it). This prompts the astronomers at Saro University to seek the cause of this anomaly. Eventually, they discover that the only possible cause of the deviation is an astronomical body that orbits Lagash.
Beenay, through his friend Theremon 762, a reporter, has learned some of the beliefs of the group known as the Cult ("Apostles of Flame" in the novel). They believe the world would be destroyed in a darkness with the appearance of stars that unleash a torrent of fire. Beenay combines what he has learned about the repetitive collapses at the archaeological site, and the new theory of potential eclipses; he concludes that once every 2049 years, the one sun otherwise visible is eclipsed, resulting in a brief "night". His theory is that this "night" was so horrifying to the people who experienced it, they desperately sought out any light source to try to drive it away: particularly, by frantically starting fires which burned down and destroyed their successive civilizations. He also postulates that the "Apostles of the Flame" started out as vague surviving legends and myths after the last eclipse: small children too young to understand what was happening did not go insane but grew up half-feral in the ruins, and as they grew older, the only clues they had were the insane ramblings of adults who had lived through the eclipse. Over the centuries, these vague stories became legend, and then a cult of religious devotion.
Since the current population of Lagash has never experienced general darkness, the scientists conclude that the darkness would traumatize the people and that they would need to prepare for it. When nightfall occurs, the scientists (who have prepared themselves for darkness) and the rest of the planet are most surprised by the sight of hitherto invisible stars outside the six-star system filling the sky. Never having seen other stars in the sky, the inhabitants of Lagash had come to believe that their six-star system contained the entirety of the universe. In one horrifying instant, anyone gazing at the night sky – the first night sky which they have ever known – is suddenly faced with the reality that the universe contains many millions upon billions of stars: the awesome realization of just how vast the universe truly is drives them insane. This night sky is very different from that of Earth's, because Lagash and its stars reside in a globular cluster, where hundreds of thousands of stars are visible in the now-darkened sky.
The short story concludes with the arrival of the night and a crimson glow that was "not the glow of a sun", with the implication that societal collapse has occurred once again. In the novel and X Minus One program, civil disorder breaks out; cities are destroyed in massive fires and civilization collapses, with the ashes of the fallen civilization and the competing groups trying to seize control.

Question: Who believe the world would be destroy in darkness?
Answer: The cult.