Antispiral's Universe

Super Spiral Space (超螺旋宇宙, Chō Rasen Uchū, or the Super Spiral Universe) is an isolated universe located between the membranes of 10th and 11th dimensions created by the Anti-Spirals to hid their planet or homeworld. A grotesque and vivid otherworld, where the Anti-Spiral war lurked in. It is an extra-dimensional space that is completely uncommon to common sense. Mega galaxies that fills the heavens in very clear way with countless backdrop of jewel-like stars like a painting of surrealism. It's a surprisingly different world that humanity has never set foot on. The universe itself has become an enemy of Simon and the others, bared its fangs.

Super Spiral Space is a brane universe (also known as bulk or hyperspace) with a different set of dimensional axes and exist beyond the time and space corresponding up to 11 dimensional reality that is created, occupied and fully controlled by the Anti-Spirals according to their very own whim. It's a universe with its own law of physics where every imaginable thought becomes reality, the Multiverse Labyrinth is being composed inside the Super Spiral Space is a further proof it has up to 11 dimensional constructed. The space is later destroyed after the Anti-Spiral is killed.

Tengen Toppa Gurren Lagann creates the whole Super Spiral Space within itself to challenge the Anti-Spiral.

Trivia

 * "Even if the infinite universe stands in our way!" was said by Leeron in episode 27, indicating the Super Spiral Space spreads endlessly and consisting infinite numbers of Super Spiral galaxies.

Source

 * 1) Final Drill Guidebook
 * 2) https://www.japanator.com/the-secrets-of-gurren-lagann-answered--6714.phtml