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Years later, when Foster unintentionally became the host of the Aether, she had a vision of Malekith extracting it from her body in his final plan to consume the Earth, darken the Sun, and turn all of Yggdrasil via the Aether back into dark matter. However, Thor and Foster managed to defeat Malekith before this could come to pass.
The tree in the Hall of Science is connected to Yggdrasil and indicates the health and well-being of the Nine Realms. If Ragnarök happens, the branches which represent the affected realms would fall off.