Kevin Langhoff and colleagues in their recent paper studied the eternally inflating multiverse using the global spacetime approach.
The holographic principle is a property of quantum gravity theories which resolves the black hole information paradox within string theory. It states that a fundamental description of quantum gravity resides in a space-time, often non-gravitational, whose dimension is lower than that of the bulk spacetime.
An idea of holography can be implemented via two approaches. The first approach start from global spacetime of general relativity & identify independent quantum degrees of freedom using the quantum extremal surface (QES) prescription. Another approach starts with a description that is manifestly unitary and understand how the picture of global spacetime emerges.
Kevin Langhoff and colleagues in their recent paper studied the eternally inflating multiverse using the first approach which begins with global spacetime. They showed that the multiverse exists on spatial region “R” (which has finite volume), surrounded by an inverted island ‘I’, in a bubble universe. They also suggested that, the fundamental degrees of freedom associated with certain finite spatial regions describes the semiclassical physics of multiverse, which allows them to address cosmological measure problem.
“While one might feel that this is too drastic a conclusion, in some respects it is not. What happens in the multiverse is an”inside out” version of the black hole case”
In the black hole case, the region R encloses I, so I looks geographically like an island. However, in Langhoff et al. setup (as shown in fig. 1 above), I encloses R so it no longer appears as an island. Thus, we can call I an “inverted island”.
In other words, you can treat the regions R and I as “land” and everything else as “water.” Following this convention, cauchy surface Ξ has a central land R surrounded by a moat ¯R ∪ IΞ¯ which separates R from IΞ, where IΞ = D(I)∩Ξ. To describe the multiverse at the semiclassical level, one only needs fundamental degrees of freedom associated with the complement of IΞ on Ξ, ¯IΞ¯ = R∪(¯R ∪ IΞ¯). This is the region corresponding to the castle, where the multiverse lives in.
“The island arises due to mandatory collisions with collapsing bubbles, whose big crunch singularities indicate redundancies of the global spacetime description.”
Finally, they concluded that, the emergence of the island and the resulting reduction of independent degrees of freedom provides a regularization of infinities which caused the cosmological measure problem. Their paper strongly suggests the existence of a description of the multiverse on finite spatial regions.
Reference: Kevin Langhoff, Chitraang Murdia, Yasunori Nomura, “The Multiverse in an Inverted Island”, Arxiv, pp. 1-11, 2021. https://arxiv.org/abs/2106.05271
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