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Question: Is there already a theory (formula) available for emergent entropic gravity from Quantum Entanglement in de Sitter space?

For detailed background information please refer to a recent interview at the International Society for Quantum Gravity entitled "Entropic Gravity from Quantum Entanglement! | with Professor Erik Verlinde", see Link below https://www.youtube.com/watch?v=zkgZ0ShfbUE

In this interview Prof. Erik Verlinde admitted that a quantum information theory based approach to emergent entropic gravity for the De-Sitter space would have to be worked out yet; so far there is only such a theory for the Anti-de-Sitter space (AdS/CFT- Correspondence).

This is a follow-up request to a question which was already asked on the Physics Stack Exchange website 7 years ago: Has Verlinde's theory made significant advance recently? In particular, evidence appears stll missing, whether Prof. Verlinde's recent idea of a quantum information theory based approach to emergent gravity can be considered valid or not for the de Sitter space?

UN73
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Let me first clarify that there is a "non-entropic" version of emergent gravity that works, namely the well-known AdS/CFT correspondence that exemplifies the holographic principle, and in which a non-gravitational CFT in flat space is equivalent to a quantum-gravitational theory in emergent extra spatial directions.

Erik Verlinde's specific 2010 proposal (that gravity is an "entropic force") has some well-known problems, illustrated by neutrons in a double-slit experiment (Kobakhidze, Motl) and n-body interactions (Visser).

At Strings 2011, he gave a talk implying that he would refine the concept: "entropy" means phase space volume, "temperature" means density of energy levels, and gravity far from event horizons is an "adiabatic reaction force".

He never wrote a paper about this, but there are some traces of this refined concept in his 2016 paper that begins to address De Sitter space. Here he is also trying to work with a De Sitter analogue of AdS/CFT, in which the observable universe is holographically dual to a description on the cosmological horizon, and the dark sector (dark matter, dark energy) is actually a perturbation of gravity, due to an "elastic memory effect" which is a manifestation of this holographic duality.

Once again, I don't think any of his heuristic formulas have been derived from an exact fundamental theory. But Sabine Hossenfelder claimed she could get Milgrom's MOND formula (a way to dispense with dark matter by instead modifying gravity) from a version of Verlinde's theory.

That's where my knowledge runs out. There was a 2020 question here about getting MOND from Verlinde's De Sitter gravity, that has received no reply.

Mitchell Porter
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