Abstract
Recent theoretical progress indicates that spacetime and gravity emerge together from the entanglement structure of an underlying microscopic theory. These ideas are best understood in Anti-de Sitter space, where they rely on the area law for entanglement entropy. The extension to de Sitter space requires taking into account the entropy and temperature associated with the cosmological horizon. Using insights from string theory, black hole physics and quantum information theory we argue that the positive dark energy leads to a thermal volume law contribution to the entropy that overtakes the area law precisely at the cosmological horizon. Due to the competition between area and volume law entanglement the microscopic de Sitter states do not thermalise at sub-Hubble scales: they exhibit memory effects in the form of an entropy displacement caused by matter. The emergent laws of gravity contain an additional ‘dark’ gravitational force describing the ‘elastic’ response due to the entropy displacement. We derive an estimate of the strength of this extra force in terms of the baryonic mass, Newton’s constant and the Hubble acceleration scale a_0 =cH_0a0=cH0, and provide evidence for the fact that this additional ‘dark gravity force’ explains the observed phenomena in galaxies and clusters currently attributed to dark matter.
Highlights
An important lesson that has come out of the complementarity, firewall [25] and ER=EPR [26] discussions is that the quantum information counted by the Bekenstein-Hawking entropy is not localized on the horizon itself [27], but either represents the entanglement entropy across the horizon or is interpreted as a thermodynamic entropy which is stored non-locally
We propose that microscopically de Sitter space corresponds to an ensemble of metastable quantum states that together carry the Bekenstein-Hawking entropy associated with the cosmological horizon
We propose that precisely this phenomenon occurs in de Sitter space and is responsible for the presence of a cosmological horizon
Summary
According to Einstein’s theory of general relativity spacetime has no intrinsic properties other than its curved geometry: it is merely a stage, albeit a dynamical one, on which matter moves under the influence of forces. There are well motivated reasons, coming from theory as well as observations, to challenge this conventional point of view. The fact that 95% of our Universe consists of mysterious forms of energy or matter gives sufficient motivation to reconsider this basic starting point. From a theoretical perspective, insights from black hole physics and string theory indicate that our ‘macroscopic’ notions of spacetime and gravity are emergent from an underlying microscopic description in which they have no a priori meaning
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