From Emergent Gravity to Dark Energy and Dark Matter

There are strong indications that Einstein gravity can be derived from a microscopic description of emergent spacetime in terms of entangled quantum information. An essential ingredient in the derivation of the Einstein equations is that the entanglement entropy of the vacuum obeys an area law. In Anti-de-Sitter space this condition is known to hold due to the work of Ryu and Takayanagi. We will argue that in de Sitter space due to the positive dark energy, that the microscopic entanglement entropy also contains also a volume law contribution in addition to the area law. This volume law contribution is related to the thermal properties of de SItter space and leads to a total entropy inside the static patch that precisely matches the Bekenstein-Hawking formula for the cosmological horizon. We study the effect of this extra contribution in the derivation of the emergent laws of gravity, and argue that it leads to a modification compared to Einstein gravity. We provide evidence for the fact this modification explains the observed phenomena in galaxies and clusters currently attributed to dark matter