Sommerfeld Theory Colloquium, The observed deviations from the laws of gravity of Newton and Einstein

in galaxies and clusters can logically speaking be either due to

the presence of unseen dark matter particles or due to a change in

the way gravity works in these situations. Until recently there was

little reason to doubt that general relativity correctly describes gravity

in all circumstances. In the past few year insights from black hole

physics and string theory have lead to a new theoretical framework in

which the gravitational laws are derived from the quantum entanglement

of the microscopic information that is underlying space-time.

An essential ingredient in the derivation is of the Einstein equations

is that the vacuum entanglement obeys an area law, a condition that

is known to hold in Anti-de Sitter space 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 that precisely matches the

Bekenstein-Hawking formula for the cosmological horizon. We study

the effect of this extra contribution on 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.