From Emergent Gravity to Dark Energy and Dark Matter

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.