Testing Verlinde's emergent gravity in early-type galaxies
  Verlinde derived gravity as an emergent force from the information flow,
through two-dimensional surfaces and recently, by a priori postulating the
entanglement of information in 3D space, he derived the effect of the
gravitational potential from dark matter (DM) as the entropy displacement of
dark energy by baryonic matter. In Emergent Gravity (EG) this apparent DM
depends only on the baryonic mass distribution and the present-day value of the
Hubble parameter. In this paper we test the EG proposition, formalized by
Verlinde for a spherical and isolated mass distribution, using the central
velocity dispersion, $\sigma$ and the light distribution in a sample of 4260
massive and local early-type galaxies (ETGs) from the SPIDER sample. Our
results remain unaltered if we consider the sample of 807 roundest field
galaxies. We derive the predictions by EG for the stellar mass-to-light ratio
(M/L) and the Initial Mass Function (IMF), and compare them with the same
inferences derived from a) DM-based models, b) MOND and c) stellar population
models. We demonstrate that, consistently with a classical Newtonian framework
with a DM halo component, or alternative theories of gravity as MOND, the
central dynamics can be fitted if the IMF is assumed non-universal. The results
can be interpreted with a IMF lighter than a standard Chabrier at low-$\sigma$,
and bottom-heavier IMFs at larger $\sigma$. We find lower, but still
acceptable, stellar M/L in EG theory, if compared with the DM-based NFW model
and with MOND. The results from EG are comparable to what is found if the DM
haloes are adiabatically contracted and with expectations from spectral
gravity-sensitive features. If the strain caused by the entropy displacement
would be not maximal, as adopted in the current formulation, then the dynamics
of ETGs could be reproduced with larger M/L. (abridged)
