Verlinde's Theory Research Articles

Decoherence-free entropic gravity: Model and experimental tests

Erik Verlinde's theory of entropic gravity [arXiv:1001.0785], postulating that gravity is not a fundamental force but rather emerges thermodynamically, has garnered much attention as a possible resolution to the quantum gravity problem. Some have ruled this theory out on grounds that entropic forces are by nature noisy and entropic gravity would therefore display far more decoherence than is observed in ultra-cold neutron experiments. We address this criticism by modeling linear gravity acting on small objects as an open quantum system. In the strong coupling limit, when the model's unitless free parameter $\sigma$ goes to infinity, the entropic master equation recovers conservative gravity. We show that the proposed master equation is fully compatible with the \textit{q}\textsc{Bounce} experiment for ultra-cold neutrons as long as $\sigma\gtrsim 250$ at $90\%$ confidence. Furthermore, the entropic master equation predicts energy increase and decoherence on long time scales and for large masses, phenomena which tabletop experiments could test. In addition, comparing entropic gravity's energy increase to that of the Di\'{o}si-Penrose model for gravity induced decoherence indicates that the two theories are incompatible. These findings support the theory of entropic gravity, motivating future experimental and theoretical research.

Testing emergent gravity on galaxy cluster scales

Verlinde's theory of Emergent Gravity (EG) describes gravity as an emergent phenomenon rather than a fundamental force. Applying this reasoning in de Sitter space leads to gravity behaving differently on galaxy and galaxy cluster scales; this excess gravity might offer an alternative to dark matter. Here we test these ideas using the data from the Coma cluster and from 58 stacked galaxy clusters. The X-ray surface brightness measurements of the clusters at 0.1 < z < 1.2 along with the weak lensing data are used to test the theory. We find that the simultaneous EG fits of the X-ray and weak lensing datasets are significantly worse than those provided by General Relativity (with cold dark matter). For the Coma cluster, the predictions from emergent gravity and general relativity agree in the range of 250 – 700 kpc, while at around 1 Mpc scales, EG total mass predictions are larger by a factor of 2. For the cluster stack the predictions are only in good agreement at around the 1 – 2 Mpc scales, while for r ≳ 10 Mpc EG is in strong tension with the data. According to the Bayesian information criterion analysis, GR is preferred in all tested datasets; however, we also discuss possible modifications of EG that greatly relax the tension with the data.

Tsallis' entropy, modified Newtonian accelerations and the Tully-Fisher relation

In this paper we have shown that the connection between the number of bits and the area of the holographic screen, where both were established in Verlinde's theory of entropic gravity, may depend on the thermostatistics theory previously chosen. Starting from the Boltzmann-Gibbs (BG) theory, we have reobtained the usual dependence of both, bits number and area. After that, using Tsallis' entropy concept within the entropic gravity formalism, we have derived another relation between the bits number and the holographic screen area. We have used this new relation to derive three Newtonian-type accelerations in the context of Tsallis' statistics which are a modified gravitational acceleration, a modified MOND theory and a modified Friedmann equation. Moreover we have obtained a nonextensive version of the Tully-Fisher (TF) relation which shows a dependence of the distance of the star in contrast to the standard TF expression. The BG limit gives the standard TF law.

Cosmological considerations in Kaniadakis statistics

We have shown that the connection between the number of bits and the area of the holographic screen, where both were established in Verlinde's theory of entropic gravity, may depend on the previously chosen thermostatistics theory. Starting from the Boltzmann-Gibbs (BG) theory, we have reobtained the usual dependence of the number of bits and the holographic screen area. After that, using the Kaniadakis microcanonical entropy formula within the entropic gravity formalism, we have derived another relation between the bits number and the holographic screen area. We have used this new relation to derive three Newtonian-type accelerations in the context of Kaniadakis' statistics which are a modified gravitational acceleration, a modified MOND theory and a modified Friedmann equation. We have obtained a kappa version of the Tully-Fisher (TF) relation which displays a dependence of the distance from the star in contrast to the standard TF expression.

Verlinde’s emergent gravity versus MOND and the case of dwarf spheroidals

In a recent paper, Erik Verlinde has developed the interesting possibility that spacetime and gravity may emerge from the entangled structure of an underlying microscopic theory. In this picture, dark matter arises as a response to the standard model of particle physics from the delocalized degrees of freedom that build up the dark energy component of the Universe. Dark matter physics is then regulated by a characteristic acceleration scale $a_0$, identified with the radius of the (quasi)-de Sitter universe we inhabit. For a point particle matter source, or outside an extended spherically symmetric object, MOND's empirical fitting formula is recovered. However, Verlinde's theory critically departs from MOND when considering the inner structure of galaxies, differing by a factor of 2 at the centre of a regular massive body. For illustration, we use the eight classical dwarf spheroidal satellites of the Milky Way. These objects are perfect testbeds for the model given their approximate spherical symmetry, measured kinematics, and identified missing mass. We show that, without the assumption of a maximal deformation, Verlinde's theory can fit the velocity dispersion profile in dwarf spheroidals with no further need of an extra dark particle component. If a maximal deformation is considered, the theory leads to mass-to-light ratios that are marginally larger than expected from stellar population and formation history studies. We also compare our results with the recent phenomenological interpolating MOND function of McGaugh {\it et al}, and find a departure that, for these galaxies, is consistent with the scatter in current observations.

First test of Verlinde's theory of emergent gravity using weak gravitational lensing measurements

Verlinde (2016) proposed that the observed excess gravity in galaxies and clusters is the consequence of Emergent Gravity (EG). In this theory the standard gravitational laws are modified on galactic and larger scales due to the displacement of dark energy by baryonic matter. EG gives an estimate of the excess gravity (described as an apparent dark matter density) in terms of the baryonic mass distribution and the Hubble parameter. In this work we present the first test of EG using weak gravitational lensing, within the regime of validity of the current model. Although there is no direct description of lensing and cosmology in EG yet, we can make a reasonable estimate of the expected lensing signal of low redshift galaxies by assuming a background LambdaCDM cosmology. We measure the (apparent) average surface mass density profiles of 33,613 isolated central galaxies, and compare them to those predicted by EG based on the galaxies' baryonic masses. To this end we employ the ~180 square degrees overlap of the Kilo-Degree Survey (KiDS) with the spectroscopic Galaxy And Mass Assembly (GAMA) survey. We find that the prediction from EG, despite requiring no free parameters, is in good agreement with the observed galaxy-galaxy lensing profiles in four different stellar mass bins. Although this performance is remarkable, this study is only a first step. Further advancements on both the theoretical framework and observational tests of EG are needed before it can be considered a fully developed and solidly tested theory.

Coulomb force as an entropic force

Motivated by Verlinde's theory of entropic gravity, we give a tentative explanation to Coulomb's law with an entropic force. When trying to do this, we find the equipartition rule should be extended to charges and the concept of temperature should be reinterpreted. If one accepts the holographic principle as well as our generalizations and reinterpretations, then Coulomb's law, the Poisson equation and the Maxwell equations can be derived smoothly. Our attempt can be regarded as a new way to unify the electromagnetic force with gravity, from the entropic origin. Possibly some of our postulates are related to the D-brane picture of black hole thermodynamics.