Emergent Gravity and the Dark Universe (1611.02269v2)

Abstract: Recent theoretical progress indicates that spacetime and gravity emerge together from the entanglement structure of an underlying microscopic theory. These ideas are best understood in Anti-de Sitter space, where they rely on the area law for entanglement entropy. The extension to de Sitter space requires taking into account the entropy and temperature associated with the cosmological horizon. Using insights from string theory, black hole physics and quantum information theory we argue that the positive dark energy leads to a thermal volume law contribution to the entropy that overtakes the area law precisely at the cosmological horizon. Due to the competition between area and volume law entanglement the microscopic de Sitter states do not thermalise at sub-Hubble scales: they exhibit memory effects in the form of an entropy displacement caused by matter. The emergent laws of gravity contain an additional dark' gravitational force describing theelastic' response due to the entropy displacement. We derive an estimate of the strength of this extra force in terms of the baryonic mass, Newton's constant and the Hubble acceleration scale a_0 =cH_0, and provide evidence for the fact that this additional `dark gravity~force' explains the observed phenomena in galaxies and clusters currently attributed to dark matter.

• The paper proposes an emergent gravity model where gravity arises from entanglement-driven elastic responses in spacetime.
• It explains dark matter phenomena, such as flat galaxy rotation curves, without requiring additional unseen matter.
• A key scaling relation links baryonic matter to apparent dark matter effects, aligning with empirical relations like the Tully-Fisher law.

Emergent Gravity and the Dark Universe

The paper by Erik Verlinde suggests a novel approach to understanding gravity and dark matter phenomena by employing principles from quantum information theory and insights from string theory. It challenges traditional views that treat spacetime and gravity as fundamental, proposing instead that these concepts are emergent from an underlying microscopic framework where entanglement plays a pivotal role.

Overview of Emergent Gravity

Verlinde posits that spacetime and gravity emerge from the entanglement structure inherent in a deeper microscopic theory. This idea aligns with developments primarily understood within Anti-de Sitter (AdS) spaces, where the AdS/CFT correspondence elucidates how entanglement leads to physical laws. However, extending these insights to de Sitter (dS) space, the geometry pertinent to our Universe, requires an understanding of cosmic horizons that carry entropy and temperature.

Entropic Considerations in de Sitter Space

In dS space, Verlinde argues that a volume law entropic contribution surpasses the area law at the cosmological horizon, attributed to positive dark energy. This scenario results in an elasticity-like response from the spacetime fabric when perturbed by mass—akin to entropic displacement leading to a gravitational force. Intriguingly, this model offers an entropic origin for dark energy, suggesting it is constituted by long-range entangled states with volume law contributions to entropy.

Implications on Dark Matter Phenomena

Verlinde's framework provides a fresh perspective on the "dark matter problem." By reinterpreting dark matter effects as emergent phenomena from the response of an entropic spacetime, the paper claims that observed gravitational effects in galaxies and clusters, typically attributed to dark matter, can be explained without invoking unseen matter. Emerging from the proposed elasticity model, an additional gravitational force aligns with empirical observations, such as flattened galaxy rotation curves, by balancing between the elastic medium's entropic response and traditional gravitational dynamics.

Theoretical Predictions and Outcomes

A critical result derived is a scaling relation connecting the apparent dark matter effects to the distribution of visible (baryonic) matter:

$$\Sigma_D^2 = \frac{a_0}{8\pi G} \frac{\Sigma_B}{d-1}$$

Where $\Sigma_D$ and $\Sigma_B$ are surface mass densities of dark and baryonic matter, respectively, $a_0$ the Hubble acceleration scale, and $d$ the spacetime dimensions. This relation aligns with the well-known Tully-Fisher relation and provides a new theoretical underpinning within the emergent gravity framework.

Speculative Future Directions

While the paper focuses primarily on static and isolated systems, potential applications to broader cosmological questions remain speculative. For instance, the role of emergent gravitational principles in the cosmic evolution, structure formation, or CMB phenomena needs further exploration. Moreover, correlating this emergent model with the established successes of the $\Lambda$CDM paradigm necessitates a deeper understanding of how such frameworks can coexist or if they demand a paradigm shift altogether.

Conclusion

Verlinde's proposition offers an intriguing theoretical lens to interpret phenomena traditionally ascribed to dark matter as manifestations of emergent gravitational physics. By bridging quantum information theory and cosmology, the paper extends the discourse on fundamental physics, challenging researchers to further examine the intersection of entanglement, spacetime, and gravity. While ambitious, the claim demands rigorous examination and empirical scrutiny to validate its viability against observed cosmic phenomena.