Holographic Dual of GREA and Dark Energy Suggests Cosmological Constant Origin in Fundamental Degrees of Freedom

The accelerating expansion of the universe, currently explained by the enigmatic cosmological constant, presents a fundamental challenge to modern physics, and scientists are actively seeking alternative explanations. Juan García-Bellido from the Instituto de Física Teórica UAM-CSIC, Universidad Autónoma de Madrid, and colleagues explore a radical possibility, proposing a holographic connection between our universe and a distant boundary. This research demonstrates that the apparent acceleration experienced within our universe could, in principle, arise from the properties of this boundary, effectively meaning the universe’s expansion isn’t driven by a mysterious energy, but by information encoded at its edge. The team extends this ‘holographic principle’ to include matter, developing a model, known as GREA, where the evolving boundary of our observable universe generates an entropic acceleration, offering a potential explanation for the observed cosmic expansion and raising the possibility that future observations will reveal whether our universe will ultimately settle into a stable or flat state.

If cosmic acceleration arises from something other than a constant, it would significantly broaden the scope of cosmological inquiry. The team investigates a simple cosmological model, an empty and flat space possessing a cosmological constant Λ, and demonstrates that its holographic dual can be interpreted as a theory of fundamental quantum degrees of freedom at the boundary. Crucially, the research establishes that an observer within the universe, conducting long-range observations of both electromagnetic and gravitational phenomena, cannot differentiate between acceleration caused by the cosmological constant Λ and that resulting from the thermodynamic properties of the boundary’s de Sitter horizon. By incorporating matter into the universe, the team further refines this understanding of the relationship between gravity and thermodynamics in a cosmological context.

Entropy Drives Accelerated Expansion Without Dark Energy

Gravitational Entropic Repulsive Acceleration (GREA) theory provides a framework for describing dynamics in general relativity, particularly in situations where systems are not in equilibrium. A key feature of this theory is the explicit breaking of time reversal invariance when entropy increases, resulting in an entropic force that behaves like a negative pressure. This formalism suggests that the source of spacetime curvature is the Helmholtz free energy, rather than just matter and radiation. In cosmology, this predicts that the present acceleration of the universe arises from the growth of entropy associated with cosmic and black hole horizons, without requiring a cosmological constant.

The standard cosmological model (ΛCDM) includes a term for the cosmological constant. In GREA, this bulk term is replaced with a boundary term associated with horizons, specifically the Gibbons-Hawking-York (GHY) term. This substitution leads to a holographic correspondence, suggesting that the dynamics of spacetime are indistinguishable whether driven by a constant matter component or by a de Sitter boundary. This implies that a constant energy density in the universe is equivalent to a de Sitter boundary condition. The origin of the cosmological constant remains a significant challenge, as estimates of vacuum energy from quantum fields are vastly different from observed values.

GREA proposes that the holographic correspondence may offer a quantum interpretation of this constant. Considering a comoving sphere around the origin, the trace of the extrinsic curvature of the horizon is related to the temperature and entropy associated with the de Sitter horizon. The GHY term for this horizon is equivalent to the total entropy multiplied by the temperature. Although the origin of this temperature is quantum mechanical, the contribution to the Hamiltonian constraint is classical, as fundamental constants cancel. This leads to the surprising result that the energy density driving acceleration is holographically dual to the quantum entropy of degrees of freedom on the boundary of de Sitter space.

The entropic force associated with the boundary of de Sitter space is indistinguishable from the acceleration induced by the cosmological constant within the universe. From the perspective of general covariance, a constant surface term is indistinguishable from a cosmological constant. In the presence of matter and radiation, the causal horizon of the universe evolves with time, growing as these components dilute. This evolving horizon also gives rise to a thermodynamical description, though in this case it is out of equilibrium, as the entropy increases. The breaking of time-reversal invariance is a key difference between GREA and ΛCDM, introducing a cosmological arrow of time.

The entropic forces have primarily acted during inflation, reheating after inflation, and at the present time, when the cosmic horizon has grown sufficiently large to induce acceleration. Eventually, this acceleration will end as the entropic term dilutes, leading to an empty Minkowski spacetime. If a non-vanishing cosmological constant exists, the causal horizon will asymptotically approach the future de Sitter horizon, resulting in a de Sitter spacetime.

Entropy Drives Universe’s Accelerated Expansion

Scientists have established a surprising connection between the expansion of the universe and the properties of its boundaries, potentially resolving a long-standing mystery surrounding the cosmological constant. The research demonstrates that the acceleration observed in the expansion of the universe, traditionally attributed to a constant vacuum energy, may instead originate from the growth of entropy at the cosmic horizon. Measurements reveal that the force associated with this expanding boundary, termed Gravitational Entropic Repulsive Acceleration (GREA), is indistinguishable from the acceleration induced by the cosmological constant within the universe. The team calculated the thermodynamic properties of the de Sitter horizon, finding that the total entropy associated with this boundary is given by SH = kB ħ 4π r2 H 4G, where rH represents the physical radius of the horizon and H is the Hubble constant.

These calculations demonstrate a direct equivalence between the energy density driving the acceleration and the quantum entropy present at the boundary of de Sitter space. Specifically, the research shows that the GREA force is mathematically equivalent to the acceleration caused by the cosmological constant, as expressed in the equation 4π κ r 3 Λ, where Λ represents the cosmological constant. Further investigations considered the evolution of the universe with matter and radiation present, revealing that the causal horizon is not constant but expands over time. This evolving boundary also generates a thermodynamic description, with entropy increasing as matter dilutes. The team discovered that this entropic force breaks time-reversal invariance, introducing a cosmological arrow of time, and becomes dominant at late times, inducing the present acceleration. Measurements predict that this period of acceleration will eventually end, leading to an empty Minkowski space-time unless a non-vanishing cosmological constant exists, in which case the universe will asymptotically approach a de Sitter state.

Horizon Entropy Drives Cosmic Expansion

Researchers have established a novel connection between the expansion of the universe and the growth of entropy at cosmic horizons, offering a potential alternative to the cosmological constant. Their work demonstrates that the observed acceleration of the universe may not require invoking a constant energy density inherent in space itself, but instead arises from the evolving boundaries of cosmic and black hole horizons. This holographic correspondence suggests that the dynamics within the universe are fundamentally linked to information encoded on its boundaries, specifically through the entropy associated with these horizons. The team’s approach reformulates the standard Einstein-Hilbert action, replacing the cosmological constant term with a boundary term related to horizon entropy, effectively attributing the observed acceleration to the increasing disorder associated with expanding horizons.

This framework proposes that the universe’s expansion is driven by the growth of entropy at its boundaries, mirroring the behaviour of black hole horizons, and offers a way to understand the cosmological constant as an emergent property rather than a fundamental constant of nature. While the research successfully establishes this holographic connection, the authors acknowledge that the assumption of homogeneity and isotropy simplifies the expressions and may not fully represent the universe’s complexity. Future research will focus on exploring the implications of this framework for understanding the ultimate fate of the universe, specifically whether it will continue to expand indefinitely or eventually reach a stable state. The team also intends to investigate how this holographic principle might apply to more complex cosmological models, potentially incorporating the effects of dark matter and dark energy. This work represents a significant step towards a deeper understanding of the universe’s expansion and its connection to.