Space Memory Explains the Acceleration of the Universe ✛ ✦

Original: "An Interplay Between Fractional Calculus and Holographic Dark Energy"
· Ayush Bidlan
arXiv:2606.22431 · 2026-06-21 · CC BY 4.0 · 1 min
The expansion of the Universe depends on its past thanks to space's 'memory'.

In the late 1990s, astronomers discovered that the expansion of the Universe is accelerating. Light from distant supernovae showed: the farther the star, the faster it's moving away. This effect, called redshift, required introducing dark energy — an invisible force pushing the cosmos apart.

Einstein once introduced the cosmological constant for balance, but later called it his biggest blunder. Today, this same constant describes dark energy, yet its value remains a mystery: calculations diverge from reality by a factor of $10^{120}$.

A new model endows space with memory. The idea came from the physics of black holes. Jacob Bekenstein and Stephen Hawking proved that the contents of a black hole are fully described by data on its surface. Gerard 't Hooft suggested: perhaps the entire Universe is a hologram, where three-dimensional reality is encoded on a two-dimensional boundary. Using fractional mathematics, scientists gave this 'hologram' the ability to remember the past. Just as a memory foam pillow restores its shape, so gravity 'recalls' the expansion history.

As a result, dark energy is not constant but changes over time. Computer simulations showed: the acceleration began about 6 billion years ago — exactly when it is seen in the cosmic microwave background, the afterglow of the Big Bang. The model agrees with string theory and may manifest in future observations of gravitational waves.

The fractional quantization used in the model resembles a walk with jumps: the particle moves sometimes smoothly, sometimes in leaps, which creates the memory effect.

S \propto A^{\frac{2+\alpha}{2\alpha}}
The horizon area A is raised to a power depending on the Lévy index α; at α=2 the standard S ∝ A is recovered.
\rho_{\mathrm{DE}} = 3c^2 H^{\frac{3\alpha-2}{\alpha}}
The dark energy density is expressed in terms of the Hubble parameter H and α. In the standard limit α→2, a constant density is obtained.
Scientists
Jacob BekensteinStephen HawkingGerard 't HooftLeonard SusskindChristian DopplerAdam Riess
Concepts
holographic dark energy early dark energy quintessence phantom divide logarithmic correction black hole thermodynamics desi wald entropy First law of black hole mechanics ecdm model hawking area law cosmic acceleration deceleration tidal charge hubble constant horizon area delay differential equation fritz zwicky schwarzschild metric quantum cosmological inhomogeneities quantum corrections