Emergent Spacetime from Vacuum Entanglement: A Unifying Cosmological Framework

This paper presents a novel theoretical framework that unifies quantum information theory with general relativity and cosmology. Based on two fundamental postulates, it proposes that spacetime geometry emerges from quantum mutual information, and that cosmic expansion is directly coupled to the growth of quantum entanglement.

The first postulate establishes a quantitative relation between spacetime distance and mutual information: d² = –ℓₚ² ln(I/I_max), where ℓₚ is the Planck length. From this, the metric tensor is derived as the second derivative of mutual information, showing that geometry is a coarse-grained manifestation of underlying quantum correlations.

The second postulate links the fractional rate of change of total cosmic entanglement E(t) to the Hubble expansion rate H(t): Ė/E = γ H. Consistency with holographic entropy scaling and Friedmann dynamics uniquely determines γ = 3, leading to the universal scaling E(t) ∝ a(t)³. This implies that entanglement density ε = E/V remains constant throughout cosmic history.

The framework yields explicit entanglement evolution for all cosmological epochs: radiation (E ∝ t³/²), matter (E ∝ t²), dark energy (E ∝ e³H₀ᵗ), and inflation (E ∝ e³H_infᵗ). Dark energy is reinterpreted as the energetic cost of creating new entanglement, with density ρ_Λ = (1/24πG)(Ė/E)², naturally resolving the fine‑tuning and coincidence problems.

Observational predictions include: CMB spectral index n_s = 1 – 2/N ≈ 0.967, matter fluctuation amplitude σ₈ = 0.764 ± 0.015, Hubble constant H₀ = 70.2 ± 1.5 km/s/Mpc, and tensor‑to‑scalar ratio r ≈ 0.01. These values lie between current early‑ and late‑universe measurements and can be tested by upcoming experiments (Euclid, CMB‑S4, LiteBIRD).

The work suggests that spacetime, gravity, and cosmic acceleration are emergent phenomena rooted in the dynamics of quantum entanglement, offering a unified information‑theoretic foundation for fundamental physics and

cosmology.

[Altamash Raza]

[[Email ID:- altamashraza904@gmail.com]