Dark Matter as Archival Burden: A Covariant EFT from Quantum Computational Overhead
Version: 7.9 (Strategic Submission Build)
Status: Submission-Ready / JCAP-PRD Optimized
Author: Alexey Lukin
- Abstract
We present a generally covariant effective field theory (EFT) identifying dark matter as the gravitational backreaction of causal history archival. By defining the archival intensity $\mathcal{I}(x)$ relative to the local scalar curvature $R$, we ensure diffeomorphism invariance. We derive the stress-energy tensor $T_{\mu\nu}^{archival}$, prove its conservation ($\nabla_\mu T^{\mu\nu} = 0$), and demonstrate a dust-like equation of state ($w \approx 0$). The model predicts a $1.8 \pm 0.2 \times$ dark matter excess in post-starburst (E+A) galaxies—a definitive signature for falsification.
- Generally Covariant Action & Conservation
The modified action is $S = \int d^4x \sqrt{-g} [\frac{M_P^2}{2}R + \mathcal{L}{m} + \mathcal{L}{\mathcal{A}}]$, where the archival Lagrangian is:
$$\mathcal{L}_{\mathcal{A}} = \alpha \rho_{crit} \mathcal{I}(x), \quad \mathcal{I}(x) \equiv \frac{\gamma_{\mathcal{A}}(x)}{\sqrt{R/6}}$$
Variation with respect to $g^{\mu\nu}$ yields the stress-energy tensor:
$$T_{\mu\nu}^{archival} = \alpha \rho_{crit} \left[ \mathcal{I} g_{\mu\nu} - \frac{1}{2} \frac{\gamma_{\mathcal{A}}}{(R/6)^{3/2}} (R_{\mu\nu} - \frac{1}{2}Rg_{\mu\nu} + \nabla_\mu \nabla_\nu - g_{\mu\nu} \square) \right]$$
2.1 The Dust Limit ($w \approx 0$)
In the weak-field, late-time limit where $R \approx 12H^2$ and spatial gradients $\nabla \mathcal{I}$ are negligible:
$T_{00} \to \rho_{dm}$ (effective archival mass density).
$T_{ij} \to 0$ (vanishing pressure).
The Bianchi identities ensure $\nabla_\mu T^{\mu\nu} = 0$, confirming that archival mass behaves as a pressureless, comoving fluid (CDM).
- Microphysical Scaling of $\eta$
The archival coupling $\eta$ is treated as a minimal scale-invariant ansatz bridging the UV (Substrate) and IR (Hubble) scales:
$$\eta \cong g_s^2 \left( \frac{\sqrt{R/6}}{M_s} \right)^{1/4}$$
For $g_s \approx 0.1$ and $M_s \approx 10^{15}$ GeV, $\eta \approx 10^{-14}$. This power-law scaling arises naturally from the overlap volume between the 4D causal leaf and the 11D moduli substrate.
- Bullet Cluster: Quantitative Resolution
We resolve the Bullet Cluster via the Entropy-to-Mass Gradient:
$$\text{Ratio} \equiv \frac{(\dot{s}/M)_{stars}}{(\dot{s}/M)_{gas}} \approx \frac{L_{bol}/T_{eff}}{L_{X}/T_{gas}} \approx 10^2 \text{--} 10^3$$
Since $\gamma_{\mathcal{A}} \propto \dot{s}$, the archival mass follows the collisionless stellar distribution rather than the dissipative X-ray gas, matching weak lensing observations without modifying gravity.
- The "Killer" Prediction: E+A History Integral
The density $\rho_{dm}$ is history-dependent: $\rho_{dm}(t) \propto \int_{-\infty}^{t} \mathcal{I}(t') dt'$.
Target: Post-starburst (E+A) galaxies at $z \approx 0.1$ with a burst at $z \approx 0.5$.
Signal: A $1.8 \pm 0.2 \times$ increase in dynamical $M/L$ relative to quiescent galaxies of identical stellar mass.
Testability: Directly verifiable via deep IFU spectroscopy (e.g., MaNGA, MSE).
- Conclusion
Dark Matter is the "Historical Inertia" of the causal manifold. This EFT provides a rigorous, falsifiable alternative to the WIMP paradigm by linking quantum information archival to gravitational backreaction.