Pixelated Dark Energy

TL;DR

This work presents a UV-complete cosmological model derived from F-theory on Spin(7) that replaces the inflaton with a pixelated spacetime built from wrapped five-branes, yielding a radiatively stable cosmological constant scaling as $\\Lambda \\sim 1/N$. Inflation and reheating arise from rare flux-pixel jumps that generate radiation and rapidly increase the pixel count, while late-time dark energy evolves with a time-dependent equation of state $w= -1 + rac{\\dot N}{3 H N}$, and a global relation $w_a = -\frac{3}{2}\\Omega_{m,0}(1+w_0)$; observational bounds from Planck and DES accommodate this behavior. The model predicts a large-$l$ cutoff $l_{\rm max} \\sim O(N)$ in the angular power spectrum and provides a microscopic, holographic description of de Sitter thermodynamics with $S_{\rm obs} \\sim N$ and $T_{\rm obs} \\sim 1/\\sqrt{N}$. A 1D pixel matrix model captures the dynamics of pixel/hole transitions, winding/unwinding processes, and their coupling to radiation, offering a framework to connect stringy microphysics to cosmological observables and potentially detectable gravitational signatures. Overall, the pixel cosmology links UV string theory to testable cosmological phenomenology, including a measurable time variation in dark energy and high-$l$ structure in the CMB.

Abstract

We study the phenomenology of a recent string construction with a quantum mechanically stable dark energy. A mild supersymmetry protects the vacuum energy but also allows $O(10 - 100)$ TeV scale superpartner masses. The construction is holographic in the sense that the 4D spacetime is generated from "pixels" originating from five-branes wrapped over metastable five-cycles of the compactification. The cosmological constant scales as $Λ\sim 1/N$ in the pixel number. An instability in the construction leads to cosmic expansion. This also causes more five-branes to wind up in the geometry, leading to a slowly decreasing cosmological constant which we interpret as an epoch of inflation followed by (pre-)heating when a rare event occurs in which the number of pixels increases by an order one fraction. The sudden appearance of radiation triggers an exponential increase in the number of pixels. Dark energy has a time varying equation of state with $w_a=-3Ω_{m,0}(1+w_0)/2$, which is compatible with current bounds, and could be constrained further by future data releases. The pixelated nature of the Universe also implies a large-$l$ cutoff on the angular power spectrum of cosmological observables with $l_{\rm max} \sim O(N)$. We also use this pixel description to study the thermodynamics of de Sitter space, finding rough agreement with effective field theory considerations.

Figures (7)

• Figure 1: Depiction of the instability in the static Universe solution obtained from a balancing between a stiff fluid, curvature and cosmological constant. Small perturbations lead to a subsequent rolling in the scale factor to either a collapsing or expanding phase. We emphasize that no scalar potential is actually involved in this rolling motion.
• Figure 2: Representation of a pixelated $S^3$. This leads to a cutoff on the angular momentum of the physical system $l_{\text{max}} \sim N$ with $N$ the number of pixels. In the stringy construction, each pixel originates from a five-brane wrapped on a local five-cycle of the internal geometry.
• Figure 3: Depiction of different six-chains $C_6$ and $C_6'$ of the internal space bounded by the same five-cycle $c_5$ (pink) wrapped by our metastable five-branes. By suitably localizing the branes in the internal geometry, the volume of these six-chains can be different, thus leading to a preferential decay mode to Standard Model visible states (left) rather than hidden sector states (right), which can come from 7-branes (lines) or 3-branes (points).
• Figure 4: Pixel winding and unwinding in the compactification geometry. A local five-cycle $c_5$ which bounds a six-chain $C_6$ provides a decay mechanism for five-branes in the geometry. Each five-brane defines a pixel in the 4D spacetime, and its subsequent unwinding leads to a drop in the number of flux quanta. Conversely, the number of pixels can increase through a winding process. The particular process which dominates depends on whether the 4D spacetime is expanding (winding) or contracting (unwinding).
• Figure 5: Depiction of the two level system for pixels and holes. On the collapsing branch, the pixels have higher energy while on the expanding branch the holes have higher energy. In the stringy description, unwinding a five-brane corresponds to the creation of a hole while winding up a five-brane corresponds to the creation of a pixel. The blue dashed lines in the upper panel represent off-shell axions which subsequently decay to radiation. Energy level splittings are not drawn to scale in the figure.