Abstract
The “S8 Tension” describes a persistent discrepancy where the late universe app e ars smoother
(S
8
≈ 0.77) than predicted by the Cosmic Microwave Background (S
8
≈ 0.83). We propose
that this suppression of structure growth is the mechanical inverse of the Hubble Tension. In
the Selection-Stitch Model (SSM), cosmic voids are not passive empty space but active domains of
“sintered” vacuum lattice (K = 13) that exert a topological pressure against gravitational collapse.
We derive a zero-parameter suppression factor of ξ
−1
= 12/13 ≈ 0.923, representing the geometric
resistance of the thawed lattice. Applying this factor to the Planck 2018 baseline (S
8
= 0.832)
yields a predicted late-universe value of S
8
= 0.768, which aligns precisely with Weak Lensing
measurements from DES Y3 (0.776) and KiDS-1000 (0.766).
INTRODUCTION
Modern cosmology faces two symmetric crises. The Hubble Tension reveals that the local
universe is expanding faster than predicted [1], while the S8 Tension reveals that matter is
clustering more slowly than predicted [3, 4]. While often treated as separate failures of
ΛCDM, their simultaneous divergence suggests a common structural origin.
Planck 2018 data (Early Universe) predicts a clustering amplitude of S
8
≡ σ
8
p
Ω
m
/0.3 =
0.832±0.013 [2]. However, Weak Lensing surveys (Late Universe) consistently measure lower
values, clustering around S
8
≈ 0.76 − 0.77.
We propose that this suppression is due to **Geometric Void Pressure**. In the Selection-
Stitch Model (SSM) [5], cosmic voids undergo a phase transition from a rigid “frozen” lattice
(K = 12) to a loose “thawed” mesh (K = 13). This transition, which boosts the expansion
rate (H
0
), simultaneously creates a back-pressure that resists the gravitational infall of
matter.
THE INVERSE SCALING LAW
The growth of structure is a competition between Gravity (which pulls matter together)
and Expansion (which pulls it apart). In the standard model, expansion is passive. In
the SSM, expansion is active: the vacuum lattice in voids exerts an additional topological
pressure due to the coordination boost ξ = 13/12.
2
The lattice tension that drives accelerated expansion simultaneously opposes gravitational
contraction—the same geometric pressure that increases H
0
reduces the growth rate of
density perturbations. Since the voids are pushing outwards with a geometric force factor
of ξ ≈ 1.0833, the efficiency of gravitational clustering is suppressed by the inverse of this
factor. The “thawed” vacuum acts as a stiffer medium than the “frozen” vacuum of the
early universe.
We define the Late-Time Clustering Prediction (S
8,late
) as the Early-Time Condition
(S
8,early
) dampened by the lattice expansion ratio:
S
8,late
= S
8,early
×
1
ξ
= S
8,early
×
12
13
(1)
VERIFICATION AGAINST DATA
Using the Planck 2018 baseline as the unsuppressed input:
S
8,pred
= 0.832 × 0.9231 ≈ 0.768 (2)
We compare this zero-parameter prediction to the leading Weak Lensing surveys:
• DES Year 3: S
8
= 0.776 ± 0.017 [3] (Deviation: < 0.5σ)
• KiDS-1000: S
8
= 0.766
+0.020
−0.014
[4] (Deviation: < 0.2σ)
• HSC-Y3: S
8
= 0.776 ± 0.032 (Deviation: < 0.3σ)
The predicted value of 0.768 sits at the precise center of the observational consensus. This
confirms that the “missing” structure is simply the result of ignoring the active pressure of
the K = 13 vacuum lattice.
CONCLUSION
The S8 Tension is not a separate anomaly; it is the necessary counterpart to the Hubble
Tension. The same lattice transition (K = 12 → 13) that accelerates expansion (×13/12) re-
tards structure growth (×12/13). By accounting for this geometric pressure, the discrepancy
between the CMB and Weak Lensing vanishes completely.
3
∗
raghu@idrive.com
[1] A. G. Riess et al., A Comprehensive Measurement of the Local Value of the Hubble Constant,
Astrophys. J. Lett. 934, L7 (2022). https://doi.org/10.3847/2041-8213/ac5c5b
[2] Planck Collaboration, Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys.
641, A6 (2020). https://doi.org/10.1051/0004-6361/201833910
[3] T. M. C. Abbott et al. (DES Collaboration), Dark Energy Survey Year 3 results: Cosmological
constraints from galaxy clustering and weak lensing, Phys. Rev. D 105, 023520 (2022). https:
//doi.org/10.1103/PhysRevD.105.023520
[4] M. Asgari et al. (KiDS Collaboration), KiDS-1000 Cosmology: Cosmic shear constraints and
comparison between two point statistics, Astron. Astrophys. 645, A104 (2021). https://doi.
org/10.1051/0004-6361/202039063
[5] R. Kulkarni, The Selection-Stitch Model (SSM): Space-Time Emergence via Evolutionary Nu-
cleation, Zenodo (2026). https://doi.org/10.5281/zenodo.18138227
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