Chapter 1: The Red Queen’s Race

1.2 Dimensional Inflation

“Dark energy is not a force pushing galaxies apart. It is the massive budget that the universe is forced to inject to fill the constantly cracking dimensional fissures. We are growing because the stage itself is growing wildly.”

In the previous section, we established the concept of “Synchronous Inflation”: if all scales are inflating, we cannot detect change. This explains why microscopic physical laws appear so stable.

However, the concealment is not perfect. If the universe’s underlying logic is truly Fibonacci spiral-style exponential growth, then at extremely grand scales—between galaxies with extremely weak causal connections—this growth must inevitably reveal itself.

This revelation is the ghost that has haunted modern cosmology for half a century: Dark Energy.

In the second book of Vector Cosmology, we will overturn the textbook definition. Dark energy is not a repulsive force, nor is it vacuum energy. It is the holographic projection left by Dimensional Inflation.

The Dimensional Explosion of Hilbert Space

Let us return to that unique vector $|\Psi ⟩$. It lives in projective Hilbert space $P(\mathcal{H})$. In the first book, we assumed by default that the dimension $D$ of $\mathcal{H}$ is fixed (or infinite but static).

But in the spiral universe model, this is a false assumption.

If the universe is a running program, a growing organism, then its “memory”—the maximum number of degrees of freedom it can accommodate—must necessarily grow with time.

This means that the dimension $D(\tau )$ of Hilbert space is undergoing exponential explosion:

$$D(\tau )\propto e^{\lambda \tau }$$

Every instant, the universe “inserts” new nodes in its underlying QCA grid. Between two originally adjacent logical units, countless new degrees of freedom suddenly emerge.

Budget Dilution and Replenishment

This dimensional explosion brings a serious economic consequence: Budget Dilution.

Imagine a company whose number of employees (dimensions) doubles every day. If the company’s total capital ($c_{FS}$) remains unchanged, then the operating funds allocated to each employee (degree of freedom) would instantly drop to zero. The system would immediately collapse, and heat death would arrive instantly.

To maintain the system’s “existence density”—to ensure that electrons remain electrons, atoms remain atoms, and light speed remains light speed—the universe must execute a radical monetary policy: budget expansion.

The Red Queen must run. The universe’s total budget $c_{FS}$ must keep pace with the growth rate of dimensions:

$$c_{FS}(\tau )\propto D(\tau {)}^{\gamma }$$

This is “Dimensional Inflation”.

The cosmic acceleration we observe (dark energy effect) is actually the macroscopic geometric manifestation of this “newly issued budget”.

• No repulsion: Galaxies are not repelling each other.

• Only insertion: Because between them, the number of “pixels” in the universe’s underlying structure is increasing exponentially.

Two galaxies originally 100 pixels apart become 101 pixels apart in the next second. Not because they moved ($v_{ext}$ did not change), but because the canvas carrying them was stretched. To observers, this looks like a mysterious negative pressure tearing space apart.

The Geometric Meaning of the Cosmological Constant

This perspective perfectly explains why the cosmological constant $\Lambda$ is so small, yet non-zero.

In quantum field theory calculations, $\Lambda$ should be a huge value at Planck scale ($10^{120}$ times the error). But in our model, $\Lambda$ is not vacuum energy density; it is the geometric residual of the spiral growth rate $\phi$.

It measures the tiny shear between the growth rate of $c_{FS}$ and the growth rate of dimension $D$.

• If the two are perfectly synchronized, the universe is flat and stationary.

• If budget growth is slightly faster than dimensional growth, the universe exhibits accelerated expansion.

We can observe dark energy because we are in an era of “budget surplus”. The new $c_{FS}$ injected by the universe slightly exceeds the minimum required to maintain existing structures. This excess budget cannot be locked in $v_{int}$ (matter) and can only transform into the background flow of $v_{ext}$, driving the inflation of spacetime itself.

Conclusion: We Are Patterns on a Bubble

At this point, the picture of the spiral universe becomes clear and breathtaking.

We do not live on a solid rocky sphere. We live on the surface of a soap bubble being wildly inflated.

• That unique vector $|\Psi ⟩$ is racing toward higher dimensions of Hilbert space.

• To prevent us “patterns” (material structures) from tearing apart in the expansion, the universe must continuously inject $c_{FS}$ budget to fill the stretched gaps.

Dark energy is not the shadow of death; it is the pain of growth. It is the eternal, exponential capital injection that the universe must perform to maintain our existence.

Since the universe is expanding, since the budget is being expanded, in this huge inflationary market, is there a mechanism that can actively utilize these newly issued budgets, rather than passively drifting with the flow?

This is precisely the secret of life.

Life can go against entropy because it has learned to engage in “insider trading” in this dimensional inflation. In the next volume, we will reveal the algorithm of this transaction.