Einstein’s Cosmological Constant
The idea of a “cosmic push” isn’t entirely new. In 1917, Albert Einstein introduced a term, Λ (Lambda), into his equations of General Relativity. He needed it to balance gravity and keep the universe static, which was the prevailing view at the time. When Edwin Hubble later discovered the universe is expanding, Einstein discarded Λ, calling it his “biggest blunder.”
Yet, Λ returned. In the modern Standard Model of Cosmology (ΛCDM), it represents the cosmological constant—a fixed, uniform energy density inherent to empty space itself.
This model works remarkably well descriptively, matching observations of the Cosmic Microwave Background (CMB) and the large-scale structure of the universe.While the standard ΛCDM model reproduces cosmic observations with remarkable precision, it acts as a powerful description of what is happening without explaining why. Its reliance on dark energy, particularly the Cosmological Constant (Λ), introduces many profound and unsettling puzzles in the history of science.
Fig. 1: Temperature map of the cosmic microwave background measured by the Planck spacecraft
Vacuum Catastrophe
Quantum field theory, our most successful description of the subatomic world, tells us that empty space is not empty at all. It is a roiling, energetic sea of virtual particles constantly popping into and out of existence. When physicists attempt to calculate the total energy of this vacuum, they sum up the ground-state energies of all known quantum fields.
The result is a catastrophe. The predicted energy density of the vacuum is 10¹²⁰—120 orders of magnitude larger than the value we infer from the cosmic acceleration. This is widely considered the worst theoretical prediction in the history of physics. If the vacuum's energy were this high, its repulsive force would be so powerful that it would have instantly ripped apart atoms, stars, and galaxies, preventing the universe as we know it from ever forming. The fact that we observe a gentle, stately acceleration instead of an instantaneous explosion represents a fundamental, unexplained chasm between our theories of gravity and the quantum world.In Timeflow Gravity, this contradiction dissolves. The vacuum is not a static sea of disconnected fluctuations, but a self-regulating thermodynamic medium — the Timeflow Field — whose frequency and amplitude continually rebalance to preserve the invariance of the speed of light.
What quantum field theory measures as “vacuum energy” are the microscopic vibrations of time itself. Most of that energy doesn’t gravitate because it is perfectly counterbalanced by its own structural order, so gravity is the gradient of time. This automatic self-cancellation is an expression of the Law of Entropy Equilibrium: Chaos Entropy + Order Entropy = 0
The vacuum’s apparent stillness is not emptiness, but equilibrium — a perfect balance between chaotic fluctuations (high frequency) and ordered coherence (high amplitude).
Only small deviations from this balance — as occur around matter and cosmic structure — produce observable effects such as cosmic acceleration.
Cosmic Coincidence Problem
The second puzzle is one of improbable timing. The energy densities of matter and dark energy evolve at vastly different rates.
- Matter Density: Like a crowd in an expanding room, the density of matter thins out as the universe grows. In the early universe, it was overwhelmingly dominant.
- Dark Energy Density (Λ): Being a constant property of space itself, its density never changes.
Imagine a race between a sprinter (matter) who starts incredibly fast but slows down, and a marathon runner (dark energy) who maintains a slow, steady pace forever. For most of the race's history, the sprinter was miles ahead. In the distant future, the marathon runner will be the only one left on the track.
The coincidence is this: why do we happen to be alive in the brief cosmic twilight when the two runners are side-by-side? It seems an incredible coincidence that the density of matter has diluted over 13.8 billion years to become roughly the same as the constant density of dark energy right now. The standard ΛCDM model offers no reason for this improbable timing; it is simply an initial condition we must accept.
In TG, this "coincidence" is a direct and necessary consequence of the theory. Dark energy is not an independent, constant entity. It is a dynamic thermodynamic response of the Timeflow field, inextricably linked to the presence of matter.
The effective vacuum energy density (ρv) is dynamically sourced by the matter density (ρm) through a thermodynamic response function (μ):
$$ \rho_v = \left(\frac{1 - \mu}{\mu}\right)\rho_m $$
The theory demands that these two densities remain fundamentally related at all times. They are comparable today because the vacuum energy is generated as a response to the matter content of the universe.
Is Cosmological Constant a Constant?
The ΛCDM model depends entirely on dark energy being constant throughout cosmic history. But in 2025 Dark Energy Spectroscopic Instrument (DESI) released results indicating that the density of dark energy may be slowly decreasing over time. In other words, the vacuum itself might be evolving.
If this trend is confirmed, it would challenge one of the deepest pillars of modern cosmology. It would mean that the energy driving cosmic acceleration is not a fixed background property of spacetime, but a living, dynamic quantity that changes as the universe matures.
This evolving behavior is a direct and inevitable consequence of the TG framework. Because in Timeflow Gravity, the vacuum is alive with thermodynamic activity. Its frequency and amplitude continuously adjust to maintain the constancy of light’s propagation and the balance between order and chaos.
As galaxies form and energy condenses, the universe increases its structural order (amplitude). To maintain global equilibrium, the surrounding vacuum compensates by expanding — increasing its “chaotic” component (frequency). This expansion is observed as cosmic acceleration, and its gradual slowdown as the universe cools and smooths out naturally explains the observed decline of dark energy density.
The Hubble Tension
There is a significant discrepancy in measurements of the Hubble constant (H0), the current expansion rate of the universe. Measurements in the local, late universe (using supernovae) yield H0≈73 km/s/Mpc. Measurements inferred from the early universe (using the Cosmic Microwave Background) yield H0≈67 km/s/Mpc. In the standard ΛCDM model, this conflict suggests a fundamental flaw.
The Hubble Tension is a fundamental prediction of TG. The source of acceleration in TG is the thermodynamic function μ, which evolves dynamically, unlike the static cosmological constant Λ.
In the dense early universe, the thermodynamic response was negligible (μ≈1), and the expansion followed standard matter-dominated rules. In the late universe, as density dropped, the dynamics are altered by the enhanced thermodynamic response (μ<1).
The "tension" is the measurable difference between the true, local expansion rate driven by present-day thermodynamics, and the value extrapolated from an early universe that behaved according to a different physical regime.
Why Our Universe is Expanding?
Dark energy is not a mysterious, static substance filling the void. It is the thermodynamic activity of spacetime itself, governed by the Law of Entropy Equilibrium. This law states that the universe maintains a constant total entropy by balancing the Drive for Order (gravity/structure) against the Drive for Chaos (entropy/dissipation).
When gravity builds structure (increasing Order), the universe must generate a corresponding amount of Chaos to maintain the balance. The accelerated expansion of the cosmos is the mechanism the universe uses to generate this required entropy.
Dark energy is the manifestation of the universe's fundamental drive to maintain equilibrium. It is not constant, because the thermodynamic state of the universe is not constant. It evolves, driven by the deep interplay of matter, gravity, and time.