NUVO Galaxy Curves Without Dark Matter

🌌 NUVO Galaxy Curves Without Dark Matter

Galactic rotation curves present one of the most persistent challenges to Newtonian and relativistic gravity: stars at the outer edges of galaxies rotate at speeds that far exceed what standard gravity predicts based on visible mass. This discrepancy has traditionally been attributed to dark matter — a hypothetical mass component invoked to explain the missing gravity.

In NUVO Theory, no exotic matter is needed. The flat rotation curves arise naturally from the scalar modulation of inertial and spatial units in galactic-scale scalar fields.

🌀 Classical Problem: Rotation Curve Discrepancy

In Newtonian gravity, the orbital velocity of a star at radius \( r \) from a central mass \( M(r) \) is:

\(
v_{\text{Newton}}(r) = \sqrt{ \frac{G M(r)}{r} }
\)

However, observations show that:

\( v_{\text{observed}}(r) \) remains roughly constant as \( r \) increases,
even when \( M(r) \) becomes negligible outside the galactic core.

This inconsistency is the key evidence for dark matter.

🌠 NUVO Explanation: Scalar Modulation of Dynamics

In NUVO Theory, both inertial response and spatial geometry are modulated by scalar fields. The effective unit length and local inertia at radius \( r \) are altered by the scalar modulation function \( \lambda(r) \), leading to an adjusted orbital velocity that accounts for the observed flatness.

The modified dynamics yield:

\(
v_{\text{NUVO}}(r) = \sqrt{ \lambda(r) \cdot \frac{G M(r)}{r} }
\)

This increase in effective velocity is not due to extra mass, but due to how inertia and frame geometry stretch outward in scalar-coherent space.

🧮 Scalar Modulation Across the Galactic Disk

The scalar field profile across a galaxy is not dominated by point-source potentials, but by a distributed sinertia field. The scalar modulation grows more slowly than near a compact object, and can be modeled as:

\(
\lambda(r) \approx 1 + \epsilon \cdot \left( \frac{r}{r_0} \right)^n
\)

Where:

\( \epsilon \) is a small modulation coefficient,
\( r_0 \) is a characteristic scale (e.g. galactic core radius),
\( n \in (0, 1) \) depending on the galaxy’s profile.

This allows for gradual modulation that mimics the gravitational pull of dark matter halos, without invoking any unobserved mass.

📊 Reproducing Flat Rotation Curves

For \( \lambda(r) \propto r^n \) with \( n \approx 0.5 \), the modified velocity becomes:

\(
v(r) \sim \sqrt{ \frac{G M(r)}{r} } \cdot \left( \frac{r}{r_0} \right)^{n/2}
\)

In the outer galaxy where \( M(r) \approx \text{const} \), this produces:

\(
v(r) \sim \text{const}
\)

—a flat rotation curve matching observations.

🧠 Physical Interpretation

Concept	Standard Gravity + Dark Matter	NUVO Scalar Geometry
Curve Flattening Mechanism	Additional halo mass	Scalar modulation of inertia and space
Source of gravity	Visible + dark mass	Scalar sinertia field
Mass-energy content	85% invisible	100% accounted for (no dark matter)
Time dilation effects	Curvature-based (GR)	λ(r)-based modulation

🔬 Observational Match

NUVO scalar modulation can be tuned to reproduce:

Flat velocity curves
Mass-to-light ratios
Rotation behavior of low-surface-brightness galaxies

These fits arise from the geometry itself, not from fine-tuning matter distributions.