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Existence of dark matter depends on cosmic dust, not the shape of rotation curves!
Dark matter thought to hold galaxies together depending on the shape of rotation curves is false as ALL galaxy velocities are overstated by the redshift in cosmic dust that concentrates at the outer edges of the galaxy disk
Cold dark matter cosmology is based on galaxies of stars, gas , and cosmic dust embedded in surrounding halo of dark matter. In the local Andromeda (M31) galaxy having low-redshifts (Z < 0.001), the mass of dark matter within a galaxy disk increases with disk radius becoming dominant in the outer disk producing flat rotation velocity curves which have been interpreted as the signature of dark matter.
However, high-redshift (0.6 < Z < 2.6) galaxies in the distant Universe from about 10 billion years ago were recently found  to have falling rotation curves. The redshift intensity plot of the Hα line for GS4 43501 is shown in the upper panel of the thumbnail. The bulge intensity in red corresponds to a maximum redshift Z = 1.6 with minimum Z < 0.6 at the outer disk edge in purple. The lower panel shows the rotation velocities along the direction of the white line. Unlike the flat rotation curves common to local galaxies, distant galaxies appear to have falling rotation curves, at least for short distances. Regardless, modern cosmology that relies on the invariance of dark matter permeating both the local and distant Universe is placed in question by an unexpected redshift dependence.
In this regard, high-redshift galaxies were thought baryon-dominated, with dark matter playing a smaller part in the falling rotation curves than in the local Universe; and second, the large velocity dispersion of turbulence in high-redshift disks introduces a substantial pressure term  that leads to a decrease in rotation velocity with increasing radius. In the upper panel of the thumbnail, the Bernoulli equation gives the rotational velocity Vrot = Vo of the gas if the pressure term dP/dr vanishes. Therefore, to explain the falling rotation curves in high redshift galaxies, a substantial pressure term dP/dr < 0 is required to reduce the rotation velocity Vrot < Vo. But this argument is problematic. Pressure does not exist in the vacuum of space to justify the claim that rotation velocities are reduced by gas pressure. In optically thin gas disks, collisions between gas molecules do transfer momentum, but this has nothing to do with pressure in the continuum implicit in the Bernoulli equation.
Since the 1970's, dark matter was thought to exist because the rotational velocities found in Andromeda M31 and other galaxies having redshift Z < 0.001 were higher than expected by Newtonian mechanics which suggested the galaxies could not be held together as they appear. Following Hubble's methodology, the rotation velocities were inferred from the redshift of spectral emission from the galaxy, the consequence of which was flat rotation curves are the signature of dark matter holding M31 together. But the redshifted galaxy light undergoes an additional redshift upon absorption in the cosmic dust that concentrates at the outer edge of spiral galaxies. Since the redshift in dust significantly overstates the rotation velocities, the premise that dark matter must be present to hold the M31 galaxy together is therefore false.
But the same argument may be made for the distant GS4 43501 galaxy as the thumbnail shows falling rotation velocities < 150 km/s are similar to M31. Hence, dark matter is still necessary to hold GS4 43501 together. What this means is cosmic dust is overstating the velocities of ALL rotation velocities in both low and high-redshift galaxies. See "Ghost galaxy: Evidence for cosmic dust as the source of dark matter," at https://www.nanoqed.org, 2018
In near and far galaxies, the shape of the rotation curves has nothing to do with the existence of dark matter. Both flat and falling curves have rotation velocities < 150 km/s which still require dark matter to hold the galaxies together. See Ibid, "It's the redshift in cosmic dust, stupid!," 2018.
Nearby Galaxies Cosmic dust concentrates at the outer edge of nearby galaxies to increase the redshift in the spectral line emissions from the galaxy to significantly overstate actual velocities giving the false impression that dark matter exists to hold the galaxy together.
Distant Galaxies In high-redshift galaxies, cosmic dust makes the galaxies appear more distant than actual distances. Indeed, the redshift Z = 1.6 of the bulge of GS4 43501 shown in the thumbnail is grossly overstated by cosmic dust. To show dark matter exists, redshift measurements at the outer disk edge require Z << 0.001, but appear problematic.
The shape of the rotation curves has nothing to do with dark matter. Both near and far galaxies still require dark matter to hold the galaxies together. But if redshift in ALL galaxies is indeed corrected for cosmic dust, dark matter need not exist to hold galaxies together as galaxy dynamics is governed by Newtonian mechanics.
 R. Genzel, et al., "Strongly Baryon-Dominated Disk Galaxies at the Peak of Galaxy Formation Ten Billion Years Ago", Nature, 543, 397–401, 2017.
 A. Burkert, et al., "High-redshift star-forming galaxies: angular momentum and baryon fraction, turbulent pressure effects, and the origin of turbulence", Astrophys. J.,725,2324–
Page Updated Last on: Apr 19, 2018