Volume 6, Issue 1, pages 1-32
In a recent paper—The Fractal Corresponds to Light and Quantum Foundation Problems—the author described the forward-looking progressive perspective of a fractal. In this paper the author modelled the complementary and dual perspective of the same fractal: its retrospective perspective, this time it pertaining specifically to cosmology. Recent discussions as to whether the universe is fractal concluded with the 2012 WiggleZ Dark Energy Survey findings in (part) agreement with fractal-cosmology proponents that the small-scale observable universe is fractal; however, beyond this, the smooth large-scale—and thus the universe—is not fractal. Is this smoothness and other ΛCDM properties what one would expect to observe (within) if the universe is a fractal? Current fractal-cosmology models seek repeating patterns of larger scale further out. Though these structures have since been found in the smooth; in this paper the growth from the perspective within a growing fractal was modelled. An experiment was conducted on a ‘simple’ (Koch snowflake) fractal. New triangle sizes of arbitrary size were held constant and earlier triangles were allowed to expand as the fractal set iterated (grew). Classical kinematic equations—velocity and acceleration—were calculated for the total area total and the distance between arbitrary points. Hubble-Lemaitre’s Law, accelerated expansion, and changing size distribution, all corresponding to cosmological observations and conjectures were tested for. Results showed: the area expanded exponentially from an arbitrary starting size; and as a consequence, the distances between measured points—from any location within the set—receded away from the ‘observer’ at increasing velocities and accelerations. It was concluded, the universe is not only fractal, but that it is a fractal. At the expense of the cosmological principle, the fractal is a geometrical match to the cosmological observations and conjectures, able to demonstrate the inflation epoch, Hubble-Lemaitre and accelerated expansion. The large-scale smoothness is a property of a growing fractal and is expected. From this model— from planet Earth— we are observing within ‘the branches’ looking out and back in time to ‘the boughs’ (the large quasar structures) and ‘the trunk’ (the CMB—which was once seedling sized Planck area size) of a fractal shaped universe. Other problems—including the horizon problem and the vacuum catastrophe—were addressed. Based on a previous work on the quantum with the fractal, the fractal may offer a direct mechanism to marrying quantum problems with cosmological problems—unifying the two realities as being two aspects of the same modern geometry.
