as the folded back edge at (À0.75, 0i) and the Misiurewicz point at
(À1.543689012692, 0i), are present in both higher- and lower-dimensional cases.
Condensation appears to be a generic feature of a large variety of theories,
including various flavors of emergent, entropic, thermodynamic, and holographic
gravity theory. It is also obviously a feature of Cosmology if we envision a hot Big
Bang preceded by some form of Inflation. Most of the concepts presented do not
depend on an exotic higher-d framework, but they fit well with ideas that came about
that way, like DGP gravity, as well as with more mainstream cosmologies. Conventional inflationary universe theory has its share of problems, as was pointed out by
Professor Steinhardt at FFP11 (Steinhardt 2010), and which later became a feature
article in Scientific American (twice) (Steinhardt 2011; Ijjas et al. 2017). But the
theories cited above, and the new work presented here, suggest alternate roads to the
present-day cosmos through cosmological transitions. Cosmologies based on M in
the octonions show octonionic inflation ending in a 5-d volume, which flips into a
4-d spacetime at (À0.75, 0i). The fact we now live in a 3-d space plus time, or a 4-d
spacetime, may not mean that the current background dimensionality was always
present, and it likely does not mean the dimensionality of space was always so welldefined. It is claimed that theories of emergent gravity like Verlinde’s work as stated
only if the fabric of spacetime is also emergent. In the context of gravitation by
condensation, as a process of dimensional reduction, this happens automatically. In
Mandelbrot gravity theory, we see represented desirable long-range features of
higher-d theories combined with short-range behavior in line with the theories of
Newton and Einstein that emerge from condensation, without having to put
adjusting factors in by hand.
Acknowledgement The author wishes to thank the conference organizers, the MUDIC staff, the
people and official representatives of Orihuela and Elche, and the Universidad Miguel Hernandez,
for the warm reception and collegial atmosphere.
References
Anderson MH et al (1995) Observation of Bose-Einstein condensation in a dilute atomic vapor.
Science 269(5221):198–201
Connes A (2000) Noncommutative Geometry Year 2000, arXiv:math/0011193
de Rham C et al (2008a) Cascading gravity and degravitation. J Cosmol Astropart Phys 2008.
arXiv:0712.2821
de Rham C et al (2008b) Cascading gravity: extending the Dvali-Gabadadze-Porrati model to
higher dimension. Phys Rev Lett 100:251603
Deffayet C (2001) Cosmology on a brane in Minkowski bulk. Phys Lett B 502(1-4):199–208.
arXiv:hep-th/0010186
Dickau JJ (1987) Cosmology and the Mandelbrot set. Amygdala 1(7):2–3
Dickau JJ (2009) Does the Mandelbrot set offer clues to the cosmological evolution of form? In:
2nd Crisis in Cosmology Conference, CCC-2, ASP Conference series, vol 413, pp 116–121
Dickau JJ (2016a) Charting trends in the Mandelbrot set & showing their significance for cosmology. Prespacetime J 7(9):1319–1332
7 Gravitation by Condensation
75
(À1.543689012692, 0i), are present in both higher- and lower-dimensional cases.
Condensation appears to be a generic feature of a large variety of theories,
including various flavors of emergent, entropic, thermodynamic, and holographic
gravity theory. It is also obviously a feature of Cosmology if we envision a hot Big
Bang preceded by some form of Inflation. Most of the concepts presented do not
depend on an exotic higher-d framework, but they fit well with ideas that came about
that way, like DGP gravity, as well as with more mainstream cosmologies. Conventional inflationary universe theory has its share of problems, as was pointed out by
Professor Steinhardt at FFP11 (Steinhardt 2010), and which later became a feature
article in Scientific American (twice) (Steinhardt 2011; Ijjas et al. 2017). But the
theories cited above, and the new work presented here, suggest alternate roads to the
present-day cosmos through cosmological transitions. Cosmologies based on M in
the octonions show octonionic inflation ending in a 5-d volume, which flips into a
4-d spacetime at (À0.75, 0i). The fact we now live in a 3-d space plus time, or a 4-d
spacetime, may not mean that the current background dimensionality was always
present, and it likely does not mean the dimensionality of space was always so welldefined. It is claimed that theories of emergent gravity like Verlinde’s work as stated
only if the fabric of spacetime is also emergent. In the context of gravitation by
condensation, as a process of dimensional reduction, this happens automatically. In
Mandelbrot gravity theory, we see represented desirable long-range features of
higher-d theories combined with short-range behavior in line with the theories of
Newton and Einstein that emerge from condensation, without having to put
adjusting factors in by hand.
Acknowledgement The author wishes to thank the conference organizers, the MUDIC staff, the
people and official representatives of Orihuela and Elche, and the Universidad Miguel Hernandez,
for the warm reception and collegial atmosphere.
References
Anderson MH et al (1995) Observation of Bose-Einstein condensation in a dilute atomic vapor.
Science 269(5221):198–201
Connes A (2000) Noncommutative Geometry Year 2000, arXiv:math/0011193
de Rham C et al (2008a) Cascading gravity and degravitation. J Cosmol Astropart Phys 2008.
arXiv:0712.2821
de Rham C et al (2008b) Cascading gravity: extending the Dvali-Gabadadze-Porrati model to
higher dimension. Phys Rev Lett 100:251603
Deffayet C (2001) Cosmology on a brane in Minkowski bulk. Phys Lett B 502(1-4):199–208.
arXiv:hep-th/0010186
Dickau JJ (1987) Cosmology and the Mandelbrot set. Amygdala 1(7):2–3
Dickau JJ (2009) Does the Mandelbrot set offer clues to the cosmological evolution of form? In:
2nd Crisis in Cosmology Conference, CCC-2, ASP Conference series, vol 413, pp 116–121
Dickau JJ (2016a) Charting trends in the Mandelbrot set & showing their significance for cosmology. Prespacetime J 7(9):1319–1332
7 Gravitation by Condensation
75