# Theoretical Physics

### Developments of the Relativistic Bohm-Poisson Equation and Dark Energy

Download PDF (636 KB) PP. 26 - 39 Pub. Date: March 1, 2019

### Author(s)

**Carlos Castro Perelman**^{*}

Center for Theoretical Studies of Physical Systems, Clark Atlanta University, Atlanta, GA, 30314, United States

### Abstract

### Keywords

### References

[1] “Dark Energy” http://en.wikipedia.org/wiki/Dark?energy

[2] S. Carroll, “The cosmological constant”. Living Reviews in Relativity 4 (2001) 1.

[3] M. Sami and R. Myrzakulov, “Late time cosmic acceleration: ABCD of dark energy and modified theories of gravity”. International Journal of Modern Physics D 25 1630031 (2016).

[4] A. Joyce, L. Lombriser, F. Schmidt, “Dark Energy vs. Modified Gravity”. Annual Review of Nuclear and Particle Science 66 (2016) 1-29.

[5] A. Starobinsky, “Spectrum Of Relict Gravitational Radiation And The Early State Of The Universe”. Journal of Experimental and Theoretical Physics Letters. 30 (1979) 682.

[6] A. Arbey, “Is it possible to consider Dark Energy and Dark Matter as a same and unique Dark Fluid? http://arxiv.org/abs/astro-ph/0506732”

[7] A. Arbey, “Dark Fluid: a complex scalar field to unify dark energy and dark matter http://arxiv.org/abs/astroph/ 0601274”

[8] C. Corda, “The future of gravitational theories in the era of the gravitational wave astronomy” International Journal of Modern Physics D 27, No. 5 (2018) 1850060.

[9] S. Capozziello and M. De Laurentis “The dark matter problem from f(R) gravity viewpoint” , Annalen der Physik 524, 9-10 (2012) 545-578.

[10] S. Capozziello and M. De Laurentis, “Extended Theories of Gravity” Phys. Rep. 509 4-5 (2011) 167-321.

[11] S. Capozziello, P. Jovanovic, V. Borka Jovanovic and D. Borka“Addressing the missing matter problem in galaxies through a new fundamental gravitational radius” JCAP 06 (2017) 044.

[12] M. Milgrom, “A modification of the Newtonian dynamics as a possible alternative to the hidden mass hypothesis”. Astrophysical Journal. 270 (1983) 365-370.

[13] P. Kroupa, M. Pawlowski and M. Milgrom (2012). “The failures of the standard model of cosmology require a new paradigm”. International Journal of Modern Physics D 21 (14) (2012) 1230003.

[14] J. Bekenstein, “Relativistic gravitation theory for the modified Newtonian dynamics paradigm”, Physical Review D 70 (8) (2004) 083509.

[15] P. Mannheim, “Alternatives to Dark Matter and Dark Energy”, Prog. Part. Nucl. Phys. 56 (2) (2005) 340.

[16] B.G. Sidharth and A. Das, “Anomaly of Dark Matter” arXiv : 1609.04246

[17] A. Maeder, “Dynamical effects of the scale invariance of the empty space: The fall of dark matter ? ” arXiv : 1711.07740.

[18] S.I. Pekar, “Untersuchungen uber die Elektronentheorie der Kristalle” Akademie Verlag, Berlin, 1954, pp-29-34.

[19] R. Ruffini and S. Bonazzola, “Systems of self-gravitating particles in general relativity and the concept of an equation of state”, Phys. Rev. 187 (1969) 1767

[20] M. Bahrami, A.Grossardt, S. Donadi, and A. Bassi, “The Schr¨odinger-Newton equation and its foundations” New J. Phys. 16 (2014) 115007.

[21] R. Pathria, “The Universe as a Black Hole”. Nature. 240 (5379): 298-299.

[22] I. Goody, “Chinese universes”. Physics Today. 25 (1972) 7.

[23] P. Landsberg, “Mass Scales and the Cosmological Coincidences”. Annalen der Physik. 496 (2) (1984) 88-92.

[24] Black Hole Cosmology, http://en.wikipedia.org/wiki/Black?hole?cosmology

[25] E. Santamato, “Geometric derivation of the Schr¨odinger equation from classical mechanics in curved Weyl spaces”, Phys. Rev. D 29, (1984) 216.

[26] E. Santamato, “Statistical interpretation of the Klein-Gordon equation in terms of the space-time Weyl curvature”, Journal of Mathematical Physics 25, 2477 (1984).

[27] E. Santamato and F. De Martini. “A Weyl-gauge invariant proof of the Spin-Statistics Theorem” arXiv : 1604.06253.

[28] E. Santamato and F. De Martini. “Solving the Quantum Nonlocality Enigma by Weyl’s Conformal Geometry Geometrodynamics” arXiv : 1203.0033.

[29] C. Castro, “Nonlinear Quantum Mechanics as the Weyl Geometry of a Classical Statistical Ensemble ”. Found. Physics Letters, vol.4, no.1 (1991) 81.

[30] C. Castro, “On Weyl Geometry, Random Processes and Geometric Quantum Mechanics ”. Foundations of Physics. vol 22, no.4 (1992) 569- 615.

[31] D. Durr, S. Goldstein, T. Norsen, W. Struyve, Nino Zangh?, “Can Bohmian mechanics be made relativistic?” arXiv : 1307.1714.

[32] I. Tavernelli, “On the Geometrization of Quantum Mechanics” Annals of Physics 371 (2016) 239.

[33] C. Castro, “Exact Solutions of the Newton-Schroedinger Equation, Infinite Derivative Gravity and Schwarzschild Atoms” Physics and Astronomy International Journal 1, issue 4 (2017) 1-8

[34] J. Klauder, Enhanced Quantization: Particles, Fields and Gravity, World Scientific, 2015.

[35] J. Klauder, “Quantum Field Theory with No Zero-point energy”, arXiv : 1803.05823.

[36] A. Faraggi, “The Equivalence Postulate of Quantum Mechanics, Dark Energy and The Intrinsic Curvature of Elementary Particles”, arXiv : 1204.3185.

[37] A. Shojai and F. Shojai, “Constraints Algebra and Equations of Motion in Bohmian Interpretation of Quantum Gravity”, arXiv : gr-qc/0311076.