Gravitational Quantisation and Dark Matter

Gravitational Quantum Mechanics—Implications for Dark Matter

“…As noted above, the photon energy is such that the particle is gravitationally bound both before and after the scattering event, and the final and initial wavefunctions are assumed to be describable in terms of mixtures of bound gravitational eigenstates. The dark characteristics of halo particles arise through the relative differences in the structure, position, and range of the initial and final bound eigenstates in potential wells whose gradient decreases with radius [14,17]. This is very different behaviour to that calculated for spherical-square, finite, or infinite-sided potential wells [21] and for particles in field-free regions [10].…”

“…A better approximation to real halo potentials is, of course, one that leads to flat rotation curves [16] and has a density profile of ρ(r) ∝ 1/r 2 . In this case, the potential has a logarithmic form V(r) = −(GmM 0 /R 0 )ln(R 0 e/r) [16], where e is the exponential constant and R 0 and M 0 can be related to the virial parameters of the halo. Schrödinger's equation must be solved numerically in this logarithmic potential case.…”

“…This quantum "environmental" darkness (so-called quantum dark matter or QDM) eliminates a need to invoke new physics or new particles beyond the standard model. This should be possible without significant modification to the relatively successful LCDM paradigm [14]. GQM may also be able to solve other observational conflicts of LCDM, including the "cusp" problem, the "satellite abundance" problem, and the "angular momentum problem."…”

“…This article is organized as follows. Sections 2 and 3 provide a review of previous work in GQM reported elsewhere [12][13][14][16][17][18][19][20][21]. They include a description of the mathematical procedure for interaction cross sections calculations and a discussion of the physical structure of the eigenstates that leads to them being "dark," as well as the trends in "particle darkness" with quantum parameters for simple systems 3 .…”

“…They include a description of the mathematical procedure for interaction cross sections calculations and a discussion of the physical structure of the eigenstates that leads to them being "dark," as well as the trends in "particle darkness" with quantum parameters for simple systems 3 . Section 3 extends the GQM work of [12][13][14][16][17][18][19][20][21] and then presents new work reported at conferences of calculations of the eigenspectra of simple "toy model" Gaussian wavefunctions needing only a range of low quantum-value eigenfunctions for their approximate description. The trends in particle darkness with quantum numbers seen in these simple wavefunctions suggest how GQM might solve some astrophysical problems, some of which are described in Section 4.…”