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Feb 23, 2023
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Why isn't Dark Matter thought of as a rubber band that is expanding(stretching)? Can black holes be snaps in the strands that hold everything together? I'm probably way off. If anyone can help answer the whys and why nots of my questions.
 
Why isn't Dark Matter thought of as a rubber band that is expanding(stretching)? Can black holes be snaps in the strands that hold everything together? I'm probably way off. If anyone can help answer the whys and why nots of my questions.
I just ran across an article that proposes DM behaves as a wave function.

Gravitational wave scientists set their sights on dark matter
Incredibly sensitive instruments used in landmark discoveries could help solve one of the biggest remaining mysteries in the Universe


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The gravitational-wave observatory GEO600 is located in Ruthe near Sarstedt, 20 kilometers south of Hannover. It is a laser interferometer with 600… [more]
Thought to make up roughly 85% of all matter in the Universe, dark matter has never been observed directly and remains one of the biggest unsolved mysteries in modern physics. Even though dark matter has never been directly detected, scientists suspect it exists due to its gravitational effect on objects across the Universe. For example, a large amount of unseen matter may explain why galaxies rotate as they do, and how they could have formed in the first place.
Until recently, it was widely believed that dark matter was composed of heavy elementary particles. These were not discovered despite a multitude of efforts, and scientists are now turning to alternative theories to explain dark matter. A recent theory says that dark matter is actually something called a scalar field, which would behave as invisible waves bouncing around galaxies, including our own Milky Way.

more..... https://www.mpg.de/17828398/gravitational-wave-scientists-set-their-sights-on-dark-matter#
 

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The physics and phenomenology of wave dark matter appear to be related to a bosonic dark matter candidate lighter than about 30 eV.

Such particles have a de Broglie wavelength* exceeding the average inter-particle separation in a galaxy like the Milky Way, thus well described as a set of classical waves. The particle physics motivations for them are outlined, including the QCD axion as well as ultra-light axion-like-particles such as fuzzy dark matter. The wave nature of the dark matter implies a rich phenomenology:
  • Wave interference gives rise to order unity density fluctuations on de Broglie scale in halos. One manifestation is vortices where the density vanishes and around which the velocity circulates. There is one vortex ring per de Broglie volume on average.
  • For sufficiently low masses, soliton condensation occurs at centers of halos. The soliton oscillates and random walks, another manifestation of wave interference. The halo and subhalo abundance is expected to be suppressed at small masses, but the precise prediction from numerical wave simulations remains to be determined.
  • For ultra-light ∼ 10−22 eV dark matter, the wave interference substructures can be probed by tidal streams/gravitational lensing. The signal can be distinguished from that due to subhalos by the dependence on stream orbital radius/image separation.
  • Axion detection experiments are sensitive to interference substructures for wave dark matter that is moderately light. The stochastic nature of the waves affects the interpretation of experimental constraints and motivates the measurement of correlation functions.
Dynamical measurements tell us the dark matter mass density in the solar neighborhood is about 0.4GeVcm . From this, one can deduce the average inter-particle separation, given a dark matter particle mass. We can compare it against the de Broglie wavelength of the particle:

2π 􏰆10−22 eV􏰇􏰆250km/s􏰇 􏰆10−6 eV􏰇􏰆250km/s􏰇 λdB ≡ mv = 0.48 kpc m v = 1.49 km m v , where v is the velocity dispersion of the galactic halo, and m is the dark matter particle.

A range of local dark matter density values have been reported in the literature: e.g. 0.008 M⊙/pc3 = 0.3 GeV/cm3 (Bovy & Tremaine 2012), 0.0122 M⊙/pc3 = 0.46 GeV/cm3 (Siverts- son et al. 2018), 0.013 M⊙/pc3 = 0.49 GeV/cm3 (McKee et al. 2015).

In a Milky-Way-like environment, the average number of particles in a de Broglie volume λ3dB is:

Screenshot 2023-02-25 at 14.54.18.png

Such a light dark matter particle is necessarily bosonic, for the Pauli exclusion principle** precludes multiple occupancies for fermions—this is the essence of the bound by Tremaine & Gunn (1979). For concreteness, we focus on a spin zero (scalar) particle, although much of the wave phenomenology applies to higher spin cases as well (Graham et al. 2016b, Kolb & Long 2020, Aoki & Mukohyama 2016). There is a long history of investigations of dark matter as a scalar field (e.g., Baldeschi et al. 1983, Turner 1983, Press et al. 1990, Sin 1994, Peebles 2000, Goodman 2000, Lesgourgues et al. 2002, Amendola & Barbieri 2006, Chavanis 2011, Suarez & Matos 2011, Rindler-Daller & Shapiro 2012, Berezhiani & Khoury 2015a, Fan 2016, Alexander & Cormack 2017).

Perhaps the most well motivated example is the Quantum Chromodynamics (QCD) axion (Peccei & Quinn 1977, Kim 1979, Weinberg 1978, Wilczek 1978, Shifman et al. 1980, Zhitnitsky 1980, Dine et al. 1981, Preskill et al. 1983, Abbott & Sikivie 1983, Dine & Fischler 1983).

Its possible the mass spans a large range— experimental detection has focused on masses around 10−6 eV, with newer experiments reaching down to much lower values. For recent reviews, see Graham et al. (2015), Marsh (2016), Sikivie (2020). String theory also predicts a large number of axion-like-particles (ALP), one or some of which could be dark matter (Svrcek & Witten 2006, Arvanitaki et al. 2010, Halverson et al. 2017, Bachlechner et al. 2019). At the extreme end of the spectrum
described by the classical electric and magnetic fields.

Classical physics, for large occupancy, implies negligible quantum fluctuations. The question of how the classical description relates to the underlying quantum one is a fascinating subject. We unfortunately do not have the space to explore it here (see Sikivie & Yang 2009, Guth et al. 2015, Dvali & Zell 2018, Lentz et al. 2020, Allali & Hertzberg 2020).
is the possibility of an ALP with mass around 10-22nd - 10-20th
that naturally matches the observed dark matter density. More generally, ultra-light dark matter in this mass range is often referred to as fuzzy dark matter (FDM).

Fuzzy Dark Matter was proposed by Hu, Barkana & Gruzinov (2000) to address small scale structure issues thought to be associated with conventional cold dark mater (CDM) (Spergel & Steinhardt 2000). It remains unclear whether the small scale structure issues point to novelty in the dark matter sector, or can be resolved by baryonic physics, once the complexities of galaxy formation are properly understood (for a recent review, see Weinberg et al. 2015).

For a further elucidation, see: https://arxiv.org/pdf/2101.11735.pdf

* DeBroglie wavelength, also called matter wave, any aspect of the behaviour or properties of a material object that varies in time or space in conformity with the mathematical equations that describe waves. By analogy with the wave and particle behaviour of light that had already been established experimentally, the French physicist Louis de Broglie suggested (1924) that particles might have wave properties in addition to particle properties.

Three years later the wave nature of electrons was detected experimentally. Objects of everyday experience, however, have a computed wavelength much smaller than that of electrons, so their wave properties have never been detected; familiar objects show only particle behaviour. De Broglie waves play an appreciable role, therefore, only in the realm of subatomic particles.


de Broglie wavelength


De Broglie waves account for the appearance of subatomic particles at conventionally unexpected sites because their waves penetrate barriers much as sound passes through walls. Thus a heavy atomic nucleus occasionally can eject a piece of itself in a process called alpha decay. The piece of nucleus (alpha particle) has insufficient energy as a particle to overcome the force barrier surrounding the nucleus; but as a wave it can leak through the barrier—that is, it has a finite probability of being found outside the nucleus.

See: https://www.britannica.com/science/de-Broglie-wave

** Pauli exclusion principle is the assertion that no two electrons in an atom can be at the same time in the same state or configuration, proposed (1925) by the Austrian physicist Wolfgang Pauli to account for the observed patterns of light emission from atoms. The exclusion principle subsequently has been generalized to include a whole class of particles of which the electron is only one member.

Subatomic particles fall into two classes, based on their statistical behaviour. Those particles to which the Pauli exclusion principle applies are called fermions; those that do not obey this principle are called bosons. When in a closed system, such as an atom for electrons or a nucleus for protons and neutrons, fermions are distributed so that a given state is occupied by only one at a time.

Italian-born physicist Dr. Enrico Fermi draws a diagram at a blackboard with mathematical equations. circa 1950.

See: https://www.britannica.com/science/Pauli-exclusion-principle

Particles obeying the exclusion principle have a characteristic value of spin, or intrinsic angular momentum; their spin is always some odd whole-number multiple of one-half. In the modern view of atoms, the space surrounding the dense nucleus may be thought of as consisting of orbitals, or regions, each of which comprises only two distinct states. The Pauli exclusion principle indicates that, if one of these states is occupied by an electron of spin one-half, the other may be occupied only by an electron of opposite spin, or spin negative one-half. An orbital occupied by a pair of electrons of opposite spin is filled: no more electrons may enter it until one of the pair vacates the orbital. An alternative version of the exclusion principle as applied to atomic electrons states that no two electrons can have the same values of all four quantum numbers.

The dark matter sector could well be peppered with different kinds of particles. This has a certain plausibility in string theory, which generically predicts a variety of axions*. Most of them would be too massive to be a suitable dark matter candidate. But if one of them is light enough to be dark matter, perhaps there may be more .
Hartmann352

* Axions are hypothetical lightweight particles whose existence would resolve two major problems.

The first, fussed over since the 1960s, is the strong charge-parity (CP) problem, which asks why the quarks and gluons that make up protons and neutrons obey a certain symmetry. Axions would show that an unseen field is responsible.

The second is dark matter. Axions “are excellent dark matter candidates,” said Asimina Arvanitaki, a theoretical physicist at the Perimeter Institute for Theoretical Physics in Waterloo, Canada. Axions would clump together in exactly the ways we expect dark matter to, and they have just the right properties to explain why they’re so hard to find — namely, they’re extremely light and reluctant to interact with regular matter.

See: https://www.quantamagazine.org/a-hint-of-dark-matter-sends-physicists-looking-to-the-skies-20211019/
 
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Classical physics, for large occupancy, implies negligible quantum fluctuations. The question of how the classical description relates to the underlying quantum one is a fascinating subject.
As musician, I particularly like the concept of String theory. It appears to me as the most fundamental expression of dynamical action.
De Broglie waves account for the appearance of subatomic particles at conventionally unexpected sites because their waves penetrate barriers much as sound passes through walls. Thus a heavy atomic nucleus occasionally can eject a piece of itself in a process called alpha decay. The piece of nucleus (alpha particle) has insufficient energy as a particle to overcome the force barrier surrounding the nucleus; but as a wave it can leak through the barrier—that is, it has a finite probability of being found outside the nucleus.

See: https://www.britannica.com/science/de-Broglie-wave
I have always been fascinated with the DeBroglie-Bohm Pilot wave model as the extreme expression of the wave function. i.e. the universe itself is a wavelike object (string)?

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Artist’s concept of an oscillating or ‘ringing’ universe.

(is the universal wave in a seventh cresting mode?)

Two physicists at the University of Southern Mississippi – Lawrence Mead and Harry Ringermacher – announced today (June 26, 2015) that our universe might not only be expanding outward from the Big Bang, but also oscillating or “ringing” at the same time. The Astronomical Journal published their paper on this topic in April.
https://earthsky.org/space/is-our-universe-ringing-like-a-crystal-glass/

I read that the earliest measurable spectrum lacked very long wave lengths, indicating a "small" beginning.
question: as the wave spectrum continues to flatten out, is the wave spectrum itself expanding.
 
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