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\begin{document}

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\section*{MOND}

\hypertarget{context}{}\subsubsection*{{Context}}\label{context}

\hypertarget{physics}{}\paragraph*{{Physics}}\label{physics}

[[!include physicscontents]]

\hypertarget{gravity}{}\paragraph*{{Gravity}}\label{gravity}

[[!include gravity contents]]

\hypertarget{contents}{}\section*{{Contents}}\label{contents}

\noindent\hyperlink{idea}{Idea}\dotfill \pageref*{idea} \linebreak
\noindent\hyperlink{consistent_theory_embedding}{Consistent theory embedding?}\dotfill \pageref*{consistent_theory_embedding} \linebreak
\noindent\hyperlink{related_concepts}{Related concepts}\dotfill \pageref*{related_concepts} \linebreak
\noindent\hyperlink{references}{References}\dotfill \pageref*{references} \linebreak
\noindent\hyperlink{original_articles}{Original articles}\dotfill \pageref*{original_articles} \linebreak
\noindent\hyperlink{review}{Review}\dotfill \pageref*{review} \linebreak
\noindent\hyperlink{experimental_constraints}{Experimental constraints}\dotfill \pageref*{experimental_constraints} \linebreak
\noindent\hyperlink{mond_phenomenology_from_actual_dark_matter}{MOND phenomenology from actual dark matter}\dotfill \pageref*{mond_phenomenology_from_actual_dark_matter} \linebreak


\hypertarget{idea}{}\subsection*{{Idea}}\label{idea}

The [[standard model of cosmology]] including [[dark energy]] and [[dark matter]] is in very good agreement with observation on scales above those of galaxies, but in its standard version becomes problematic below this scale (there are variants that address this, such as [[fuzzy dark matter]]).

Curiously though, the particular behaviour of experimental data on these ``small'' cosmological scales turns out to have a remarkably simple and universal phenomenological fit by a simple modification of the [[force]] law of [[Newtonian mechanics]] (``Newton's third law'', corrections from [[general relativity]] are typically very small for the effects in question).

\emph{MOND} is the abbreviation for this \emph{modified Newtonian dynamics} (\hyperlink{Milgrom83a}{Milgrom 83 a}, \hyperlink{Milgrom83b}{Milgrom 83 b}, \hyperlink{Milgrom83c}{Milgrom 83 c}). This refers to the proposal of modifying Newton's third law

\begin{displaymath}
F = m a
\end{displaymath}
relating the [[force]] experienced by a body of [[mass]] $m$ to its [[acceleration]] $a$ by an expression of the form

\begin{displaymath}
F = m \,\mu(a/a_0)\, a
\end{displaymath}
for some acceleration scale $a_0$ and some interpolating function $\mu \colon \mathbb{R} \to \mathbb{R}$.

The motivation is that choosing the constant $a_0$ and the function $\mu$ suitably, then such a modified formula fits the rotation-velocities of observed [[galaxies]] in dependence of the [[radius]] remarkably well, something which the [[standard model of cosmology]] with [[dark matter]] still has some problems with (but see \hyperlink{KaplinghatTurner02}{Kaplinghat-Turner 02}, \hyperlink{BLSF09}{BLSF 09}, \hyperlink{Chan13}{Chan 13}).

\hypertarget{consistent_theory_embedding}{}\subsection*{{Consistent theory embedding?}}\label{consistent_theory_embedding}

Of course an ad-hoc such modification of the basic laws of physics breaks many established properties of physics, such as the [[principle of equivalence]] in [[general relativity]] and various [[conservation laws]]. It must be that this modified Newtonian force law is the effect of some more fundamental theory. The only proposal for such a theory apart from [[gravity]]+[[dark matter]] itself (\hyperlink{KaplinghatTurner02}{Kaplinghat-Turner 02}, \hyperlink{BLSF09}{BLSF 09}, \hyperlink{Chan13}{Chan 13}) is to add to Einstein gravity a unit vector field and a [[scalar field]] (\hyperlink{Bekenstein04}{Bekenstein 04}, ``TeVeS''), themselves thus otherwise unobserved ``dark fields'', as it were, but, as opposed to say the [[axion]] dark matter candidate, not motivated beyond the desire to fit galaxy rotation curves.

From \hyperlink{Bekenstein04}{Bekenstein 04, p. 9} one sees explicitly that TeVeS is just Einstein-gravity coupled to peculiar ``matter'' fields:



\hypertarget{related_concepts}{}\subsection*{{Related concepts}}\label{related_concepts}

\begin{itemize}%
\item An alternative proposal is that of [[fuzzy dark matter]], where the theory of gravity is left as is, but one assumes that there is [[dark matter]] which is so extremely light that its [[de Broglie wavelength]] is of the scales of galaxies. Such [[fuzzy dark matter]] models make the same prediction as cold dark matter on cosmological scales, but change behaviour on scales of galaxies due to the [[quantum physics|quantum]] nature of these light particles becoming relevant here. This change of behaviour has been argued to account for the kind of effects that MOND is a fit for.

\end{itemize}
\hypertarget{references}{}\subsection*{{References}}\label{references}

\hypertarget{original_articles}{}\subsubsection*{{Original articles}}\label{original_articles}

The concept of MOND is due to

\begin{itemize}%
\item [[Mordehai Milgrom]], \emph{A modification of the Newtonian dynamics as a possible alternative to the hidden mass hypothesis}, Astrophysical Journal. 270: 365--370. (1983) doi:10.1086/161130.


\item [[Mordehai Milgrom]], \emph{A modification of the Newtonian dynamics - Implications for galaxies}, Astrophysical Journal. 270: 371--389. (1983) doi:10.1086/161131.


\item [[Mordehai Milgrom]], \emph{A modification of the Newtonian dynamics - Implications for galaxy systems}, Astrophysical Journal. 270: 384. (1983) doi:10.1086/161132



\end{itemize}
and its most popular relativistic completion TeVeS is due to

\begin{itemize}%
\item [[Jacob Bekenstein]], \emph{Relativistic gravitation theory for the modified Newtonian dynamics paradigm}, Physical Review D, 70 (8): 083509, (\href{https://arxiv.org/abs/astro-ph/0403694}{arXiv:astro-ph/0403694})

\end{itemize}
\hypertarget{review}{}\subsubsection*{{Review}}\label{review}

General review includes

\begin{itemize}%
\item Beno\^i{}t Famaey and Stacy S. McGaugh, \emph{Modified Newtonian Dynamics (MOND): Observational Phenomenology and Relativistic Extensions},2012, Living Reviews in Relativity, 15, 10 (\href{https://arxiv.org/abs/1112.3960}{arXiv:1112.3960})


\item Joe Silk, Gary A. Mamon, \emph{The Current Status of Galaxy Formation} (\href{http://arxiv.org/abs/1207.3080}{arXiv:1207.3080})


\item Wikipedia, \emph{\href{https://en.wikipedia.org/wiki/Modified_Newtonian_dynamics}{Modified Newtonian dynamics}}


\item Wikipedia, \emph{\href{https://en.wikipedia.org/wiki/Tensor%E2%80%93vector%E2%80%93scalar_gravity}{Tensor--vector--scalar gravity}}



\end{itemize}
\hypertarget{experimental_constraints}{}\subsubsection*{{Experimental constraints}}\label{experimental_constraints}

The stark failure of plain MOND to fit data on large cosmological scales is highlighted in

\begin{itemize}%
\item Scott Dodelson, \emph{The Real Problem with MOND}, Int. J. Mod. Phys. D, 20, 2749 (2011). (\href{https://arxiv.org/abs/1112.1320}{arXiv:1112.1320})

\end{itemize}
The instability of its relativistic completion by TeVeS was pointed out in

\begin{itemize}%
\item Michael D. Seifert, \emph{Stability of spherically symmetric solutions in modified theories of gravity}, Phys.Rev.D76:064002, 2007 (\href{https://arxiv.org/abs/gr-qc/0703060}{arXiv:gr-qc/0703060})

\end{itemize}
 The detection of [[gravitational waves]] coincident with [[electromagnetic radiation]] from merging [[neutron stars]] (event GW170817, \href{LIGO-Virgo#LIGOVirgo17}{LIGO-Virgo 17}) constrains relativistic completions of MOND:

\begin{itemize}%
\item Jose Mar\'i{}a Ezquiaga, Miguel Zumalac\'a{}rregui, \emph{Dark Energy after GW170817} (\href{https://arxiv.org/abs/1710.05901}{arXiv:1710.05901})


\item Sibel Boran, Shantanu Desai, Emre Kahya, Richard Woodard, \emph{GW170817 Falsifies Dark Matter Emulators} (\href{https://arxiv.org/abs/1710.06168}{arXiv:1710.06168})



\end{itemize}
The observation of a galaxy that does not exhibit the effect which MOND claims is universal (otherwise attributed to the presence of [[dark matter]]) is reported in

\begin{itemize}%
\item Pieter van Dokkum et.al. \emph{A galaxy lacking dark matter}, Nature volume 555, 2018 pages 629–632 (\href{https://arxiv.org/abs/1803.10237}{arXiv:1803.10237}, \href{https://www.nature.com/articles/nature25767}{doi:10.1038/nature25767})

\end{itemize}
\begin{quote}%
Regardless of the formation history of NGC1052–DF2, its existence has implications for the dark matter paradigm. Our results demonstrate that dark matter is separable from galaxies, which is (under certain circumstances) expected if it is bound to baryons through nothing but gravity. The ``[[bullet cluster]]'' demonstrates that dark matter does not always trace the bulk of the baryonic mass, which in clusters is in the form of gas. NGC1052–DF2 enables us to make the complementary point that dark matter does not always coincide with galaxies either: it is a distinct ``substance'' that may or may not be present in a galaxy. Furthermore, and paradoxically, the existence of NGC1052–DF2 may falsify alternatives to dark matter. In theories such as [[MOND]] and the recently proposed emergent gravity paradigm a ``dark matter'' signature should always be detected, as it is an unavoidable consequence of the presence of ordinary matter. In fact, it had been argued previously that the apparent absence of galaxies such as NGC1052–DF2 constituted a falsification of the standard cosmological model, and evidence for modified gravity.


\end{quote}
\hypertarget{mond_phenomenology_from_actual_dark_matter}{}\subsubsection*{{MOND phenomenology from actual dark matter}}\label{mond_phenomenology_from_actual_dark_matter}

Derivations of the MOND phenomenology from actual [[dark matter]] is discussed in the following articles:

\begin{itemize}%
\item Manoj Kaplinghat, Michael S. Turner, \emph{How Cold Dark Matter Theory Explains Milgrom's Law}, Astrophys.J. 569 (2002) L19 (\href{https://arxiv.org/abs/astro-ph/0107284}{arXiv:astro-ph/0107284})


\item Jean-Philippe Bruneton, Stefano Liberati, Lorenzo Sindoni, Benoit Famaey, \emph{Reconciling MOND and dark matter?}, Journal of Cosmology and Astroparticle Physics, Issue 03, pp. 021 (2009) (\href{https://arxiv.org/abs/0811.3143}{arXiv:0811.3143})


\item Man Ho Chan, \emph{Reconciliation of MOND and Dark Matter theory}, Phys. Rev. D, 88, 103501 (2013) (\href{https://arxiv.org/abs/1310.6801}{arXiv:1310.6801})



\end{itemize}
and specifically for [[axion|axionic]] [[fuzzy dark matter]]:

\begin{itemize}%
\item [[Lam Hui]], [[Jeremiah Ostriker]], [[Scott Tremaine]], [[Edward Witten]], \emph{On the hypothesis that cosmological dark matter is composed of ultra-light bosons}, Phys. Rev. D 95, 043541 (2017) (\href{https://arxiv.org/abs/1610.08297}{arXiv:1610.08297})

\end{itemize}
and for fuzzy dark matter with [[superfluid]]-effects includes in

\begin{itemize}%
\item [[Lasha Berezhiani]], [[Justin Khoury]], \emph{Theory of Dark Matter Superfluidity}, Phys. Rev. D 92, 103510 (2015) (\href{https://arxiv.org/abs/1507.01019}{arXiv:1507.01019})


\item [[Justin Khoury]], \emph{Another Path for the Emergence of Modified Galactic Dynamics from Dark Matter Superfluidity}, Phys. Rev. D 93, 103533 (2016) (\href{https://arxiv.org/abs/1602.05961}{arXiv:1602.05961})



\end{itemize}


\end{document}