A brief understanding about dark matter

Acknowledgment I am very glad and fortunate that I had Prf Dr Ha Huy Bang as my supervisor During the process in writing this thesis, I received a lot of his kindness and help He taught me almost everything, how to compute an interaction process both in general and detail, how to display a thesis or simply, how to search necessary documents He also gave many useful documents which I could not find by myself I am very thanks his about that I also send my thanks to Asso Prf Dr Nguyen Anh Ky who taught me about cosmology and inspired me to Dark Matter which is the soul of this thesis Cosmology is really an interesting field and it owns have many mysterious things And, he lead me step by step how to understand universe In addition, in the past time, I not know how I could go on smoothly without advices of Mrs Huong Thanks for her time that she spent with me in the department lab, her guides, her encourages and her enthusiasm I want to send my big thanks to all teachers in the department of theoretical physics who made the good conditions for finishing my thesis Finally, I really thank you all my friends, especial my best friends who side by side me and help me pass over the past hard time Due to the limit of time, knowledge, this thesis cannot avoid some mistakes I hope to receive your comments for the perfect complete of this work Thanks all so much August 26, 2013 Student Nguyen Thi Hien Ng u yễn Th ị H i ền Contents Introduction Chapter 1: Introduction to Particle physics 1.1 What is particles physics? 1.2 Discovering the particle world .4 1.3 The Standard Model Chapter 2: Dark Matter 2.1 A brief understanding about Dark Matter .7 2.1.1 What is dark matter? 2.1.2 The evidence for dark matter 2.1.3 Type of dark matter 2.1.4 Particles candidate for dark matter 2.1.5 Detecting for dark matter 10 2.2 Neutrinos 11 2.2.1 Neutrinos – What are they? 11 2.2.2 Where are they coming from? 12 2.2.3 Interactions and properties 12 2.2.5 Direct searches for neutrino mass 15 2.2.6 Neutrino oscillation experimental techniques 18 Chapter 3: Some interactions of neutrinos 20 3.1 Neutrino – Electron scattering 20 3.2 Neutrino-electron scattering with U-particle .8 Conclusion 13 Appendix 14 Appendix A Dirac matrices 14 Appendix B Trace of the product of matrices 14 References 16 Ng u yễn Th ị H i ền Introduction The history of the physics of the infinitely small is largely the history of the uncovering of successive layers of structure, from big to small and smaller The question of what constitutes an elementary particle in fact is not static but evolves with time, changing in step with technological advances, or precisely with the growth in the power of the sources of energy that become available to the experimenter The higher the energy of the particle beam used to illuminate or probe the object under study is, the shorter are the wavelengths associated with the incoming particles and the finer the resolutions obtained in the measure Thus, it is successively discovered that matter is built up from molecules; that the molecules are composed of atoms; the atoms of electrons and nuclei; the nuclei of protons and neutrons[3]; and the protons and neutrons of quarks As the power of the modern particle accelerators keeps on increasing, it has become possible to accelerate particles to higher and higher velocities, to attain resolutions surpassing 10-6 centimeters and to observe more violent, collisions between particles, which have revealed all the wonders of the subatomic universe, not only the presence of ever finer structure levels, but also in the existence at every level of new particles of ever grater masses Particle physics has now become synonymous with high-energy physics[3] Electron was discovered in 1895 opening the beginning of seeking fundamental particles era Or by theory, the physicist Dirac predicted the existence of positron in 1928 and in the 1932, it was detected In addition, in 1932, the first time, by experiment, Chadwick observed neutron directly[4] And over many years later, a numerous particles were predicted by theory and demonstrated by evidence All of it creates a whole picture of particle physics Life is searches and in the infinite universe the knowledge of human about it just like a drop in the whole huge sea Over many years, human still K54-H.P.HUS Page Ng u yễn Th ị H i ền keeps looking for and finding out the universe But, we just understood a mini part of it We just “see” about percent of matter in the universe, the rest…stills in the “dark”, so we count it as dark matter(96 percent!) In fact, theory is a useful method to predict new particles and is the theoretical basic to set up the experiment for demonstrating the true of prediction or not Neutrino electron, for example, it was predicted by theory in 1930 by Wolfgang Pauli and was demonstrated in 1956 by Reins[5] By this way, in this thesis, I’ll postulate some interaction process of neutrinos with hoping to understand more about dark matter which is a mysterious issue in cosmology This thesis includes three main parts: *Introduction: introduce to a preview of particle physics and propose of this thesis *Three chapters: - Chapter 1: Introduction to particle physics - Chapter 2: A brief understanding about Dark Matter - Chapter 3: Neutrino-Electron scattering *Conclusion: Summary some result of computing process and comments K54-H.P.HUS Page Ng u yễn Th ị H i ền Chapter 1: Introduction to Particle physics 1.1 What is particles physics? The physics term which deals with the interactions of elementary articles at high energies, is an important component of cosmological models of the early universe, when the universe was dominated by radiation and its average energy density was very high Because of this, pair production, scattering processes and decay of unstable particles are important in cosmology As a thumb rule, a scattering or a decay process is cosmologically important in a certain cosmological epoch if its relevant time scale is smaller or even to the time scale of the universe expansion, which is 1/H with H being the Hubble constant at that time This is roughly equal to the age of the universe at that time Cosmological observations of phenomena such as the cosmic microwave background and the cosmic abundance of elements, together with the predictions of the Standard Model of particle physics, place constraints on the conditions of the early universe The success of the Standard Model at explaining these observations provides a confirmation of its validity outside of laboratory conditions In addition, phenomena extrapolated from cosmological observations, such as dark matter and CP-violation, suggest a need for physics that goes beyond the Standard Model Protons, electrons, neutrons, neutrinos and even quarks are often featured in news of scientific discoveries All of these are tiny sub-atomic particles too small to be seen even in microscopes While molecules and atoms are the basic elements of familiar substances that we can see and feel, we have to "look" within atoms in order to learn about the "elementary" subatomic particles and to understand the nature of our Universe The science K54-H.P.HUS Page Ng u yễn Th ị H i ền of this study is called Particle Physics, Elementary Particle Physics or sometimes High Energy Physics (HEP) 1.2 Discovering the particle world Atoms were postulated long ago by the Greek philosopher Democritus, and until the beginning of the 20th century, atoms were thought to be the fundamental indivisible building blocks of all forms of matter Protons, neutrons and electrons came to be regarded as the fundamental particles of nature when we learned in the 1900's through the experiments of Rutherford and others that atoms consist of mostly empty space with electrons surrounding a dense central nucleus made up of protons and neutrons The science of particle physics surged forward with the invention of particle accelerators that could accelerate protons or electrons to high energies and smash them into nuclei — to the surprise of scientists, a whole host of new particles were produced in these collisions By the early 1960s, as accelerators reached higher energies, a hundred or more types of particles were found Could all of these then be the new fundamental particles? Confusion reigned until it became clear late in the last century, through a long series of experiments and theoretical studies, that there existed a very simple scheme of two basic sets of particles: the quarks and leptons (among the leptons are electrons and neutrinos), and a set of fundamental forces that allow these to interact with each other By the way, these "forces" themselves can be regarded as being transmitted through the exchange of particles called gauge bosons An example of these is the photon, the quantum of light and the transmitter of the electromagnetic force we experience every day (We should state here that all these sets of particles also include their anti-particles, or in plain language what might roughly be called their complementary opposites These make up matter and anti-matter.) Today, the Standard Model is the theory that describes the role of these fundamental particles and interactions between them And the role of Particle Physics is to test this model in all conceivable ways, seeking to discover K54-H.P.HUS Page Ng u yễn Th ị H i ền whether something more lies beyond it Below we will describe this Standard Model and its salient features 1.3 The Standard Model All of the known matter in the Universe today is made up of quarks and leptons, held together by fundamental forces which are represented by the exchange of particles known as gauge bosons (u) (c) (t) up-quark charm-quark top-quark mass = 0.005 mass = 1.5 mass = 186 (d) (s) (b) down-quark strange-quark bottom-quark Charge = -1/3 mass = 0.009 mass = 0.16 mass = 5.2 (νe) (νµ ) (ντ) elec-neutrino muon-neutrino tau-neutrino mass ~ mass ~ mass ~ (e) (µ) (τ ) electron muon tau Charge = +2/3 Quark Lepton mass = 0.00054 mass = 0.11 Charge =0 Charge = -1 mass = 1.9 Forces and Interactions Now we must tackle the fundamental forces or interactions among the quarks and leptons: Gravity, the Weak Force, Electromagnetism, and the Strong Force Of these, our everyday world is controlled by gravity and electromagnetism The strong force binds quarks together and holds nucleons (protons & neutrons) in nuclei The weak force is responsible for the radioactive decay of unstable nuclei and for interactions of neutrinos and other leptons with matter K54-H.P.HUS Page Ng u yễn Th ị H i ền Relative Gauge Strength Boson Gluon(g) 1/37 Weak Gravity Force Strong Electromagnetic K54-H.P.HUS Mass Charge Spin 0 Photon(γ) 0 10-9 W±, Z 86,97 ±1, 10-38 Graviton(G) 0 (rel to proton) Page Ng u yễn Th ị H i ền Chapter 2: Dark Matter TABLE II: The total number of scatters within a human body per year for the given WIMP masses and WIMP-proton scattering cross-sections The CoGeNT, CRESST, and DAMA benchmarks are those that best fit the data for the respective experiments (CRESST has two maximum likelihood points); these points are all strongly disfavored by the null results of CDMS and XENON in the standard framework used in this analysis The XENON benchmarks are compatible with the null results of CDMS and XENON We assume a human mass of 70 kg and identical couplings to the proton and neutron.[10] Most of the matter in the universe is dark Without dark matter, galaxies and stars would not have formed and life would not exist It holds the universe together What is it? 2.1 A brief understanding about Dark Matter 2.1.1 What is dark matter? Today, dark matter is one of the biggest problems in cosmology The dark matter problem has been with us since 1930s, and was first postulated in K54-H.P.HUS Page Ng u yễn Th ị H i ền the 1930s by Dutch astronomer Jan Oort and Swiss astrophysicist Fritz Zwicky[7] Calculations show that it is five times more abundant in the universe than standard matter, but since it doesn’t emit, absorb, or reflect light, it is very tricky to spot In fact, its existence can only inferred from the gravitational force it exerts on its surroundings By the early 1980’s, better cosmological technology enabled scientists to collect experimental evidence about the rotation of spiral galaxies[6] However, the orbital velocities measured did not obey Kepler’s law in the relative between orbital velocity and mass of planet There is not enough visible mass in the galaxy to account for the velocities So that, there must existence another form of matter and we call it is Dark Matter They find out that dark matter constitutes over ninety percent of the matter in the universe including 74% dark energy and 22% dark matter [2] However it has never been directly detected In fact, it does not respond to the strong or electromagnetic force because it does not emit or absorb light Dark matter interacts with the ordinary matter only weakly and gravitationally 2.1.2 The evidence for dark matter * Evidence for dark matter in spiral galaxies In spiral galaxies like the Milky Way, we derive the gravitational mass from observing the motions of stars and gas clouds in the disk as they orbit the center The rotation curve of a galaxy shows how the velocity of stars around the center varies as the distance from the center increases Most spiral galaxies show flat rotation curves out as far as we can trace them, even where no more stars are visible Therefore we conclude that the gravitational mass is more than 10 times more massive than the luminous mass *Evidence for dark matter in clusters of galaxies In clusters of galaxies, we derive the gravitational mass by measuring the orbital motions of the member galaxies Since the galaxies in a cluster are roughly at the same distance from us, we can interpret any spread in their redshifts as orbital motion around the center of the cluster; it might amount to more than 1000 km/sec! By measuring the red-shifts of lots of galaxies in the K54-H.P.HUS Page Ng u yễn Th ị H i ền +In the laboratory system: electron at rest, p1 = We have: s  m  2mE ; E : incoming neutrino energy t  2m( Ee  m)  2mTe Put y  Te t  E s  m2 We imply the following relations: k1 p2  k p1  m( m  E  Ee )  mE (1  y )  ( s  t  m ) / k1 p1  k2 p2  mE  ( s  m ) / ; k1.k2  t / ; Q  2mE y; And (3.2)  Q  ( s  m2 ) / 2; d 1 2   | M z |  d cos cm 32 s  spin   y   m2 s 1 d 2  M | |    z dQ 16 ( s  m2 )  spin  (3.3)  Because of massless neutrino, the product q u( k2 )  (1   )u(k1 ) vanishes So, from (1) we have: ig  u(k2 )      )  u( k1 )  Mz  2  ( q  M z )8cos W    u( p2 )     gV  g A  )  u( p1 )  (3.4) GF g2  With 2 8M z cos W K54-H.P.HUS Page Ng u yễn Th ị H i ền  Mz   u(k2 )      )  u( k1 )    q  2 8M z cos W 1    Mz  ig 2   u( p2 )     gV  g A  )  u( p1 )  Q2  q2  iGF u ( k2 )  (1   )u ( k1 )  u ( p2 )   ( gV  g A  )u ( p1 )   Mz  (1  Q M z2 )  (3.5) GF2 1      Mz     k k u( ) ) u( )    spin 2(1  Q M z2 )    u( p2 )     gV  g A  )  u( p1 )   GF2 1  ( A.B)  2  2(1  Q M z )    Using: * u (k ', s ')u (k , s)  Tr (k ' m)(k  m)  where         s ,s ' *{          v   v   2   2         *Trace of an odd number of   ' s vanishes  A        A * AZ    u( k2 )      )  u( k1 )  We calculate: Here,       )     [     )]     )   spin K54-H.P.HUS Page Ng u yễn Th ị H i ền  AZ  Tr  k     )k   )         k    )(k 1 v  k 1  v )   Tr  (k    Tr  k   k 1 v  k   k 1  v  k    k 1 v  k    k 1  v     Tr  k   k 1 v  k   k 1   v  k   k 1 v   k   k 1 v     (3.6)  2Tr  k   k 1 v (1   )    *BZ    u( p2 )     gV  g A  )  u( p1 )  Here,      gV  g A  )     gV + g A  )   spin  B  Tr[( p  m    gV  g A  )( p1  m  gV  g A  )  v ] = Tr ( p + m)γ μ (gV - g A γ )( p1 + m)(gV - g A γ )γv    = Tr (gV p γ μ - g A p γμ γ + mgV γ μ - mg A γμ γ )  (gV p1 γv + g A p1 γ γv + mgV γv + mg A γ γv )  = Tr  gV2 p γμ p1 γv + gV g A p γμ p1γ γv + mgV2 p γ μ γv + mgV g A p γμ γ γv  -gV g A p γμ γ p1γv - g A2 p γμ γ p 1γ γv - mgV g A p γ μ γ γv - mg A2 p γ μ γ γ γv +mgV2 γ μ p γv + mgV g A γμ p 1γ γv + m gV2 γμ γv + m gV g A γ μ γ γv K54-H.P.HUS Page Ng u yễn Th ị H i ền -mgV g A γμ γ p1γv - mg A2 γ μ γ p1 γ γv - m gV g A γ μ γ γv - m g A2 γ μ γ γ γv   = Tr  p γμ p1γv (gV2 + g A2 - 2gV g A γ )+ m2 (gV2 - g A2 )γμ γv    Trace of other components equal zero because it is set of an odd number of γ’s Using the relation: Tr          (a  b )  Tr          (c  d  )   32  ac(        bd     )  We obtain:  d dQ  dQ s  64(k1 k  p1 p2 ) ( gV2  g 2A )(        2gV g A      )  2m2 ( gV2 - g 2A )Tr  k1 k 2        v         )    v   64[( gV2  g 2A )(k1 p1 ).(k p2 )  ( gV2  g 2A )(k1 p2 ).(k p1 ) 2gV g A (k1 p1 ).(k p2 )  2gV g A (k1 p2 ).(k p1 ) 2m ( gV2 - g 2A ).4k1 k 2 ( g  g v  g  g v  g v g  ).4 g v ] (3.7)  64[( gV  g A ) (k1 p1 ).(k p2 )  ( gV  g A ) (k1 p2 ).(k p1 ) m ( gV2 - g 2A )(k1.k )] Putting (3.3) into (3.7): K54-H.P.HUS Page Ng u yễn Th ị H i ền 2 2  (s  m ) (s  m  Q )  ( gV  g A ) AZ BZ  64  ( gV  g A ) 4  Q2  2  m ( gV - g A )   GF2 d   dQ 4 ( s  m ) (1  Q M z2 )  ( gV  g A ) ( s  m ) ( gV  g A ) ( s  m  Q )  m ( gV2 - g 2A )Q  (3.8) Neglecting m2  s, Q the integrated cross-section becomes: d GF2 s  ( gV  g A ) 2    dQ    dQ  (1  s M z ) s M z2 ( gV  g A ) s  2M z2 2M z2  M z2   s    1 log           s s  s   M z2     (3.9) For s  M z2 the logarithm term of (8) in powers of s M z2 , then in the first approximation, the cross-section depends linearly on s: GF2 s  2  ( g  g )  ( g  g ) V A V A  4  (3.10) The Z0 propagator effect through (1  Q M z2 ) 2 in (3.8) is very important at high energy, since for s  M Z the cross-section in (3.9) ceases to increase with s, it bends down and tends asymptotically towards a constant GF2 M Z2  2 gV    g A   lim    e     e     s  2    (3.11) In the laboratory frame, at low energy mE  M Z , we neglect Q M z2 and use (3.2), then (3.8) and (3.9) can be written as K54-H.P.HUS Page d    e     e   dy Ng u yễn Th ị H i ền GF2 mE   ( gV  g A )2  ( gV  g A ) 1  y    2  GF2 mE     e     e   2    2 g g g g (  )  (  ) A V A  V  (3.12) The y distrinution as well as the integrated cross-section enable us to extract gV,gA For the antineutrino   scattering   (k1 )  e ( p1)   (k2 )  e ( p2 ) ,   its cross-section can be deduced from   ( k1 )  e ( p1 )    ( k2 )  e ( p2 )   by simply substitution g R  ( gV  g A )  g L  ( gV  g A ) This rule can 2 2 be traced back to (3.5) for which the current u (k )   (1   )u ( k1 ) replace by  (k1 )   (1   ) (k2 ) , i.e k1  k2 and the substitution g R2  g L2 comes    G mE from (3.8) in which the last term proportional to m is neglected Thus: d    e      e   dy     e    e    F 2 GF2 mE  2   ( gV  g A )2  ( gV  g A ) 1  y      2 (  )  (  ) g g g g V A V A   Numerically, with GF mE  27.05  10     e      e   4.3       e      e   4.3 K54-H.P.HUS 42 (3.13) cm  E / GeV  we get: E  4  42 2 2sin sin  w 10 cm      w GeV   E  2 4sin 2sin 10 42 cm       w w   GeV   Page Ng u yễn Th ị H i ền 3.2 Neutrino-electron scattering with U-particle CV 1 : du 1   1     CVee   : du 1  1     - Vertex : - Propagator : iAdU e  idU  2sin  dU   q  dU 2   q  q   g   q   Here, q  in s-channel Basing on Feynman diagram and applying Feynman’s rule:    iAdU e  idU  CV q  q  dU   iM U  u (k2 ) dU 1   1    u ( k1 )    q    g   2sin d q   U        CVee  u (p ) dU 1   1    u (p1 )     K54-H.P.HUS Page    Ng u yễn Th ị H i ền  iM U   MU  dU  iAdU e  idu 2sin  du   ( q ) 2 dU  u ( k2 )  1    u( k1 )   u (p )  1    u ( p1 )   FU u (k )  1    u(k1 )   u (p )  1    u ( p1 )   FU AU BU (3.14)  id  CVeeCV iAdU e U where FU = dU 2 2 dU  2sin  dU   (q ) Similarity to the calculation above, we have: * AU   u(k2 )     )u(k1 )   2Tr[ k   k 1 (1   )] spin  2k2 k1 Tr                  2k2 k1  g g   g g   g g    i   ( 3.14a)   k2  k1    k1.k2 g     k2 k1   ik 2 k1    BU  u (p )  1    u ( p1 )   Tr  ( p  m   (1   )( p1  m  1   )    = 2Tr  p   p  (1- γ5 )    p2 p1 Tr        (1 - γ5 ) K54-H.P.HUS Page Ng u yễn Th ị H i ền  p2 p1 Tr  g  g   g  g   g  g    i     p2 p1    p1 p2 g     p2 p1   ip2 p1    (3.14b) We imply that: AU BU   k2  k1    k1.k2 g     k2 k1   ik2 k1    8  p2 p1    p1 p2 g     p2 p1   ip2 p1     64  k2 p2  k1 p1    p1 p2  k1 k    k2 p1  k1 p2     p1 p2  k1 k    p1 p2  k1 k2    p1 p2  k1 k2     k2 p1  k1 p2    p1 p2   k1 k2    k2 p2  k1 p1     128  k1 p1  k p2    k1 p2  k2 p1    MU  iAdU e  idu   dU 2 2sin  du   ( q ) 2dU      128  k1 p1  k2 p2    k1 p2  k2 p1   (3.15) In the center of mass: p1 k1  p2 k  E  pk cos p1 k2  p2 k1  E  pk cos   p s 4m 1 ; s K54-H.P.HUS  k  s ; s  4E Page 10 Ng u yễn Th ị H i ền 2  M U  FU  128  E  pk cos    E  pk cos      256 FU  E  p k cos    s s  4m  256      s 16    s   cos      (3.16)  2m   32s FU 1  cos   s   2 The differential cross-section is:  d  MU     d  cm 64 s  2m 2 2  32s FU   cos   s 64 s   d  (3.17)  2  2m cos2    s FU   s 2 s   M d U 64 s with d   sin  d d Hence:    sin    2 0  2  2m 2 s F   cos   d U s 2 s     FU  2m2    1  cos   d cos  s  s 0  K54-H.P.HUS Page 11 Ng u yễn Th ị H i ền FU  2m cos3      cos  s  s  FU  4m    2  3s  s Or      FU  2m    1   3s    s   iAdU e idu    dU 2 2 dU 2sin  d u   (q )   K54-H.P.HUS    2m    1   3s    s  Page 12 Ng u yễn Th ị H i ền Conclusion Well, I hope I’ve shed a little light for you on dark matter, especially on neutrinos Because something cannot be seen doesn’t mean it’s not there and so does dark matter It is all around us in the universe, and there may even be dark matter passing through your body this second! We know that dark matter exists because we can observe its effects on other things in the universe The thesis some process of dark matter is time to end After all, this thesis obtained some results: First, it introduces in general to Particle physics as well as its trend finding new particles and discovering more and more the universe Second, it introduces briefly to dark matter and neutrinos in its properties, sources and its interactions with ordinary matter Finally, it supports the detail computing of the invariant amplitude of neutrino-electron scattering By this way, we can calculate the lost energy and prove the existence of neutrinos In brief, these results are basic to carry out experiments, measurements and verify the truth of theory of neutrinos and dark matter K54-H.P.HUS Page 13 Ng u yễn Th ị H i ền Appendix Appendix A Dirac matrices *Anti-comunication:             2g    *Hermitian conjungate:  0   ,   k    k ,      ,       0      where :     i 0 1 2  i 0 1 2 *Square:      k      with k  1, 2,3 2 *Relations: u ( s) s 1,2 ( p )u ( p)  p  m ( s) with s  1, 2: spin up, down along z axis Appendix B Trace of the product of matrices *Tr (ABC)  Tr(CAB)  Tr(BCA); A, B,C is abitrary matrices *TrI  4, Tr (  )  *Tr (    )  4g  , Tr             g  g   g  g  g  g  K54-H.P.HUS Page 14 Ng u yễn Th ị H i ền Trace of an odd number of   ' s vanishes Tr     0, Tr   5    0, Tr   5      0, Tr   5        Tr   5          4i   4i  K54-H.P.HUS Page 15 Ng u yễn Th ị H i ền References Vietnamese [1] Hà Huy Bằng, Lý thuyết trường lượng tử, Nxb ĐHQGHN, 2010 [2] Phạm Thúc Tuyền, Lý thuyết hạt bản, Nxb ĐHQGHN, 2010 English [3] Q Ho Kim and X.Y Pham, Elementary particles and their Interactions, 1998 [4] Annika H G Peter, arXiv: 1201.3942vl [astro-ph.CO] 18 Jan 2012 [5] W Pauli, Phys Today 3/N9:27(1978) [6] Marissa Cevallos, Distribution and Detectability of Dark Matter in the Present Universe, Research Science Institute July 27, 2004 [7] F Zwicky, Helv, Phys Acta 6, 124(1933) [8] A.A Starobinsky, arXiv: astro-ph/9603074vl 15 Mar 1996 [9] Kai Zuber, Neutrinos Physics, P Taylor and Francis Group, 2004 [10] G P Zeller, From eV to EeV: Neutrino Cross-Sections Across Energy Scales, arXiv:1305.7513v1 [hep-ex] 31 May 2013 K54-H.P.HUS Page 16 ... 2.1 A brief understanding about Dark Matter 2.1.1 What is dark matter? Today, dark matter is one of the biggest problems in cosmology The dark matter problem has been with us since 1930s, and was... 2.1 A brief understanding about Dark Matter .7 2.1.1 What is dark matter? 2.1.2 The evidence for dark matter 2.1.3 Type of dark matter 2.1.4 Particles candidate... evidence for dark matter * Evidence for dark matter in spiral galaxies In spiral galaxies like the Milky Way, we derive the gravitational mass from observing the motions of stars and gas clouds