PPhysics Education dateline DARK MATTER AND NEUTRINOS
Gazal Sharma , Anu and B. C. Chauhan Department of Physics & Astronomical ScienceSchool of Physical & Material SciencesCentral University of Himachal Pradesh (CUHP)Dharamshala, Kangra (HP) INDIA-176215. [email protected] [email protected] (Submitted 03-08-2015) Abstract
The Keplerian distribution of velocities is not observed in the rotation of large scalestructures, such as found in the rotation of spiral galaxies. The deviation from Kepleriandistribution provides compelling evidence of the presence of non-luminous matter i.e.called dark matter. There are several astrophysical motivations for investigating the darkmatter in and around the galaxy as halo. In this work we address various theoretical andexperimental indications pointing towards the existence of this unknown form of matter.Amongst its constituents neutrino is one of the most prospective candidates. We know theneutrinos oscillate and have tiny masses, but there are also signatures for existence ofheavy and light sterile neutrinos and possibility of their mixing. Altogether, the role ofneutrinos is of great interests in cosmology and understanding dark matter.
As a human being the biggest surprise for uswas, that the Universe in which we live inis mostly dark. The NASA’s Plank Mission revealed in 2013 that our Universe contains68 .
3% of dark energy, 26 .
8% of dark matter,and only 4 . a r X i v : . [ phy s i c s . pop - ph ] N ov hysics Education dateline raises a number of questions in our minds;e.g. how much and how well we know aboutour Universe? What are dark matter anddark energy? What are they made up of?The very first suggestion of dark matter inour galaxy was made by Kapteyn and Jeansin 1922 and then by Lindblad in 1926. Theyproposed the existence of dark matter whileobserving the motions of nearby stars at rightangle to the plane of our Milky way galaxy.Oort in 1932 claimed that there exists sub-stantial amount of dark matter near the sunby observing the vertical motions of stars.However, in 1991, Kuijken and Gilmore ar-gued that there were no significant evidencefor dark matter with in the galactic disk nearthe sun.Sinclair Smith and Fritz Zwicky in 1933,studied the large clusters of galaxies andfound that galaxies were on average movingtoo fast for the cluster to be held togetheronly by the mass of the visible matter. Theyconcluded that in rich clusters of galaxies, alarge portion of the matter is not visible i.e.the dark matter. The idea of dark matter ingalactic halo was given by Freeman in 1970,while studying the rotation curve for NGC300 and M33 by using the 21cm-Line of neu-tral hydrogen did not show the expected Kep-lerian decline beyond the optical radii. Thenin 1979, Vera Rubin proposed that normalspiral galaxies contain substantial amount ofdark matter present at great distances fromthe central regions. An influential model wasproposed by Caldwell and Ostriker in 1981 forthe density of core-halo type model of darkmatter. The halo model is valid till now butthe exact distribution of dark matter is still a mystery.The next question to be addressed is aboutthe constituents of dark matter. One of thebiggest discoveries made by Hubble SpaceTelescope (HST) of NASA was the confir-mation of invisible matter in the Universe.A 3D map of dark matter was derived fromlargest survey of the Universe made by theHST, the Cosmic Evolution Survey (COS-MOS). The COSMOS survey covers a suffi-ciently wide area of sky - nine times the areaof the full Moon (1.6 square degrees) - forthe large-scale filamentary structure of an in-visible form of matter that makes up mostof the mass of Universe i.e. dark matter tobe clearly evident [1]. The theory of Big-Bang nucleosynthesis (BBN), i.e. formationof light nuclei just after Big-Bang, as wellas experimental evidences from anisotropiesin Cosmic Microwave Background Radiation(CMBR) observed by NASA’s Wilkinson Mi-crowave Anisotropy Probe (WMAP) indicatethat most of the dark matter stuff is non-baryonic (which is not made up of regularmatter).Many experiments has been performed insearch of dark matter candidates. Neutrinos,which are electrically neutral and tiny parti-cles, seem potential candidates for dark mat-ter, as they are long-lived and almost non-interacting with other particles. However,the three known types of neutrinos, called ac-tive neutrinos, are not massive enough to ac-count for all of the dark matter of Universe.So, theorists proposed another type of neu-trinos that would not interact at all with theregular matter, but are massive. If the sterileneutrino is heavy enough about ∼ keV hysics Education dateline it could account for the substantial amountof dark matter. The present article aims tointroduce reader about the dark matter, itsevidences, possible constituents and the po-tential candidature of neutrinos in the com-position of dark matter. As discussed above the dark matter is thematter, which does not interact with light atall or may interact very poorly that it remainsdark and unseen. As such, a question arisesin ones mind; how one can detect somethingwhich does not interact with light. The an-swer may be ’gravity’; such that there aremany astrophysical motivations for the de-tection of dark matter. There have been ob-tained a number of observational evidencesfor the existence of dark matter because ofits gravitational effects, like galactic rotationcurves of galaxies measured by Vera Rubin,confinement of hot gas in the galaxies, mea-surement on the basis of gravitational lensing[2], etc...
Before describing observations let us see howcelestial objects respond to the gravitationalforce acting on them and how that responsecan reveal the large scale distribution of mat-ter. For the planets in orbit around the sunwhich embodies essentially all the mass of thesolar system, the decrease in gravitational at-traction with distance is given by Newton law of gravitation. It has been found that or-bital velocities of planets decreases with dis-tance from the centre of the sun. In spiralgalaxy the gas, dust and stars in the disk ofthe galaxy all orbit around a common cen-tre. Like planets in solar system, the gasand stars move in response to the combinedgravitational attraction of all other mass. Ifthe galaxy is visualized as a spheroid, we cancalculate the gravitational attraction due tomass M r lying between the centre and an ob-ject of mass m in an equatorial orbit at adistance r from the centre. If the galaxy isneither contracting nor expanding then thegravitational force is exactly equal to the cen-trifugal force on the mass at distance r isgiven by the equation GmM r /r = mv r /r, (1)where v r is the orbital velocity. When theequation is solved for v r , the value of m dropsout and the velocity of a body at a distance r from the centre is determined only by themass M r inward from its position. In the so-lar system, virtually all the mass is concen-trated near the centre and the orbital velocitydecrease as 1 / √ r hysics Education dateline Figure 1:
Variation of orbital velocity withradius [3]out. This observation has been made for dif-ferent spiral galaxies like Sa, Sb, Sc etc... Al-though each galaxy exhibits distinctive fea-ture in its rotational pattern, the systematictrends that emerge are impressive. With in-creasing luminosity galaxies are bigger, or-bital velocities are higher and the velocitygradient across the nuclear bulge is steeper.Moreover, each type of galaxy displays char-acteristic rotational properties.Therefore we can draw conclusion from ourobservation that all the rotation curves areeither flat or rising out to the visible limitsof the galaxy. There are no extensive re-gions where the velocities fall off with dis-tance from the centre, as would be predictedif mass were centrally concentrated. The con-clusion is inescapable- mass unlike luminosityis not concentrated near the centre of spi-ral galaxies. Thus the light distribution ina galaxy is not at all a guide to mass dis-tribution. Instead the mass inside any givenradial distance is increasing linearly with dis-tance and contrary to what one might expect,is not converging to a limiting mass at theedge of the visible disk. The linear increase in mass with radius indicates that each suc-cessive shell of matter in the galaxy must con-tain just as much mass as every other shell ofthe same thickness. Since the volume V ofeach successive shell increases as the squareof the radius, the density ρ of matter in suc-cessive shells must decrease in order to keep ρV constant [4].The widely accepted idea about the darkmatter is that each spiral galaxy is embed-ded into a halo of dark matter. The gravi-tational attraction of the unseen mass keepsthe orbital velocities high at larger distancefrom galactic centre. Till now we are not ableto find the exact distribution of dark matterbut we can say that it is strongly clumpedaround the galaxies. The density of dark halodecreases with distance from galactic centreas given by Caldwell and Ostriker ρ d = ρ r a . (2)They found a fit for the data with ρ = 1 . × − M (cid:12) pc − , and a = 7 . kpc hysics Education dateline According to Einstein’s theory of generalrelativity large objects with their immensemasses can distort space-time therefore largemassive objects such as galaxy clusters bendlight from distant sources, creating distortedimages that we can see here on earth. This iscalled gravitational lensing. This techniqueis especially useful for detecting dark matter.Since dark matter doesn’t interact with light,it can’t be seen directly. However, since darkmatter is very massive, it can be detected in-directly by the distorted images it creates ofnormal matter through gravitational lensing.By measuring the angle of bending, the massof the gravitational lens can be calculated-greater the bend, more massive the lens is.Therefore the angle of deflection is given by[5] α = 4 GMc b , (3)where b is the impact parameter. Us-ing this method, astronomers have confirmedthat the galactic clusters indeed have highmasses exceeding those measured by the lu-minous matter. There have been several posi-tive reports on the observation of such micro-lensing, even though typically only one in amillion stars examined is expected to showsuch an effect. The bending of light bya massive object, a general relativity effecthas been verified to extreme accuracy (bet-ter than 1%) by studying radar echoes fromthe planets when they are in conjunction.Experiments like the Large Synoptic Sur-vey Telescope (LSST), under construction inChile, aim to take advantage of gravitational lensing to map the dark matter in the Uni-verse and provide clues to its nature. MOA(Micro-lensing Observations in Astrophysics)is a Japan/NZ collaboration that makes ob-servations on dark matter, extra-solar plan-ets and stellar atmospheres using the grav-itational micro-lensing technique at the MtJohn Observatory in New Zealand. HST ofNASA recently produces several images ofgravitational lensed objects. Therefore find-ing enough gravitational lenses to constrainthe properties of dark matter structures re-quires a powerful telescope with a huge fieldof view like LSST. hysics Education dateline The power spectrum of the CMB shows usthe strength of photon-matter oscillations atdifferent parts of sky. The Far-Infrared Abso-lute Spectrophotometer (FIRAS) instrumenthas measured the spectrum of the cosmicbackground radiation, making it the mostprecisely measured black body spectrum innature. The Cosmic Background Explorer(COBE) was launched in 1989 in search oftemperature anisotropies; frequency powerspectrum; solar system and galactic dustforegrounds. The WMAP in 2010 was thefirst instrument to measure the CMB powerspectrum through the first peak of oscilla-tions, and showed that the existence of darkmatter is favoured. Comparison of such cal-culations with the observations of CMB Ra-diation by Plank mission team in 2013 haveshown that the total mass energy of theknown Universe contains 4 .
9% ordinary mat-ter, 26 .
8% dark matter and 68 .
3% dark en-ergy. Thus dark Universe constitutes 95 . The observational evidences from X- raystudies also supports the existence of darkmatter. The basic technique is to estimatethe temperature and density of the gas fromthe energy and flux of the X-rays using X-ray telescopes, which would further enablethe mass of the galactic cluster to be de-rived. The measurements of hot gas pressurein galactic clusters by X-ray telescopes, suchas CHANDRA X-ray observatory by NASA,have shown that the amount of superheated gas is not enough to account for the discrep-ancies in mass and that the visible matter ap-proximately constitutes only 12 −
15% of themass of the cluster. Otherwise, there won’tbe sufficient gravity in the cluster to preventthe hot gas from escaping [6].Recently in 2014, data came from the Euro-pean Space Agency’s (ESA’s) XMM-Newtonspacecraft, which was analysed by an inter-national team of researchers. After scouringthrough thousands of signals, they spotted aweird spike in X-ray emissions coming fromtwo different spots in the Universe: the An-dromeda galaxy and the Perseus galaxy clus-ter. The signal doesn’t correspond to anyknown particle or atom, and is unlikely tobe the result of a measurement or instrumenterror hence it could have been produced bya dark matter particle. The signal’s distribu-tion within the galaxy corresponds exactly towhat we expects with dark matter i.e. con-centrated and intense in the centre of objectsand weaker and diffuse on the edges. Scien-tists believe that there is a possibility that itcould come from dark matter candidate i.e.possibly the hypothetical heavy sterile neu-trinos; as it is believed the decay of theseparticles could produce X-rays [7]. hysics Education dateline non-luminous matter in which most of themass is attributed to baryons, most proba-bly neutrons and protons. Candidates forbaryonic dark matter include non-luminousgas, Massive Astrophysical Compact HaloObjects (MACHOs). These MACHOs mayinclude condensed objects such as black holes,neutron stars, white dwarf, very faint stars,or non-luminous objects like planets andbrown dwarfs. Baryonic dark matter can-not be detected by its emitted radiation be-cause these objects have very low luminosity,but the presence of these objects can be in-ferred from their gravitational effects on vis-ible matter [6].The nucleosynthesis of the elements andobservations of the Cosmic Microwave Back-ground Radiations (CMBR) puts constraintson the density of baryonic matter. No morethan 15% of the matter in the Universe canbe baryonic but most of dark matter stuffis non-baryonic. Non-baryonic dark matter(NBDM) is non-luminous matter made fromnon-baryonic stuff (other than protons, neu-trons etc.). Recent measurements of the mat-ter density Ω m and the energy density Ω comes from three types of observations: 1)supernova measurements of the recent expan-sion history of the Universe; 2) cosmic mi-crowave background measurements of the de-gree of spatial flatness, and 3) measurementsof the amount of matter in galaxy structuresobtained through big galaxy redshift surveysagree with each other in a region around thebest current values of the matter and energydensities Ω m (cid:39) .
27 and Ω (cid:39) .
73. WhereΩ is the energy density of Universe defined by Ω = ρρ c , (4)where ρ c is the critical density (averagedensity of Universe to halt its expansion)of the Universe and Ω represents presentenergy density of Universe. Measurementsof the baryon density in the Universe usingCMBR spectrum and primordial nucleosyn-thesis (i.e. BBN) constrain the baryon den-sity Ω b to a value less than 0.05. The dif-ference Ω m − Ω b (cid:39) .
22 must be in form ofnon-baryonic dark matter [8]. The value oftotal matter densityΩ m h = 0 . +0 . − . , (5)out of which the baryonic matter isΩ b h = 0 . +0 . − . , (6)in the form of neutrinosΩ ν h < . , (7)and the matter in the form of Cold DarkMatter (CDM) isΩ CDM h = 0 . +0 . − . . (8)The results of BBN that tell that Ω B ∼ .
01 and therefore if Ω total is truly unity,then the bulk of the mass of the Universemust be in the form of some sort of non-baryonic matter. From baryon to photon ra-tio i.e. η = η B /η γ , one can find the range for η as given by [20]4 . × − ≤ η ≤ . × − . hysics Education dateline We can find relative baryon density Ω B as0 . ≤ Ω B h ≤ . . (10)This shows that Universe is not closed bybaryonic matter and this gives the indicationof existence of dark matter. From the analy-sis of the existing data follows thatΩ DM (cid:39) . . (11)The non-baryonic dark matter is classifiedin terms of the mass of the particle thatis assumed to make it up, and the typicalvelocity dispersion of those particles (sincemore massive particles move more slowly).There are three prominent hypotheses onnon-baryonic dark matter, called Hot DarkMatter (HDM), Warm Dark Matter (WDM),and Cold Dark Matter (CDM); some com-bination of these is also possible. CDM iscomposed of substantially massive particles( ∼ GeV ) expected to be moving with non-relativistic speeds. The leading candidatesfor CDM called WIMPs (Weakly Interact-ing Massive Particles). WIMPs could includelarge number of exotic particles such as neu-tralinos, axions, photinos etc. These parti-cles forms dark matter, because they have toomuch mass to move at high speeds and thatthey are the best candidates for dark mat-ter. As WIMPs can interact through grav-itational and weak forces only, they are ex-tremely difficult to detect. There are severalexperiments setup for detection of WIMPssuch as SuperCDMS, NASA’s Fermi Gamma-Ray Space telescope, Large Hydron Collider(LHC) at Geneva etc... Experimental efforts to detect WIMPs include the search for prod-ucts of WIMP annihilation, including gammarays, neutrinos and cosmic rays in nearbygalaxies and galaxy clusters; direct detectionexperiments designed to measure the collisionof WIMPs with nuclei in the laboratory, aswell as attempts to directly produce WIMPsin colliders, such as the LHC. However all theefforts in this direction has been fruitless sofar.The HDM consists of particles to be mov-ing nearly at the speed of light, when thepre-galactic clumps began to form. HDM in-cludes massive ( ∼ eV ) neutrinos. The neutri-nos are the only hot dark matter candidateas they are light enough to move with thespeed of light. The Universe is full of neu-trinos left over from just after the Big-Bang,when matter and anti-matter were formed.There are huge amount of neutrinos, thatif they have just a tiny mass, then theycan significantly account for the dark mat-ter. The dark matter that has properties in-termediate between those of hot dark matterand cold dark matter named as Warm DarkMatter (WDM). WDM is composed of sub-relativistic particles having masses ( ∼ keV hysics Education dateline tion of structure in the Universe i.e. smallscale structures led to the formation of largescale structures. On the other hand, theHDM results in top-down formation scenarioi.e. first super-cluster formed and then galax-ies and then the formation of small structuretakes place. However, WDM has intermedi-ate role in large scale structure formation. Neutrinos are most abundant particles in theUniverse. They are electrically neutral andhave tiny mass. Out of four interactions innature neutrinos interact only via the weakinteraction and feebly via gravitational force.They rarely interact with any material, whichmakes experimental detection of these parti-cles extremely challenging. There are threetypes of neutrinos so far detected, which aredenoted as electronic ( ν e ), muonic ( ν µ ), andtauonic ( ν τ ) flavour eigenstates. In fact, inthe Standard Model of particle physics, neu-trinos are massless. However, in the late 90’sand beginning of 21 st century, physicists ob-served neutrino oscillation, a quantum me-chanical effect which would not occur unlessneutrinos have mass. The theory of neutrinooscillation describes the flavor eigenstates asthe mixing or linear superposition of masseigenstates ν , ν , ν . For two flavour casethe mixing is shown as (cid:18) ν e ν µ (cid:19) = (cid:18) cos θ sin θ − sinθ cos θ (cid:19) (cid:18) ν ν (cid:19) , (12)where θ is a mixing angle. From the ob-servation of the neutrino oscillations phe- nomenon, it is confirmed that neutrinos havemass. The nature of neutrinos is not yet un-derstood i.e. whether they are Dirac or Ma-jorana particles. In case of Dirac nature neu-trino and antineutrino are different, while inthe Majorana nature they are the same par-ticle. Despite the tininess, the neutrino masshas far-reaching implications in astrophysicsand cosmology.Neutrinos are considered to be the con-stituent of dark matter via thermal mecha-nism. As discussed above the hot dark matteris the matter that was relativistic until justbefore the epoch of galaxy formation, neutri-nos of very low mass are strongest candidatesfor hot dark matter. It is believed that neu-trinos were in thermal equilibrium with thehot plasma which filled the early Universe.As the Universe expanded and cooled, therates of weak interaction processes decreasesand neutrino decoupled when these rates be-came smaller than the Hubble expansion rate.Since for the three known light neutrinos withmasses smaller than 1 eV , the decoupling oc-curred when they were relativistic called hotrelics. As their interaction of cross sectionwith matter is very small therefore, the di-rect detection of these relativistic neutrinosis an extremely difficult task. In early Uni-verse, when 1 M eV ≤ T γ ≤ M eV hysics Education dateline trino is given by[13]Γ = n < σv >, (13)where n is the number density of targetparticles, σ is the cross-section and v is theneutrino velocity. The bracket denote thethermal averaging. For weak interaction pro-cesses < σv > = G F T γ , (14)where the temperature ( T γ ) gives the orderof magnitude of the energies of the relativisticparticles participating in the reactions. Asthe number density of relativistic particles isgiven as n ∼ T γ , the interaction rate for eachneutrino became Γ ∼ G F T γ . (15)So we can say that interaction rate de-creases rapidly with the decrease of the tem-perature due to expansion of the Universeand we obtain the decoupling temperature forneutrinos T νγ ∼ M eV .If the active neutrinos have a non-zeromass, as indicated by several neutrino oscil-lation experiments, the sterile neutrinos willtake part in the neutrino oscillations. Thesterile neutrinos are ’sterile’ as they practi-cally inactive, and they don’t interact via anyother interactions with active neutrino exceptby mixing [21]. This allows a possibility fora radiative decay under emission of an X-rayphoton with energy of half the sterile neu-trino mass. However, it needs much moreconfirmation before one accepts this as theexplanation. The sterile neutrino was originally pro-posed as a dark matter candidate by Dodel-son and Widrow in 1993 to solve the discrep-ancies between the CDM predicted structureformation and observations [20]. Since neu-trinos were relativistic at the time of decou-pling, the number density of relic neutrinosis given by the relativistic expression inde-pendent from the values of their masses. Inother words, light neutrinos are hot relics andcontribute to the hot dark matter in the Uni-verse. Sterile neutrinos have been invoked togenerate masses for light neutrinos; as suchthe mix with light neutrinos and hence canbe produced via oscillations [20]. With thismechanism, their relic density is estimated tobe Ω N ≈ (cid:18) sin θ × − (cid:19) (cid:18) M N keV (cid:19) . . (16)Here, θ is the mixing angle between thesterile neutrinos N with mass M N and theactive neutrinos. It has been seen that a vi-able sterile neutrino to be the dark mattercandidate requires a mass of keV hysics Education dateline [13] Ω ν h = (cid:80) i m i . eV . (17)Thus, the neutrino energy density is pro-portional to the sum of neutrino masses. Thisvalue is relevant for the present energy bal-ance if there are neutrinos with masses of theorder of 1 eV or more. Before the neutrino de-coupling around T γ (cid:39) M eV , the weak pro-cesses were in equilibrium.Ω >
1, implies a closed Universe, whichmeans that at some time the gravitation at-traction will stop the expansion and Universewill collapse again. An Ω <
1, means a Uni-verse which expands forever. However Ω = 1means a flat Universe. At present time, Ωis changing on time scale of seconds. Sinceour existence is not compatible with the Uni-verse which is either closed or continuouslyexpanding, the only long term value that Ωis close to unity. Although the detailed phys-ical mechanism for driving the expansion isnot well determined and differs in differentgrand unified theories.The phenomenon of sudden and fast ex-pansion of Universe caused by a scalar fieldpresent in the nascent stage is known as ’in-flation’. Inflation provides a possible mecha-nism to set the initial conditions. From theinflation paradigm, it is the argument thatthe only long lived natural value for Ω is unityand that inflation provided the early Universewith the mechanism to achieve that value andthereby solve some of the main problems ofstandard model of cosmology; e.g. the flat-ness and smoothness problems.The WMAP-7 data provides a quite strin-gent constraint on the sum of neutrino masses of (cid:80) m ν < . eV at 95% c.l. [10], which ismore constrained than ≈ . eV , that is thefirst releases [11]. However, the most recentand sophisticated analysis of Lyman-a datagives an upper bound of 0.9 eV for the sum ofneutrino masses. In summary, at present thebound on the sum of neutrino masses can bein the range between 0.3 and more than 2 eV,depending on the data and parameters used.The bound can be relaxed somewhat whenmore parameters, such as sterile neutrinos( ν s ) are included. In the most conservativecase the bound is above 2.5 eV if only CMBdata is used. When CMB data is combinedwith LSS data in the linear or almost linearregime, combined with a prior on the Hub-ble parameter the upper bound is robustlybelow 1 eV. This is true even for extendedmodels. Here it should perhaps also be notedthat the bound on neutrino mass from cos-mic structure formation applies to any other,hypothetical particle species which decoupleswhile still relativistic. This could for exam-ple be low mass sterile neutrinos. It couldalso be relatively high mass axions which de-couple after the QCD phase transition.Neutrinos have a kinematical advantagesover the dark matter candidates is that theycluster on large scales, where the dark matteris needed to hold the large clusters of galaxies.In HDM, since they decoupled at a temper-ature of the order of 1 M eV hysics Education dateline non-relativistic at some red-shift Z nr . Thus,only the HDM perturbations with wavelengthlarger than the horizon distance at Z nr sur-vive and can take part in the generation ofstructure in the Universe. Since the horizondistance at Z nr is typically much larger thanthe volume corresponding to the galactic sizemasses, so in a Universe dominated by HDM,the formation of structures must proceed ac-cording to top-down mechanism. Howeverthe observed statistical properties favoursbottom-up mechanism i.e. small structuresleading to the formation of large scale struc-tures. Hence the HDM contribute to the for-mation of small scale structures while CDMis responsible for binding of large scale struc-tures [13].The standard model does not predict anymasses for the active neutrinos, but as statedabove the masses are required by the ex-perimentally verified neutrino oscillations.A simple way to incorporate the neutrinomasses is to extend the model with the right-handed neutrinos just as done for the other el-ementary particles of SM. It is possible to addan arbitrary number of sterile neutrinos, butat least three sterile neutrinos are needed toexplain the neutrino oscillations, the baryonasymmetry, and the dark matter [14]. Thesuccessful ’three sterile neutrinos’ extensionof the standard model is called the (Neu-trino Minimal Standard Model)( ν MSM). It isre-normalisable and in agreement with mostparticle physics experiments [15]. The Big-Bang production of He increases with η .Thus upper limit to He abundance and alower limit to baryon density lead to an upperlimit to number of neutrino species N ν (i.e. so called BBN bound). The lower limit tobaryon density is based on the Big-Bang pro-duction of deuterium H , which rises rapidlywith decreasing baryon density. Since all theneutrons end up in forming He , which is themost tightly bound stable light nucleus, themass fraction of He is denoted as Y p , and isgiven by [13] Y p (cid:39) (cid:18) n n n n + n p (cid:19) (cid:39) . . (18)As per recent estimates of Y p with con-servative assumptions - for He chemi-cal evolution and Y p = 0 . N ν > . < N ν < .
48 [BBN](68%CL); 3 . < N ν < .
59 [WMAP5+SDSS-DR7+Ho ] (95% C.L.); 3 . < N ν < . . 66 [WMAP3](68% CL).Using recombination-era observablesincluding the CMB, the shift parame-ter RCMB and the sound horizon fromBaryon Acoustic Oscillations (BAO)severely constrain the sterile neutrinosin 2 θ < . m s /eV ) − . hysics Education dateline data and direct experimental searches forsterile neutrinos.[18] Electron neutrino-sterileneutrino mixing bound [19] from joint fitsof solar, KamLAND, Daya-Bay and Renoexperiments is sin 2 θ es < . . and the analy-sis of cosmological data in terms of Λ CDM constrains the mass square difference withone sterile family ∆ m < . eV . hysics Education dateline replace the usual CDM component. But dueto their large thermal velocity (smaller thanthat of active neutrinos), they would behaveas WDM and erase small-scale cosmologicalstructures. At present the neutrino physicsand neutrino astrophysics and cosmology areat the cross roads. On the one hand, it is im-possible to deny that neutrinos oscillate andthus presumably have small masses, and onthe other unless a sterile neutrino truly ex-ists, there is a sense that neutrino masses aretoo small to be of very much cosmological in-terests.In the galaxy formation scenario, galax-ies can only form by the collapse of super-clusters. The detailed study shows that thecollapse of super-clusters only happens verylate and may be in contradiction with the ex-istence of quasars of large red shift. Althoughthe evidences for dark matter is wide anddeep and existence of dark matter is basedon the assumption that the laws of motionand gravity as formulated by Newton and ex-tended by Einstein apply. On the other handthe modification in the theory of gravity canexplain the effects attributed to dark mat-ter and some scientists have proposed MOND(Modified Newtonian Dynamics). Accordingto this theory at very low acceleration, corre-sponding to large distances, the usual law ofgravitation is modified. Although MOND hashad some success in explaining observationsof galaxies, but failed to explain the obser-vation of Bullet Clusters. So we need moreexperimental evidences to give a conclusivetheory of dark matter. Acknowledgments We thank Debasish Majumdar, SINP, for giv-ing useful inputs. The Inter-University Cen-tre for Astronomy & Astrophysics (IUCAA),Pune is also acknowledged for providing re-search facilities during the completion of thiswork. References [1] Massey, R. et al., Dark mattermaps reveal cosmic scaffolding,doi:10.1038/nature05497, 7 January2007 as the related references.[2] E. Copeland, Dark Matter in the Uni-verse Dark Matter in Spiral Galax-ies , Sc. Am. 248(6), 1983.[5] A.C. Melissinos, Lecture Notes on Par-ticle Astrophysics, Physics 593- Spring1995.[6] S. Sharma, Bulletin of the Indian Asso-ciation Of Physics Teachers , 6(9), 2014.[7] A. Boyarsky, O. Ruchayskiy, D.Iakubovskyi and J. Franse, UnidentifiedLine in X-Ray Spectra of the AndromedaGalaxy and Perseus Galaxy Cluster hysics Education dateline [8] P. Gondolo, Introduction to Non-Baryonic Dark Matter , Lecture deliv-ered at the NATO Advanced Study In-stitute, France [astro-ph/0403064].[9] S. R. Sorensen, Sterile neutrinos as adark matter candidate , Master Thesis inPhysics, Niels Bohr Institute, Dark Cos-mology Centre, August 25, 2006.[10] E. Komatsu et al., Seven-Year WilkinsonMicrowave Anisotropy Probe (WMAP)Observations: Cosmological Interpre-tation , WMAP Collaboration, Astro-phys.J.Suppl. 192 18 (2011).[11] K. Ichikawa, M. Fukugita and M.Kawasaki, Phys. Rev. D 71, 043001(2005).[12] S. Dodelson and L. M. Widrow, Sterile-neutrinos as dark matter , Phys. Rev.Lett. 72 (1994) 17?20.[13] C. Giunti, C. W. Kim, Fundamental ofNeutrino Physics and Astrophysics , Ox-ford University Press, New York, 2007.[14] T. Asaka and M. Shaposhnikov, , Phys.Lett. B 620, 17, 2005.[15] T. Araki and Y. F. Li, Q FlavourSymetry Model for the Extension of theMSM by the three Right Handed Ster-ile Neutrinos , Phys. Rev. D85, 065016,2012.[16] P. C. de Holanda and A. Yu. Smirnov,hep-ph/1012.5627 [references containedtherein]. [17] A. C. Vincent, E. Fernandez Martinez,P. Hernandez, M. Lattanzi, O. Mena,JCAP 04 (2015)006.[18] O. Ruchayskiy, A. Ivashko, JHEP 1206(2012) 100.[19] A. Yu. Samirnov, Nucl. Phys. Proc.Suppl. 235, 431 (2013) [references con-tained therein].[20] S. Bilenky, Introduction to the Physics ofMassive and Mixed Neutrinos , Springer,Lecture Notes in Physics, 817, 2010.[21] Signe Riemer-Srensen, Sterile neutrinosas a dark matter candidate , Master The-sis in Physics Niels Bohr Institute, 2006.[22] C. J. Copi, D. N. Schramm, and M. S.Turner, Big-bang Nucleosynthesis limitto the number of neutrino species , Phys.Rev. D 55, 3389, 1997.[23] A. Aguilar-Arevalo, et al. , (LSND Col-laboration), Evidence for neutrino os-cillations from the observation of anti-neutrino(electron) appearance in a anti-neutrino(muon) beam , Phys.Rev. D 64,112007, 2001.[24] A. Aguilar-Arevalo, et al. , (MiniBooNECollaboration), Phys, Rev, Lett. 102,101802, 2009.[25] A. Aguilar-Arevalo, et al. , (MiniBooNECollaboration), Phys. Rev. Lett. 110,161801, 2013.[26] G. Mention et al. hysics Education dateline [27] T. Mueller et al. , Phys. Rev. C 83,054615, 2011.[28] D. Frekers et al. , Phys. Lett. B 706, 134,2011.[29] S. Antusch et al. , Unitarity of the Lep-tonic Mixing Matrix , JHEP 0610, 084,2006.[30] D. O. Caldwell, Neutrino Dark Matter ,University of California, Santa Barbara,CA 93106-9530, USA, hep-ph/9902219.[31] G. G. Raffelt, Neutrino Astrophysics AtThe cross roads , Proc. of Summer Schoolin High Energy Physics & Cosmologyat ICTP Italy, World Sc., 1998 [ hep-ph/9902271].[32] K. Zuber,