Muraki, Y

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29th International Cosmic Ray Conference Pune (2005) 9, 227230Neutrino mass and the Void structure of our UniverseY. Muraki (a) Solar-Terrestrial Environment Laboratory, Nagoya University, Nagoya 464-8601, JapanPresenter: Y. Muraki (muraki@stelab.nagoya-u.ac.jp), jap-muraki-Y-abs1-he23-posterRecent neutrino oscillation experiments limit the range of the squared mass difference of two neutrino typeswith good accuracy. Combining the oscillation results with beta decay experimental result and the 2df result,the mass range of tau neutrino is constrained to be in the range 	. Using of this result, the authorcomes to the very interesting conclusion that if one kind of neutrino has a mass of	, the void structureof our universe can be naturally explained.1. IntroductionMuraki (1990) [1] discussed a relation between neutrino mass and dark matter of our Galaxy, noting that ifone kind of neutrino had a mass of about , the dark matter of our Galaxy could be explained naturally bythe neutrino mass. Since then, 15 years have passed and cosmic ray physicists have made great effort to limitthe neutrino mass in a narrow range based on neutrino oscillation experiments. The experiments were eitherperformed by using the long distance baseline between the Sun and the Earth or a short distance baseline in theatmosphere of the Earth [2, 3].By this method, the difference of squared masses between two kinds of neutrinos is obtained in the form: or . However by this method, the absolute mass of each neutrino type cannot bedetermined. Therefore we must use other data obtained by the beta decay experiment to determine the massof the electron neutrino. According to current result obtained by the beta decay experiment, the upper limit ofelectron neutrino mass is less than [4].A further upper limit on the neutrino mass has been obtained by using cosmological data. By combining dataobtained by WMAP (the microwave background fluctuation) and 2df (the measurement of the distribution ofgalaxies), the upper limit for the total mass of neutrinos is set at ﬀ  ﬂﬁﬃ [5]. This provides the currentupper limit on the absolute value of the neutrino mass. Taking account of these results, little freedom is nowleft on the range of the neutrino mass. So the hypothesis that the neutrino mass is the origin of the dark matterin our Galaxy must be abandoned. Therefore in this paper the author discusses another role of the neutrinomass in the universe. First we will fix the most plausible mass of neutrinos of each kind, i.e., for electronneutrino (   ), muon neutrino (  ) and tau neutrino (   ). Then we will propose a possible scenario of therole of neutrino mass in our universe.2. The neutrino mass and its role in our universeThe super Kamiokande experimental results show that the squared mass difference of neutrinos must be  "!$# and "!$# for %& and %respectively. On the other hand we knowfrom cosmological data that the total sum of neutrino mass. They must be less than "!$# . So the maxi-mum masses of neutrinos must be less than '  	(for  ﬂ , for  '		, and for   '	.Let us call this possibility case 1.In the other case, neutrinos should have a mass of at least )  (*. This conclusion results from the neutrinooscillation experiments [3]. Therefore in case 2, we can set the mass for each neutrino to be  ,+ *,228 Y. MurakiFigure 1. A pictorial presentation of the bubble void structure of our universe. On the surface of the bubble, matter galaxiesare formed, while inside one bubble, neutrinos do exist.+ and  ﬂ + . These masses are the lowest mass allowed for neutrinos. The mass of is not provided by the oscillation experiment itself, so I have assumed it by the analogy of the massdifference between charged leptons, -".0/ + 1.	.In case 1, a dramatic thing is expected from the fact that neutrinos have the mass. Our scenario is as follows:1. neutrinos have mass.2. neutrinos are Dirac particles and they have a spin !	.3. for Dirac particles, the degeneracy force must be considered.4. massive neutrinos are attracted by the gravitational force.5. however because of the degeneracy force, they will not collapse to form a super black hall.6. the Jeans mass of neutrinos grows and fluctuation of the baryonic matter will be erased.7. the fluctuation of the baryonic matter can grow only at the border between neutrino bubbles.8. the observed void structure of the universe [6] was formed by the neutrino degenerate force and growthof the density fluctuation at the border.According above scenario we can estimate the size of condensed neutrino clouds. The method is the same asdescribed in the paper of reference [1]. The radius of a neutron star can be obtained by the balance betweenthe degenerate force of neutrons and the gravitational force: 2$3 + 	465!07"8ﬂ4!ﬂ938;:<4!38;=:<?>@(A,where93 corresponds to a  Bsolar mass neutron star and h is Planck constant divided by	$C. As theNeutrino mass and the Void structure of our Universe 229Figure 2. The relation between the radius of the neutrino cloud and the neutrino mass. In case the neutrino mass is DE FHGJI ,the radius for the neutrino cloud is expected as KDLNMPO .same way, we can obtain the radius of a neutrino cloud: 2  + 	465!07"8ﬂ4!ﬂ98Q:Q4!8R=:<. Here9corresponds to the mass of neutrino cloud or the total mass of neutrinos involved in a void. The9 maybe expressed by4SBT!C28UVUW0X AYUX YUZ[UP\W0X @T]Y. By using those relations, we canobtain a radius of the neutrino cloud of 2  +  ^_UU\<:X AYX Y+X `bac#YU\J:X Y. Herewe must consider also the contribution to the gravitational mass from other neutrinos, and   . Thereforethe above equation is modified to 2 d+^eX `fag#YU\J:X Y. If we put the neutrino mass  	(in thisequation, we will get 2  as	0million light years, still twice as large as typical observed void structure [6](note	<:+!). The photo in Figure 1 represents the void structure of our universe described in1h^.3. Application of our idea to actual phenomena of the universeWe are able to resolve the “factor two difference” above, because we did not take into account the effect ofbaryonic matter and cold dark matter in the scenario i^. However in the universe, there is much moremass than is contained as neutrinos. According to the current analysis of the WMAP data [7], j?kmlJnonSpRq is	and j  is estimated to be *. That means the mass of (dark matter r hydrogen gas) is ^times heavierthan the mass of neutrinos. Therefore if we replace the mass of  by s^ , we obtain a new relation230 Y. Muraki2V+*X `bac#YU\<:X Y. The relation is presented in Figure 2. If we put the value of tau neutrino mass(	) into the above equation, the radius the neutrino cloud is obtained as	*t`bac#or^million lightyears. This radius coincides well with the observed diameter of the void structure, Bmillion light years[6]. Therefore if neutrinos have the masses as  	 ,		and  	(respectively, we can explain the voidstructure of our universe as resulting from the neutrino mass (case 1). This model is not so beautiful from thepoint of view of particle physics. We cannot account for the existence of the seesaw mechanism [8] nor explainthe existence of flavors in nature. Of course there remains the possibility that the neutrino masses could bedescribed by case 2. In the case 2, the neutrino cloud must have a typical diameter of	`bac#or0millionlight years. However it is not certain that we can define the concept of “the diameter of neutrino bubble” ofsuch a large distance in an expanding universe. Further considerations are necessary. Various ideas concerninghot dark matter have been discussed frequently in the past [9].4. AcknowledgmentsThe author acknowledges Prof. Paul Evenson for reading manuscript.References[1] Y. Muraki, Proceed. 21st ICRC (Adelaide), 10, 54 (1990).[2] Y. Suzuki, Proceed. 28th ICRC (Tsukuba), 8, 75 (2003).[3] Neutrino Physics and Astrophysics, edited by Suzuki and Totsuka, North Holland (1999).[4] Ch. Kraus et al., Eur. Phys. J. C, 40, 447 (2005).[5] M. Tegmark et al., Phys. Rev., D69, 103501 (2004).[6] See the web site of Harvard Smithsonian observatory;http://cfa-www.harvard.edu/ huchra/zcat/ and alsohttp://www.aao.gov.au/2df/press/modmag.html[7] See for example, Review of Particle properties, Phys. Lett. B, 592, 210-215 (2004) and references are in.[8] T. Yanagida, in Proceedings of the workshop on Unified Theory and Baryon number of the Universe(1979).M. Gell Mann, P. Ramond and R. Slansky, in Supergravity (1979).[9] S. Hayakawa, Progr. Theor. Phys., 33, 538 (1965).M. A. Markov, The neutrinos ( Russian edition was published in 1964, Nauka, Moscow).R. Coswik and J. McClelland, Astrophy. J., 180, 7 (1973).H. Sato and F. Takahara, Progr. Theor. Phys., 64, 2029 (1980).D. Shramm and G. Steigman, Astrophys. J., 243, 1 (1981).

Neutrino mass and the Void structure of our Universe

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