Dark Matter, Mass Scales Sequence, and Superstructure in the Universe (with extension and summary) Wuliang Huang Institute of High Energy Physics, Chinese Academy of Sciences, P.O.Box 918(3), Beijing 100049, China Xiaodong Huang Department of Mathematics, University of California, Los Angeles Los Angeles, CA 90095, U.S.A. Abstract The original intention of the first version of this paper is to search for the mass rang of dark matter particles (fermions or bosons) md according to the material state equations in 1 the evolved universe. It shows the mass rang of md is around 10 eV , i.e. into H- decoupling area. The dark matter particles with low (light) mass are related to the superstructure and belong to a mass scale sequence in the universe. The cosmic structure is not only from primary perturbation of early universe but also from perturbation and Jeans density wave of dark matter in the superstructure. The environment inside superstructure (SS) speed up the formation of sub-structure in SS by H-decoupling period. If dark matter is dominated by bosons, the cosmology principle is needed; if dark matter is dominated by fermions, it tends to spherical universe (finite universe). The second section (extension section) of this paper describes the extension of the mass scales sequence (mass tree) and describes new particles (u -particle, Planck particle, A -particle, -particle, graviton, -particle, heavy electron…). This can be used to explore the state of matter with super-high density, inflation, lightest black hole (LBH), BSM, CGB etc. in the early universe. Measuring the rate of change of c and at the present time is one way to check whether the cosmological constant/dark energy exists or not. The third section of this paper is a summary. From mass tree, the evolution of the universe is described by three stages: chaos, inflation and expansion. The first two stages have c mutations and the inflation appears as a step by step fission process of black holes. The dark matter particles with low mass ( and ) are described in a dual/two-fold SM with new symmetry and new interaction, and -particle is like inert neutrino but has baryon number (L-B conservation). We emphasize how to search for -particle, how to research critical energy, critical density cr , background particles, and spherical universe. cr relates to a type of pseudo-balance black holes/celestial bodies. Minimum black hole radius rmin rp means we live in a sphere universe, which belong to a big universe, mainly characterized by proton. It appears in a new manner for the super-high energy physics, which may determine the applicable region for the modern physics including relativity. PACS numbers: 95.35. +d, 98.65.D, 98.80. -K Keywords: large number, mass scales sequence (mass tree), superstructure, dark matter, critical energy, critical density, cosmological constant, lightest black hole (LBH), BSM, inflation, background particles, spherical universe To current knowledge, the stable elementary particles existing in nature are nucleon n (mass mn ), electron e , photon and neutrino ( can be put into the category of dark matter). Dark matter particles d (mass md ) could be fermions f with mass m f or bosons b with mass mb . Because and make only a small contribution to the total mass of the universe at the present time, we are confronted with a multi-component ( n d ) universe, in which the typical mass scal e is the solar mass M . On the other hand, from the fundamental physical constants (except electric charge) the speed of light c , the gravitation constant G and the Planck constant , a mass scale c (Planck mass): m ~ ~ 1019GeV can be deduced. First, we discuss the pl G internal relations of mpl, , md , and M. When a star collapses into a neutron star, it can be simplified as a degenerate system composed of neutral nucleons (fermions). Inside the neutron star, the boundary momentum of fermions comes to the maximum value mnc. At this time the total number of nucleons in the star with a gVp3 volume of V is N o [1], where g 2 and p = m c. The neutron star mass 6 2 3 o n is M Nmn, and the minimum mass of a black hole (BH) collapsed from a GM star is M ~ M. Since the classical black hole radius (CBHR) is r ~ star star star 2 c and the nucleon radius is rn ~ , mnc 3 mpl 0 Mstar ~ 2 ~ 10 M (1) mn (** annotation at April, 2020: Eq(1) can be expressed for degenerate celestial bodies 3 m pl as M n ~ 2 , for n=0,1,2,… and used to next sections) mn This is the scale of the free stream scale (FSS) of nucleons at the early era of M m the universe. From Eq (1), star ~ ( pl )3 , and mn mn mpl c ~ 2 A (2) mn Gmn This is the large number used in this paper, A ~ 1019, so M 3 r star ~ A , star ~ A (3) mn rn 1 G Gmpl From c,G, , a length scale (Planck length) rpl ~ 3 ~ 2 can be mn c c composed which also has the form of CBHR. Suppose a Planck particle has mass and radius rpl , then mn 1 rn ~ A , ~ A n d (4) mpl rpl 57 That is to say, a nucleon can contain ~ 10 Planck particles (string [2] 57 phenomenology) as a star can contain ~10 nucleons, but mn mpl. Why is ? Wi th the aid of the large number A , the nucleon radius can be ~ ~ Gmn G 2 38 expressed in a CBHR form, rn ~ 2 , where A ~ 10 . This is just the mpl c G right ratio of two nucleons’ strong interaction force to their gravitation interaction force. So, a nucleon is like a “strong BH” under a “strong ~ gravitation” interaction with a “strong gravitation constant”G , and confines “strong signals”. The main results discussed above can be summarized as follows: radius mass CBHR FSS Gm m Am r ~ pl pl n pl c 2 rn Arpl 3 2 3 GMstar mpl rstar A rpl Mstar A mn rstar ~ 2 2 ~ Mstar c mn From this table, one could infer that the next mass scale is 4 19 [3][8] MF A mn ~ 10 M , which is the superstructure scale in the universe . In a ( ) universe, the scale of MF may also have a connection with m3 another FSS, M ~ pl . From the equations and F 2 md 0.5 1 , we can obtain md ~ A mn ~ 10 eV . This means that the mass of non-baryoni c dark matter particles (NBDMP) is in an 101eV order of magnitude. Thus, there is a sequence of mass scales from micro-cosmos to 1.5 1 2 3 macro-cosmos: A mpl , A mpl, A mpl, and A mpl, corresponding to the mass scales of dark matter particles, nucleons, stars and superstructures respectively. 2 We shall now directly calculate the mass and state of NBDMP to check the above deduction about the mass of NBDMP and the sequence of mass scales. If the NBDMP is dominant in the universe at the present time, the direct calculationf can be simplified and done for a one-component universe composed of NBDMP only. First, we can suppose that the NBDMP are stable and weakly interacting massive fermions ( f ) and calculate the mass m f , as well as the state parameters (chemical potential f and temperature Tf ) of -particles using three equations. Under the standard cosmological model and the non-relativistic condition, the state equation is 5 3 2 2 gm f (kTf ) ZdZ 2 f 1 f h c (5) o exp(Z ) 1 22 2 3 where g is the variety number of -particles, f . The critical density of kTf 2 3H100 3 1 1 Ho the universe is c= (1 z) , H100 100km sec Mpc , h ( z is red 8G H100 shift). The evolutionary equation of temperature is [1] ~ kTf 0T 0 2 kT f 0T 0 T (1 z) = (6) f 2 2 m f c m f c where T 0 is the microwave background temperature, T 0 2.7 K . Tf 0 is the ~ T f 0 -particles temperature when m 0. T (1 z) 2 . Here, is a f f 0 kT 0 phenomenological parameter representing non-relativity, 1. The m c 2 f third equation is in relation to the superstructure of the universe mentioned above. In the last decade some reports related to the very large scale [3][7] structure (superstructure) in the universe were published . Specifically, reports about the periodic superstructure [6],[7] enlightened us. We think the formation of such structure may be related to the gravitation and the hydrodynamic effect in cosmic medium. Since the scale of the superstructure has been 1% - 10% of the present horizon, it is appropriate to adopt the sound velocity vs in cosmic medium: =0.01c 0.1c . 3/ 2 10 kTf Z dZ ZdZ vs / ~ 0.01c 0.1c (7) 0 0 9 m f exp(Z ) 1 exp(Z ) 1 3 From the three equations, we can obtain the results [8] : vs 0.01c 0.1c 1 2 m f 10 10 eV 5 4 f f 10 10 eV 3 2 Tf 10 10 K 1 2 10 10 m f g for z 0 and w 1 ~ 80. The above values of mean that the - 2 f h particles are in a degenerate state. Under the degenerate approximation, 2 3 T kT 4 2 c 3 2 f 0 we have m f 1 3 , f m f vs ; ~ .