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Ten Arguments Against the Proclaimed Amount of Dark Matter M ISSN 0202-2893, Gravitation and Cosmology, 2018, Vol. 24, No. 4, pp. 350–359. c Pleiades Publishing, Ltd., 2018. Ten Arguments Against the Proclaimed Amount of Dark Matter M. Krˇ ı´ zekˇ ∗ Institute of Mathematics, Czech Academy of Sciences, Zitnˇ a´ 25, 115 67 Prague 1, Czech Republic Received February 26, 2018; in final form, April 10, 2018 Abstract—According to the Standard cosmological model, our universe needs a significant amount of dark matter (DM), about six times that of the usual baryonic matter, besides an even larger amount of dark energy. But to date, both DM and dark energy have remained conceptually delusive, without concrete evidence based on direct physical measurements. In this survey paper, we present ten counterarguments showing that such a claimed amount of DM can be a result of vast overestimation and does not conform to reality. Some of those counterarguments can be convincingly verified even by simple hand calculations. DOI: 10.1134/S020228931804014X Dedicated to Professor Lawrence Somer on his 70th birthday The term DM (dunkle Materie in German) can be last 5 Gyr, see, e.g., [20, 24]. From Fig. 1 we may found in Zwicky’s 1933 paper [51, p. 125] and stands deduce that for astronomic matter that could not be accounted for the ratio of masses of dark matter from estimated luminous mass. It was also briefly mentioned in Oort’s earlier 1932 paper [38, p. 285], to baryonic matter ≈ 6:1. (1) again for mass that was not visible. None of those authors claimed that DM must be nonbaryonic other The aim of this paper is to collect arguments than just optically invisible. But in modern terms, showing that this ratio is exaggerated. We do not DM stands for the nonbaryonic DM, it does not in- claim that DM does not exist. However, we do claim clude baryonic matter that is not luminous. that the ratio on the left-hand side of (1) is smaller and can even be zero. The idea that the universe could have “zero radius” in the very distant past was first stated by A. Fried- mann in 1922 [13]. In 1927, Belgian cosmologist G.H. Lemaıˆtre came up with the claim that the ex- pansion speed of the universe is 625 km/(s Mpc), see [32, p. 56]. Two years later, the expansion of the Universe was independently confirmed by E. Hubble. DarkDark In [16], he published a chart showing that the radial BaryonicBaryonic mattermatter component of velocity of a galaxy depends approxi- energyenergy mately linearly on its distance from us, and the expan- DarkDark sion speed is about 500 km/(s Mpc). Current mea- mattermatter suring technologies lead, however, to a much smaller value of approximately 70 km/(s Mpc), see [40]. DM should decelerate the expansion of the uni- verse. Nevertheless, according to the standard ΛCDM cosmological model (i.e., Λ-Cold Dark Mat- Fig. 1. According to the scientific results of the Planck satellite [40], our Universe is composed of about 68% ter), an accelerating expansion of the universe is of dark energy (DE), 27% of DM, and less than 5% observed due to dark energy. This proposition is of baryonic matter. However, these data were obtained based on the fact that the expansion function (scale from the ΛCDM cosmological model which is based on factor) seems to have been strictly convex over the excessive extrapolations (cf. Section 2). It is said that dark and baryonic matter should slow down the expansion ∗E-mail: [email protected] of the universe, while DE should cause its acceleration. 350 TEN ARGUMENTS AGAINST 351 Number of galaxies, bin size 200 km/s 30 25 20 15 10 5 0 0 5000 10000 15000 20000 Velocity, km/s Fig. 2. Histogram of radial velocities less than 25 000 km/s of galaxies projected to the Coma cluster region. Here we consider only those galaxies whose magnitude does not exceed 20. These data are available in [1, 6, 10]. Galaxies possessing blueshift are on the left. The dark line represents the Gaussian curve fitted to data that correspond to galaxies belonging to the Comma cluster. Other galaxies are not contained in this cluster since their velocities with respect to the cluster’s center of gravity are too large. They should not be used to calculate the virial mass (3), because they do not form a bound system. 1. ANALYSIS OF ZWICKY’S METHOD If the virial parameter is Q := T/|V | =0.5,then the virial mass M is given by (3). However, it seems In 1933 Fritz Zwicky predicted the existence of that Q>0.5 (i.e., the cluster dissolves), and then some hypothetic DM which holds together the Coma from (2) we get galaxy cluster A1656. Using the Virial Theorem 5Rv2 V +2T =0, (2) M< . 3G he estimated its mass M by the formula Considering a nonuniform mass distribution, the fac- 5/3 5Rv2 tor in (3) can be made smaller (see [23, pp. 112– M = , (3) 115] for details). Also, Sinclair Smith [47] assumes 3G that this factor is only 1/2 or 1 for the Virgo cluster. − 3 2 Taking into account the relativistic effects of high where V = 5 GM /R is the total potential energy of the cluster, T = 1 Mv2 is the kinetic energy, R is velocities, gravitational redshift, gravitational lensing 2 in a curved space, the decreasing Hubble parameter, the cluster radius, and v is the mean quadratic speed intergalactic baryonic matter, gravitational aberra- with respect to the center of gravity of the cluster. tion, etc., the proclaimed virial mass M and also the In [51], Zwicky stated that to explain the fast motion ratio (1) can be essentially reduced by means of actual of galaxies for which v>1000 km/s in the Coma data (see Fig. 2). These arguments are not accounted cluster, he had to assume the existence of a 400 times for in Zwicky’s method, see [21] for details. larger amount of nonluminous than luminous matter Finally note that the Coma cluster is located near to keep the cluster gravitationally bound together. the north Galactic pole. Therefore, its recession speed In [52], he reduced this ratio to 150. However, he from the Sun is practically equal to that of a Coma used very imprecise data and made many simplifying cluster galaxy from the Milky way, even though the assumptions. Thus, he was mistaken by an order orbital speed v = 230 km/s of the Sun about the when estimating the distance of the cluster, and by Galactic center is relatively high. The mean recession two orders when calculating the masses of galaxies speed can be established by Pogson’s equation, for from their luminosity, he replaced galaxies by point details see [23, p. 111]. masses, he used Newtonian classical mechanics in flat Euclidean space, he measured the recession ve- locities with an accuracy of ≈100 km/s, he assumed 2. EXCESSIVE COSMOLOGICAL that the Virial Theorem (2) holds absolutely exactly, EXTRAPOLATIONS etc. Therefore, the DM to baryonic matter mass ratio Each equation of mathematical physics has cer- later reduced to (1). tain ranges of the size of investigated objects where GRAVITATION AND COSMOLOGY Vol. 24 No. 4 2018 352 KRˇ I´ ZEKˇ ΩΛ the so-called mass density parameter is defined by 8πGρ(t) 1.4 Ω (t):= , (4) M 3H2(t) where ρ(t) is the mass density, H(t):=˙a/a is the 1.2 Hubble parameter, a = a(t) is the scale factor of the Universe, and the dot denotes a time derivative. The vacuum energy density is defined by 1.0 Λc2 SNeSNe Ω (t):= , (5) Λ 3H2(t) 0.8 where Λ is the cosmological constant and c the speed 0.7 of light in vacuum. 0.6 A tiny intersection of admissible sets of cosmolog- ical parameters determined by three different methods of Baryonic Acoustic Oscillations (BAO), Cosmic Microwave Background (CMB), and Supernovae 0.4 CMBC type Ia explosions (SNe) should demonstrate that M B the Universe consists of approximately 70% of dark BAOBAO energy and 30% of dark and baryonic matter, see 0.2 Fig. 3. However, these methods are not independent Flat since they are all based on the same Friedmann equa- tion, derived by questionable extrapolations, see [26]. In truth, it is more likely that the measured data 0.2 0.3 0.4 0.6 0.8 1.0 Ω sketched in Fig. 3 just indicate that the extrapolation M is wrong since it requires introduction of some exotic Fig. 3. Admissible values of the cosmological parameters DM and DE. Consequently, it seems that the real (4) and (5) obtained by three different methods: BAO, dynamics of the Universe cannot be described by the CMB, and SNe, intersect in a small region containing the simple Friedmann equation, which is an autonomous ≈ ≈ proposed parameters ΩM 0.3 and ΩΛ 0.7. However, 1 these methods are not independent, because they are all ordinary differential equation with time-independent based on the normalized Friedmann equation derived by coefficients (see [26, p. 274]). From such a simple questionable extrapolations. equation, far-reaching conclusions on the deep past and far future are made in [3, 40], . reality is modeled well and where its description fails, In the vicinity of our Galaxy, up to a distance of i.e., the modeling error essentially depends on the size 400 Mpc, we observe that the mean mass density is of these objects, see [25]. At present, the ΛCDM lower than elsewhere, see, e.g., [30, p. 172]. However, model, based on the Friedmann equation, is preferred.
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