icarus2

Relations between radius of universe and dark energy density fig11. Relations between radius of universe and dark energy density * mass density of ordinary matter = 1 proton/5m3 * [math]n_-=n_+=n, m_-=(23.3/4.6)m_+=(5.06522)m_p[/math] * [math]\bar r_{ - + } = \frac{R}{{3.27273}}[/math] * If [math]\bar r_{ - + } = \frac{R}{{2.17879}}[/math] [math](U_T \approx 0)[/math], dark energy density has a 1/3 smaller than [math]\bar r_{ - + } = \frac{R}{{3.27273}}[/math]. In a WMAP, observed value [math]\Lambda = 2.14( \pm 0.13) \times 10^{ -3} eV [/math] Dark energy density : [math] \rho _{de} = 2.09 \times 10^{ - 47} [_{ - 0.465}^{ + 0.557} ]GeV^4 [/math] Ridius of the Universe : [math] R_{UNI} = 96.76[_{ - 11.44}^{ + 12.13} ]Gly = 85.32 \sim 108.89Gly [/math] ( If [math]\bar r_{ - + } = \frac{R}{{2.17879}}[/math], [math] R_{UNI} = 118.8[_{ - 14.0}^{ + 14.9} ]Gly = 104.8 \sim 133.7 Gly [/math]) ========= Hypothesis of Dark Matter and Dark Energy with Negative Mass : http://vixra.org/abs/0907.0015

Fig23. MACS J0025.4-1222 Cluster. We can see that ordinary matters(yellow line) are close to each other(center), and dark matters(red line) are on the far side. (http://arxiv.org/abs/0806.2320v2) ========== i)Positive mass, positive mass : attractive ii)Negative mass(dark matter), negative mass(dark matter) : repulsive iii)Massive positive mass(Galaxy and Galaxy Cluster), negative mass : attractive ==> Uniformly distributed negative mass receives attractive effect from massive positive mass(Galaxy and Galaxy cluster), so dark matter which has negative mass is clustered around galaxy because of attraction of galaxy. iv)Result : At least, from 3 characteristics above, we can predict that positive mass and positive mass are arranged on the close side, and negative mass(dark matter) and negative mass(dark matter) are arranged on the far side.

How can distinguish conves and concave gravitational lensing effect? Generally, it is possible to examine the existence of dark matter with the existence of additional mass with the effect of gravitational lensing. If negative mass is dark matter, so if we try to examine the effect of gravitational lensing, previously the gravity between positive mass is attraction, so it has the shape of convex lens to collect within the form, whereas the force between negative mass and positive mass is repulsion, so a set of massive negative mass can make the effect that distorts observation target in the form of concave lens. If existing measuring instrument recognizes the effect of gravitational lens with distorted aspect of galaxy or galaxy cluster, the effect of concave gravitational lensing owing to the existence of negative mass also plays a role of distorting galaxy or galaxy cluster, so it can be the basis of invisible dark matter. Additionally, in the distribution of dark matter suggested with previously measured effect of gravitational lens, dark matter may be created purely by positive mass, but also it can be created by the distribution of dark matter by negative mass. But in the hypothesis of dark matter with negative mass in this study, negative mass is distributed out of galaxy, not within galaxy. Therefore, the effect of concave gravitational lensing by negative mass out of galaxy will be presented to an observer on the earth in the same form as the effect of convex gravitational lensing which galaxy works. fig19.Concave Gravitational lensing effect. The left side is the Gravitational lensing effect that occurs when the galaxy is surrounded by negative mass and the right side is Gravitational lensing effect that occurs when positive mass exists alone No the effect of concave gravitational lensing by negative mass has been observed. However, we have never thought about negative mass itself, so we might not have thought about the concave gravitational lensing as well, and it might be difficult to classify the effect of concave gravitational lensing and the effect of convex gravitational lensing. For the situation presented on the left when observing the light on the earth which passed through galaxy surrounded with negative mass, this study suggested that there is invisible dark matter in galaxy, and owing to this gravity it can be happened owing to the effect of convex lens, it means, if there is any matter on the left and right side of galaxy that plays a role of concave lens, it is difficult to classify convex lens and its form. According to the explanation of the effect of concave gravitational lensing from the viewpoint of gravity, not geometrical optics, there is the effect of centripetal force by the distribution of negative mass out of galaxy with the effect of centripetal force in galaxy as described previously, so there is real mass of galaxy plus the gravity when filling the whole galaxy with positive mass that has the same density as that of negative mass in galaxy. Therefore, if the light from the exterior passes inside of galaxy or near galaxy, real gravity of galaxy plus gravity of dark matter(by negative mass) is added, and finally it will present much greater effect of gravitational lensing. If we consider the situation that we can observe purely the effect of concave gravitational lensing, that situation is just the same as the situation when there is single concave lens on the right in Figure above. First, an observer on the earth must observe it on Position B and C after moving by considerably great distance as compared with the size of galaxy, but the earth has never changed the position of observation from the target for distant observation. second, real observation on the earth is the single B or C situation in Figure on the right, and if an observer on the earth performed observation previously on C, generally an observer of C would describe the effect of gravitational lensing is generated because there is invisible dark matter on the right of black and white area(circle drawn with dotted line on the right). As observed the effect of concave gravitational lensing, this can be the evidence for the existence of negative mass. I had read below paper. Charles R. Keeton1(June 2002), [ A Catalog of Mass Models for Gravitational Lensing ] http://arxiv.org/abs/astro-ph/0102341v2 While composite models provide a great deal of freedom and complexity, they are not completely general. This limitation is eliminated in the elegant algorithm by Saha & Williams (1997; also Williams & Saha 2000) for finding non-parametric lens models. The approach is to introduce a set of mass pixels and construct a large linear programming problem for determining their masses. The problem is severely underconstrained, but by requiring positive-definite masses and imposing some smoothness criteria it is possible to find a wide but finite range of non-parametric models consistent with the data. A limitation of the Saha & Williams algorithm is that the constraint of a positive-definite surface density is weaker than the constraint of a positive 3-d mass density — or,better yet, a positive-definite quasi-equilibrium distribution function. In other words, while parametric models may provide too little freedom, the Saha & Williams non-parametric models provide too much. For example, their method does not determine whether models are consistent with stellar dynamics, and many of the models found by the method probably are not consistent. Maybe, Gravitational lensing method has not distinguish positive mass and negative mass. How can distinguish conves and concave gravitational lensing effect at the Earth? If some gravitational lensing method can distinguish it, please know to me. Paper and article!

Thanks michel~ II-2. Negative mass cannot form the structure greater than atom As examined the equation of motion for negative mass, it is marked in form of F= - ma (m>0), when attraction is applied together with nuclear force(when usually nuclear force is attraction, but has the form of repulsive core, and assuming nuclear force has the form of [math]\vec F=-Q®\hat r[/math], Q® is the positive function of distance r, thus nuclear force is in the form of attraction worked in the direction of -[math]\hat r [/math]. Here, for the force worked on negative mass –m, [math] \vec F=-m\vec a=-Q®\hat r [/math] [math] \vec a=\frac{{Q®}}{m}\hat r [/math] The term of acceleration is positive, so the effect of increasing distance r, namely repulsive effect appears. This means that negative mass cannot form the structure like atom(massive nucleon, baryon, particle consists of multi elementary particle), because nuclear force has not binding negative mass when it is applied to negative mass. Also, gravity has not binding negative mass(repulsive) Additionally, for the problem of mesons that mediates nuclear force or weak interaction, if there is no meson that delivers strong interaction or weak interaction, it is doubtful if strong interaction or weak interaction can be worked or not. For example, nucleon must have internal structure including meson or quark, but in case of negative mass, nuclear force is repulsive, so it cannot have the internal structure of nucleon from the beginning. That is, there is a great possibility that negative mass cannot include meson or quark which has negative mass in nucleus. The fact that it cannot make nucleon means that it is impossible to form massive mass structure like a star in addition to atomic structure. This provides proper explanation of the fact that negative mass is not seen as it has visible massive mass structure. Also generally it satisfies the nonbaryonic matters required for dark matter. If negative mass was born at the beginning of universe, there is higher possibility that it exists until now as a certain basic state born at the beginning of universe, and that it does not have strong interaction like nuclear force, weak interaction, and electromagnetic interaction(neutral or has not internal structure(positive mass elementary particle has a ±1/2, ±1/3, 2/3 charge)). This point is keeping with current characteristics required for dark matter. If negative mass and positive mass were born together at the beginning of universe, positive mass has attractive effect each other, so it forms star and galaxy structure now, but negative mass has repulsive effect each other and nuclear force cannot form nucleons by binding negative mass, so they cannot make massive mass structure like star or galaxy. If dark matter is negative mass, non-observation of dark matter star and galaxy can be explained. ======== Hypothesis of Dark Matter and Dark Energy with Negative Mass : http://vixra.org/abs/0907.0015 Merged post follows: Consecutive posts mergedV-6. Colliding with Bullet Cluster As shown in the recent observation of dark matter, dark matter seems not to interact with each other when colliding with galaxy clusters, and it can be predicted with essential characteristics of negative mass. Uniformly distributed negative mass receives attractive effect from massive positive mass, so dark matter which has negative mass is clustered around galaxy because of attraction of galaxy. If the type of force worked between negative mass when colliding with galaxy clusters is repulsive, and negative mass is distributed almost uniformly without forming massive mass structure, the shape of dark matter is not distorted or transformed even if dark matter(negative mass) and dark matter(negative mass) pass through similar area, that is, they will seem not to interact each other. Also there is repulsive effect between dark matters that are made up with negative mass, thus there will be almost no direct collision as well. Repulsive effect that is the nature between negative mass as described above provides the proper description that existing dark matters do not interact each other, although they interact gravitationally with positive mass. As the factor that breaks the uniform distribution of negative mass, First, negative mass receives the attractive effect from massive positive mass, thus for the distribution of negative mass near massive positive mass such as galaxy or galaxy cluster, the density of negative mass is higher as it is closer to galaxy or galaxy cluster, and is lower as it is farther. Second, If positive mass(like galaxy cluster) that has strong gravity or interstellar cloud that has positive mass pass through existing area that negative mass is distributed, negative mass can be disappeared when meeting positive mass or it can be drawn owing to attractive effect of massive positive mass at this moment, so there can be the area that negative mass, namely, dark matter is not uniformly distributed Fig20. Collision of Bullet Cluster. We can see that ordinary matters(red color) are close to each other, and dark matters(blue color) are on the far side. (http://arxiv.org/abs/astro-ph/0608407v1) Fig23. MACS J0025.4-1222 Cluster. We can see that ordinary matters(yellow line) are close to each other(center), and dark matters(red line) are on the far side. (http://arxiv.org/abs/0806.2320v2) ========== i)Positive mass, positive mass : attractive ii)Negative mass(dark matter), negative mass(dark matter) : repulsive iii)Massive positive mass, negative mass : attractive iv)Result : At least, from 3 characteristics above, we can predict that positive mass and positive mass are arranged on the close side, and negative mass(dark matter) and negative mass(dark matter) are arranged on the far side. Can we explain the phenomenon that dark matter is arranged on the far side and visible positive matter is arranged on the close side in Fig.20 with other dark matters? Negative mass shows the result matched with the phenomena, and it means that it is necessary to perform more strict simulation with negative mass. ======== Hypothesis of Dark Matter and Dark Energy with Negative Mass : http://vixra.org/abs/0907.0015

Strictly speaking, Your expression is wrong. [math] m_1 \vec a_1 = - G\frac{{m_1 m_2 }}{{r^2 }}\hat r [/math] It is a spherical coordinate expression. It is correct expression. [math] \vec a_1 = - G\frac{{m_2 }}{{r^2 }}\hat r [/math] G>0, m2>0, r>0. The direction of acceleration is in the direction of - r, so the distance between two objects are reduced gradually. It means that force is attraction. Strictly speaking, your expression is [math] \vec F_1 = + G\frac{{m_1 \times m_2 }}{{r^2 }}\hat a_x [/math] [math] \vec F_2 = - G\frac{{m_1 \times m_2 }}{{r^2 }}\hat a _x [/math] [math]\hat a_x [/math] is unit direction vector. So, [math] \vec F_1 = - \vec F_2 [/math] [math] |\vec F_1 | = |\vec F_2 | = G\frac{{m_1 \times m_2 }}{{r^2 }} [/math] [math]F_1 = F_2 = G\frac{{m_1 \times m_2 }}{{r^2 }}[/math] is only magnitude of force.

Thanks! Michel~ I appreciate to your opinion. I’m sorry. I can’t English well. So, my answer is short and insufficient. Proof 1) is not same to proof 2) [math] E_{de}=U_{de} = (n_ - \times n_ + )(\frac{{Gm_ - m_ + }}{{\bar r_{ - + } }}) -(80) [/math] Eq(80) can be applied at the whole time of universe. [math] U_{de} \approx - \frac{1}{2}U_s = \frac{3}{{10}}\frac{{GM^2 }}{R} -(91) [/math] But, Eq (91) can be applied only UT near to 0. Proof 1) has started from analysis for individual particle. "When the number of negative mass is n-, and the number of positive mass is n+ , total potential energy is given as follows." But, mean distance r-+ has not getting from equation (80) Therefore mean distance must be get from other method. Eq(81) = Eq(92) It is process for getting the mean distance. Negative mass originated from relativistic energy eq. [math] E^2 = p^2 c^2 + (m_0 c^2 )^2 [/math] [math] E = \pm \sqrt {p^2 c^2 + (m_0 c^2 )^2 } [/math] Therefore, [math] E = - \sqrt {p^2 c^2 + (m_0 c^2 )^2 } = - m_ - c^2 [/math] It is a solution also. However, In the modern physics and quantum mechanics, [Nature prefers stable state, and has the tendency to go to stable state. Additionally, this can be expressed in another way that nature prefers low energy state, and has the tendency to go to low energy state. Such an idea is frequently used as a logic which denies the existence of negative mass. That is, if there is negative mass and negative energy level, negative mass spontaneously emits energy to be stable, and goes to energy state of minus infinity, so finally it is confronted by catastrophe.] So, the solution of negative energy trashed away. And DIRAC applied the solution of negative energy to antiparticles. But, antiparticle's mass has a positive value. Finally, antiparticle is not negative mass particle. But, I fine out very important property of negative mass. It is that negative mass is stable at the maximum point, so the catastrophe to energy level of minus infinity never happens. Therefore, at this time, [math] E = - \sqrt {p^2 c^2 + (m_0 c^2 )^2 } = - m_ - c^2 [/math] Negative energy(mass) solution must be revived. My article has a many explains for negative mass.(20 Pages) I explained that properties of the negative mass. II-1-2)The law of motion of negative mass and positive mass. II-1-3)The law of motion of negative mass and negative mass. II-2. Negative mass cannot form the structure greater than atom. II-3. Negative mass is stable at the maximum point. II-4. The difference in mass when creating the pair of negative mass and positive mass. And I explained that collision of Bullet Cluster Among them, I will explain that the law of motion of negative mass and positive mass. Also, I will explain that collision of the Bullet Cluster. Again, I apologize for my English ability. ======== Hypothesis of Dark Matter and Dark Energy with Negative Mass : http://vixra.org/abs/0907.0015 Merged post follows: Consecutive posts merged II. Property of negative mass 1-1)The law of motion of positive mass and positive mass ---------- +m1 ------ +m2 Fig01. Positive mass +m1 and positive mass +m2 (initial velocity =0, m1 >0, m2 >0) [math] m_1 \vec a_1 = - G\frac{{m_1 m_2 }}{{r^2 }}\hat r [/math] [math] \vec a_1 = - G\frac{{m_2 }}{{r^2 }}\hat r [/math] [math] m_2 \vec a_2 = - G\frac{{m_1 m_2 }}{{r^2 }}\hat r [/math] [math] \vec a_2 = - G\frac{{m_1 }}{{r^2 }}\hat r [/math] Positive mass and positive mass : The force worked between positive mass is attraction, and two objects move toward the center of mass. The force is attraction, thus their potential energy has negative value. The direction of acceleration is in the direction of - r, so the distance between two objects are reduced gradually. Merged post follows: Consecutive posts merged1-2)The law of motion of negative mass and positive mass ---------- -m1 ------- +m2 fig02. Negative mass - m1 and positive mass +m2 (initial velocity =0, m1 >0, m_2 >0) [math] - m_1 \vec a_1 = - G\frac{{( - m_1 )(m_2) }}{{r^2 }}\hat r [/math] [math] \vec a_1 = - G\frac{{m_2 }}{{r^2 }}\hat r [/math] [math] + m_2 \vec a_2 = - G\frac{{( - m_1 )(m_2) }}{{r^2 }}\hat r [/math] [math] \vec a_2 = G\frac{{m_1 }}{{r^2 }}\hat r [/math] Negative mass and positive mass : Negative mass is accelerated in the direction of positive mass, and positive mass is accelerated in the direction to be far away from negative mass. The direction of acceleration a1 worked on negative mass – m1 is - r, so - m1 moves in the direction of reducing distance r, and the direction of acceleration a2 worked on positive mass +m2 is +r, so positive mass +m2 is accelerated in the direction that distance r increases, namely the direction of being far away from negative mass. If the absolute value of positive mass is bigger than that of negative mass, they will meet within finite time(attractive effect), and if the absolute value of positive mass is smaller than that of negative mass, the distance between them will be bigger, and they cannot meet(repulsive effect). The type of force is repulsion, so the potential energy has positive value. ==> Uniformly distributed negative mass receives attractive effect from massive positive mass(Galaxy and Galaxy cluster), so dark matter which has negative mass is clustered around galaxy because of attraction of galaxy. Merged post follows: Consecutive posts merged1-3)The law of motion of negative mass and negative mass --------- - m1 ------ - m2 fig03. Ngative mass - m1 and negative mass - m2 (initial velocity =0, m1>0, m2> 0) [math] - m_1 \vec a_1 = - G\frac{{( - m_1 )( - m_2 )}}{{r^2 }}\hat r [/math] [math] \vec a_1 = + G\frac{{m_2 }}{{r^2 }}\hat r [/math] [math] - m_2 \vec a_2 = - G\frac{{( - m_1 )( - m_2 )}}{{r^2 }}\hat r [/math] [math] \vec a_2 = + G\frac{{m_1 }}{{r^2 }}\hat r [/math] Negative mass and negative mass: Both two objects are accelerated in the direction of + r which extends distance r, so as time passes, the distance between them is greater than initially given condition, and the force between them is attraction, but the effect is repulsive. The force is attraction(-Gm1m2/r^2), thus the potential energy between them has negative value. If negative mass and positive mass were born together at the beginning of universe, positive mass has attractive effect each other, so it forms star and galaxy structure now, but negative mass has repulsive effect each other, so they cannot make massive mass structure like star or galaxy. If dark matter is negative mass, non-observation of dark matter star and galaxy can be explained. ========= Hypothesis of Dark Matter and Dark Energy with Negative Mass : http://vixra.org/abs/0907.0015

Thanks! michel123456! That’s Right! In my proof, Dark energy is gravitational potential energy has a positive value. Therefore it suggested that negative mass is existed! Assuming that negative mass and positive mass were born together at the beginning of universe(in energy and momentum conservation state), everything fits well. We studied the negative energy state at Modern physics and Quantum Mechanics Please read to the below explain. And then, please think about the means of that negative mass has a harmonic oscillation at the maximum point. ---------- II-3. Negative mass is stable at the maximum point! therefore the catastrophe to energy level of minus infinity never happens Nature prefers stable state, and has the tendency to go to stable state. Additionally, this can be expressed in another way that nature prefers low energy state, and has the tendency to go to low energy state. Such an idea is frequently used as a logic which denies the existence of negative mass. That is, if there is negative mass and negative energy level, negative mass spontaneously emits energy to be stable, and goes to energy state of minus infinity, so finally it is confronted by catastrophe. Is it right? In case of positive mass, stable state means low energy state, therefore it is not necessary to divide which one nature prefers among two states(stable state and low energy state). By the way, does stable state mean low energy state also in case of negative mass? We can get an answer, if we examine Harmonic oscillation. fig04 caption : When there is negative mass in potential which has a point of maximum value and a point of minimum value. We begin by considering the oscillatory motion of a particle that is constrained to move in one dimension. We assume that there exists a position of unstable equilibrium for the particle and we designate this point as the origin. Restoring force is in general some complicated function of the displacement and perhaps of the particle's velocity or even of some higher time derivative of the position coordinate. We consider here only case in which the restoring force F is a function only of the displacement F(x) can be expanded in a Taylor series, [math] F(x) = F(0) + \frac{x}{{1!}}F^{'} (0) + \frac{{x^2 }}{{2!}}F^{''} (0) + \frac{{x^3 }}{{3!}}F^{'''} (0) + \cdots [/math] [math] + \frac{{x^n }}{{n!}}F^{(n)} (0) + \cdots \\ [/math] Since the origin is defined to be the equilibrium point, F(0) must vanish, Then, if we confine our attention to displacements of the particle that are sufficiently small, we can neglect all terms involving [math]{x^2}[/math] and higher powers of x. We have, therefore, the approximate relation [math] F(x)=+kx [/math] The force is always the opposite directed toward the unstable equilibrium position(the origin), the derivative F'(0) is positive and therefore k is a positive constant. [math] - m\ddot x = + kx [/math] [math] \ddot x + \omega _0^2 x = 0 [/math] [math] (\omega _0^2 = \frac{k}{m}) [/math] This form of differential equation is the same as that of particle which has positive mass. But we have to notice that positive mass carries out harmonic oscillation on a point of minimum value, whereas negative mass carries out harmonic oscillation on a point of maximum value. Additionally, restoring force is +kx at this time. [math] \vec F = - \nabla U [/math] [math] U = - \frac{1}{2}kx^2 [/math] [math] {E_ -} = T + U = - \frac{1}{2}m\dot x^2 - \frac{1}{2}kx^2 \\ = - \frac{1}{2}m\omega _0^2 A^2 \\ [/math] In phase space [math] \frac{{x^2 }}{{(\frac{{ - 2E_ - }}{k})}} + \frac{{p^2 }}{{( - 2mE_ - )}} = 1 [/math] This equation is ellipses equation, because total energy [math]E_- < 0 [/math] As examined in the question of Harmonic oscillation, in case of positive mass, a point of minimum value which energy is the lowest is stable. However, in case of negative mass, stable equilibrium is a point of maximum value, not a point of minimum value. So negative mass is toward a point of maximum value to be stable, not a point of minimum value which energy is low. In the world of positive mass, ground state is a point that energy is low, but in case of negative mass, ground state is a point that energy is the highest. Accordingly, in the world of negative mass, energy level is filled from the highest to the lowest, and stable state means the highest energy state, so the catastrophe to energy level of minus infinity never happens even if negative mass spontaneously emits energy. ======== Hypothesis of Dark Matter and Dark Energy with Negative Mass : http://vixra.org/abs/0907.0015

Thanks! Airbrush! I'm sorry, I can't English well. So, My explain is short. Negative mass is not same to the antimatter. Antimatter has a value of positive mass. I explained property of the negative mass in chapter II. [ Abstract ] From the observance of the HSS team in 1998, they gained the mass density of the negative( ΩM = -0.38( ± 0.22)), using field equations which do not have the cosmological constant. The quantity of the mass couldn't be negative value in they thought, the value is trashed away. We have to know that not the field equation has disposed the value, but our thought disposed that value. In the world of positive mass, ground state is a point that energy is low, but in case of negative mass, ground state is a point that energy is the highest. Accordingly, in the world of negative mass, energy level is filled from the highest to the lowest, and stable state means the highest energy state, so the catastrophe to energy level of minus infinity never happens even if negative mass spontaneously emits energy. Assuming that negative mass exists, Newton's Law of motion was derived in between negative and positive masses and also between negative and negative masses. As a method for proving the existence of negative mass, an explanation on the revolution velocity of the galaxy through negative mass has been presented. In this process, the existence of spherical mass distribution was given; furthermore, explanation was done using this, to show observation results where dark matter effect through negative mass is proportional to distance r. If Ω_M is -0.38, universe's age is 14.225 Gyr. It is in the range estimated by other observations. Assuming that negative mass and positive mass were born together at the beginning of universe, it satisfies the various problems that previous dark matter and dark energy possess, such as, [ Dark matter ] - Centripetal force effects of galaxy and galaxy clusters from previous dark matters, - Mass effects that is proportional to the distance r, - Low interaction between dark matter when collision occurs between dark matter. [ Dark energy ] : Repulsive force needed for expansion, dark energy that has positive values, [ Fine tuning problem of mass density ] : The reason of that mass density close to the critical mass density. [ Cosmological Constant Problem ] - The reason of that dark energy seems to has a small and non-zero value. - Phase transition problem of dark energy [ Others ] - Collision of Bullet cluster, - Deceleration expansion and acceleration expansion of universe, - Age of the universe with negative mass density - Size of the universe [ Proof of that observed dark energy value ] : Dark energy observation value ([math]10^{-47}GeV^{4}[/math]) As a result, the necessity of observation focusing on exact computation and detection of negative mass is stated. ======== Hypothesis of Dark Matter and Dark Energy with Negative Mass : http://vixra.org/abs/0907.0015

Proof of that value of observed dark energy(10-47GeV4) I’m sorry, I can’t English well. Please, understand my insufficient explanation! The value of observed dark energy has been proved in accordance with theoretical computation. ρde = (0.134 ~ 3.34) X 10-47GeV4 : Theoretical computation ρobs = 10-47GeV4 : Observed value Please have a look the attached proof and inspect the findings. ============== *Potential energy between positive mass and positive mass has - value:[math]U = \frac{{ - G(m_ +) (m_ +) }}{r} = 1U_ - [/math] *Potential energy between negative mass and positive mass has + value:[math]U = \frac{{ - G( - m_ - )(m_ +) }}{r} = 1U_ + [/math] *Potential energy between negative mass and negative mass has - value:[math]U = \frac{{ - G( - m_ - )( - m_ - )}}{r} = 1U_ - [/math] When the number of negative mass is n- , and the number of positive mass is n+ , total potential energy is given as follows. [math] U_T = \sum\limits_{i,j}^{i = n_ - ,j = n_ + } {(\frac{{Gm_{ - i} m_{ + j} }}{{r_{ - + ij} }})} [/math] [math] +\sum\limits_{i,j,i > j}^{i,j = n_ - } {(\frac{{ - Gm_{ - i} m_{ - j} }}{{r_{ - - ij} }})} + \sum\limits_{i,j,i > j}^{i,j = n_ + } {(\frac{{ - Gm_{ + i} m_{ + j} }}{{r_{ + + ij} }})}---(78) [/math] [math] U_T = (n_ - \times n_ + )(\frac{{Gm_ - m_ + }}{{\bar r_{ - + } }}) [/math] [math] + (\frac{{n_ - (n_ - - 1)}}{2}(\frac{{ - Gm_ - m_ - }}{{\bar r_{ - - } }}) + \frac{{n_ + (n_ + - 1)}}{2}(\frac{{ - Gm_ + m_ + }}{{\bar r_{ + + } }})) ---(79) [/math] V-2-1)Proof from the definition equation of dark energy [ Proof Start! ] In equation (79), Dark energy is corresponding to that plus potential term in total potential energy. [math] E_{de}=U_{de} = (n_ - \times n_ + )(\frac{{Gm_ - m_ + }}{{\bar r_{ - + } }}) ---(80) [/math] If radius of the universe is 60Gyr, ordinary matter density is about proton 1ea/5m3. So, m+ = mp, [math] m_ - = km_ + \simeq (\frac{{23.3}}{{4.6}})m_ + = (5.06522)m_p [/math] (because that dark matter has about (23.3/4.6) times ordinary matter in WMAP) From equation (95) [math] \bar r_{ - + } = \frac{R}{{2.17879}} ---(95) [/math] [math] \bar r_{ - +} =(60Gyr/2.17879)=2.60533 \times 10^{26}m [/math] From analysis of V-5, If UT ≥ 0, n - ~ n+, Therefore define, n - = n+ = n [math] V = \frac{{4\pi R^3 }}{3} = \frac{{4\pi \times (5.67648 \times 10^{26} )^3 }}{3} = 7.66171 \times 10^{80} m^3 [/math] [math] n = \frac{{\rho V}}{{m_p }} = \frac{{(1m_p /5m^3 )V}}{{m_p }} = 1.53234 \times 10^{80} [/math] ( 1080 is about total proton number of our universe). [math] U_{de} = (kn^2 )(\frac{{Gm_p^2 }}{{\bar r_{ - + } }}) ---(81) [/math] [math] U_{de} = (5.06522)n^2 \frac{{(6.6726 \times 10^{ - 11} )(2.79772 \times 10^{ - 54} )}}{{2.60533 \times 10^{26} }}J [/math] [math] U_{de} = (n^2 ) \times 3.62940 \times 10^{ - 90} J = 8.52207 \times 10^{70} J [/math] 1J = 1kg(m/s)2 = 6.25 X 1018 eV Ude = 5.31948 X 1089 eV [math] \rho _{de} = \frac{{U_{de} }}{V} = \frac{{5.31948 \times 10^{89} eV}}{{7.66171 \times 10^{80} m^3 }} = \frac{{6.94294 \times 10^{ - 7} GeV}}{{cm^3 }} [/math] Planck Unit transformation(1cm =0.5063 x 1014GeV-1 ) [math] \rho _{de} = \frac{{6.94294 \times 10^{ - 7} GeV}}{{1.29784 \times 10^{41} GeV^{ - 3} }} = 5.34961 \times 10^{ - 48} GeV^4 [/math] ρde = 0.534961 X 10-47GeV4 Observation value is [math]\rho _{obs} \approx 10^{ - 47} GeV^4 [/math] If R=90Gyr, ρde = 1.203 X 10 -47GeV4 (refer to fig11). [math] \rho _{de} \approx \rho _{obs} [/math] [Proof End] In Quantum Field Theory, the energy density of the vacuum is estimated as 1070GeV4, which is about 10117 orders of magnitude large than the observation value 10-47GeV4. Therefore, You can see that negative mass hypothesis how to close to the observation and the universe. [math] E_{de}=U_{de} = (n_ - \times n_ + )(\frac{{Gm_ - m_ + }}{{\bar r_{ - + } }}) [/math] From equation (80), Origin of dark energy is particle not pressure or constant energy, because that n- and n+ are number of particle. Also, because that gravity is repulsive, it is strongly suggested that negative mass is exist. Ude is right. It means that UT is also right. Thus, from the analysis of UT, it means that analysis of the inflation, fine tuning problem, decelerating and accelerating expansion, future of our universe are right. You will know the mean which magnitude of dark energy is proved. It is saying that cosmological constant has not existed and dark energy has not come from vacuum energy. Definitely, it is against to the ΛCDM model. For all that, why did the ΛCDM model show a similar result? We can find out if we look at the total potential energy section, but if we look at the total potential energy (78 ) equation, (79 ) equation, it is in a form of : U =(positive potential term) + (negative potential term)= Λ + (ordinary gravitation potential) Which the positive term played an independent potential role as Λ. ========= If the proof above is right, please read another section of the article. Hypothesis of Dark Matter and Dark Energy with Negative Mass : http://vixra.org/abs/0907.0015 Merged post follows: Consecutive posts mergedV-2-2)Proof from the gravitational self-energy In case of, mass M and mass distribution is 0 ≤ r ≤ R and mass density is ρ. fig10 caption : Gravitational self-energy Gravitational self-energy of the universe [math] U_S = - \frac{3}{5}\frac{{GM^2 }}{R} [/math] A coefficient 3/5 is constant for geometric shape of the universe. At this time, let's analyze to the relation between total potential energy and gravitational self-energy. Equation (79) is total potential energy when the number of negative mass is n-, and the number of positive mass is n+. The other side, Us is total potential energy when all particles are positive mass. Therefore, Us is total potential energy when dark energy term has an opposite sign. General gravitational potential defined, [math] U_{gp} = - ((\frac{{n_ - (n_ - - 1)}}{2}\frac{{Gm_ - m{}_ - }}{{r_{ - - } }}) + (\frac{{n_ + (n_ + - 1)}}{2}\frac{{Gm_ + m{}_ + }}{{r_{ + + } }})) [/math] Therefore, US = - Ude + Ugp ---(88) From analysis of V-5, If UT ≥ 0, [math] \frac{{U_{\max } }}{{U_{GeneralParticle} }} = \frac{{nU}}{{n(2n - 1)U}} = \frac{1}{{(2n - 1)}} \approx \frac{1}{{2 \times 10^{80} }} [/math] We know that Umax ≥ UT = Ude + Ugp [math] \frac{{U_T }}{{U_{GeneralParticle} }} = \frac{{U_{de} + U_{gp} }}{{|U_S |}} = \frac{{U_{de} + U_{gp} }}{{U_{de} + ( - U_{gp} )}} \le \frac{1}{{2 \times 10^{80} }} [/math] Therefore, [math] U_{gp} \approx - U_{de} ---(89) [/math] Substitution equation (89) in equation (88 ) [math] U_{de} \approx - \frac{{U_S }}{2} [/math] Finally, [math] U_{de} \approx - \frac{1}{2}U_s = \frac{3}{{10}}\frac{{GM^2 }}{R} ---(91) [/math] (This equation can be applied at UT ≥ 0) i) In case of n- = n+ =n, m - = km+ (k ≥ 1) Total mass [math]M = (n_ - \times m_ - ) + (n_ + \times m_ + ) = (k + 1)nm_p [/math] [math] U_{de} = \frac{{3(k + 1)^2 n^2 }}{{10}}\frac{{Gm_p^2 }}{R} ---(92) [/math] Equation (81) = Equation (92) [math] (kn^2 )(\frac{{Gm_p^2 }}{{\bar r_{ - + } }}) = \frac{{3(k + 1)^2 n^2 }}{{10}}\frac{{Gm_p^2 }}{R} [/math] [math] \bar r_{ - + } = \frac{{10k}}{{3(k + 1)^2 }}R [/math] If [math] k=\frac{{(dark\_matter)}}{{(ordinary\_matter)}} \approx \frac{{23.3}}{{4.6}} = (5.06522)[/math] [math] \bar r_{ - + } = \frac{R}{{2.17879}}---(95) [/math] From eq(91), [math] U_{de} = \frac{3}{{10}}\frac{{GM^2 }}{R} = \frac{3}{{10}}\frac{{G(5.06522 + 1)^2 n^2 m_p^2 }}{R} = (11.036068n^2 )\frac{{Gm_p^2 }}{R} [/math] [math] U_{de} = (5.06522n^2 )\frac{{Gm_p^2 }}{{(\frac{R}{{2.17879}})}} ---(96) [/math] Eq(96) is same to the (81) Therefore, Dark Energy define equation. [math] E_{de}=U_{de} = (n_ - \times n_ + )(\frac{{Gm_ - m_ + }}{{\bar r_{ - + } }})=\frac{3}{{10}}\frac{{GM^2 }}{R} [/math] Used to the gravitational self-energy, dark energy value of today is explained. Therefore, it means that dark energy is gravitational potential energy. Also, because that gravitational potential is plus value, it is strongly suggested that negative mass is exist. ======== Hypothesis of Dark Matter and Dark Energy with Negative Mass : http://vixra.org/abs/0907.0015 Merged post follows: Consecutive posts mergedV-2-3) Relations between radius of universe and dark energy density fig11 caption : Relations between radius of universe and dark energy density * mass density of ordinary matter = 1 proton/5m3 * Proton mass= 1.67264 X 10-27kg * G =6.6726 X 10-11m3/s2kg * 1J = 6.242 x 1018 eV comment-1. Radius of the universe is at least 78.2 billion light-years(24Gpc) wide. (2003, Neil J. Cornish, "Constraining the Topology of the Universe", http://arxiv.org/abs/astro-ph/0310233v1 ) comment-2. This is the Ned Wright BEST FIT volume In his recent article (January 2007) Wright gives a version of the universe that he calls best fit (to 4 or 5 different datasets) and Omega = 1.011 According to Smoot's notes the radius of curvature R is equal to the current Hubble radius divided by the square root of (Omega - 1) and the square root of 0.011 is around 0.105, So you divide the Hubble radius 13.8 billion LY by 0.105 and you get R = 130 billion LY. - Negative mass has observed, but it was trashed away - From the observance of the HSS team(The High-z Supernova Search team) in 1998, they gained the mass density of the negative(ΩM = - 0.38( ± 0.22)), using field equations which do not have the cosmological constant. ΩM = - 0.38( ± 0.22) HSS team : http://arxiv.org/abs/astro-ph/9805201 :14P 26, 29 lines - Negative mass is stable at the maximum point!(Refer to II-3) - As examined in the question of Harmonic oscillation, in case of positive mass, a point of minimum value which energy is the lowest is stable. However, in case of negative mass(minus mass), stable equilibrium is a point of maximum value, not a point of minimum value, so negative mass is toward a point of maximum value to be stable. In the world of positive mass, ground state is a point that energy is low, but in case of negative mass, ground state is a point that energy is the highest. Accordingly, in the world of negative mass, energy level is filled from the highest to the lowest, and stable state means the highest energy state, so the catastrophe to energy level of minus infinity never happens even if negative mass spontaneously emits energy. ======== Hypothesis of Dark Matter and Dark Energy with Negative Mass : http://vixra.org/abs/0907.0015