metal like gravity

8/12/2019 Metal Like Gravity

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Metal-like Gravity

Kamal M Barghout

Department of Math and Natural Sciences, Prince Mohammad University, Al-khobar, KSA

Phone: +966-3-849-9231 Fax: +966-3-896-4566

E-mail:[email protected]
mailto:[email protected]:[email protected]:[email protected]:[email protected]


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Modification to gravity that investigates gravitational relationship between two types of mass is

presented. It is proposed that the source of a dynamical field that permeates all of space and defines thedynamics of the cosmos is the repelling self-gravitational nature of dark matter (DM) particles and the

attractive gravitational nature between DM and baryons respectively. The model attributes self-

antigravity to both baryons and DM and defines DM-Baryon gravitational interaction as like particlesrepel while unlike particles attract; a coulomb interaction. To resolve the controversy of the apparent

self-attraction of baryonic matter, metal-like force is proposed where same type mass (baryons) are

gravitationally attracted to each other when a sea of the other type DM particles are attracted to themand glue them together analogous to a metal bond. When baryonic objects defy their own repulsive

nature and come close enough to each other, other dominant forces take place such as electromagnetic

force. The proposed modification to gravity requires modification to Einsteins field equation by

introducing a negative component in the energy-momentum term. In light of this gravitationalattraction-repulsion model, intergalactic self-repulsive DM particles are proposed to result in

accelerating expansion of the universe. The model introduces gravitational DM ether that is insensible

to inertial mass as required by special theory of relativity but sensible to an accelerating mass. The

model reproduces MONDs flat RCs andexplains the large scale structure of the universe and othercosmological phenomena.

Key words: Anti-gravity; Cosmology; Dark matter; Dark energy; MOND; Relativity theory.

1. IntroductionIt has always been assumed that anti-gravitational particles are nonexistent as their existence largely

runs against observation. A recent paper investigated whether virtual gravitational dipoles could be a

solution to the dark energy (DE) problem.1While the dipoles are described there by repulsive matter

and antimatter particles, here repulsive gravitational force of same-type dark matter (DM) particles thatpermeate intergalactic space produces similar results. The analogy is similar as far as how gravitational

dipoles of virtual repulsive matter-antimatter particles contribute to vacuum energy or DM gravitational

self-repulsive nature as suggested in this paper.

Most physicists reject the concept of antigravity and are inclined to think for example that matter

and antimatter must have identical gravitational properties and will always attract.2-4

Very few argue

otherwise. Some argued that antigravity could in fact be a potential explanation for CP violation.5

Newtonian dynamics fail to explain gravitational potentials of galaxies and galaxy clusters by only

considering their baryonic mass.6 Proposed solutions either invoke dominant quantities of non-

luminous dark DM7or modification to Newtons law.

8For example, the problem of flattening of galaxy

rotation curves inspired researchers to investigate modification of gravitational theories by introducing

weakly or non-interacting matter fields.9-12

While such theories successfully explain much of

cosmological dynamics within the realm of GR, they failed to explain the source of such a field. In thispaper, such a field is presented by modification of gravitational interaction of two types of mass, one is

DM particles and the other is baryonic matter. Other works suggested that visible baryonic matter and

hypothesized DM are spatially coincident in most of the universe.13,14

These works favored the DMhypothesis over modification of Newtonian gravity.

The nature of DM particles is a mystery. Particle physics models suggest that DM is either axions,which is characterized as hypothetical new particles associated with quantum chromodynamics, or


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WIMPs, hypothetical new particles with weak interactions or TeV-scale masses, neither of which have

been detected.

If DM had self-anti-gravitational nature and DE shared the same origin, it would be an easy task to

explain DE as simply the result of DM particles gravitational self-repulsive nature in the intergalacticregion, a perfect candidate to a cosmological constant. This assumption doesnt representa challenge in

galactic regions if DM-baryonic gravitational interaction is attractive as widely accepted. This is

because heavy baryonic objects will attract relatively light DM particles and form halos. Furthermore,introducing a self-repulsive attribute of DM particles adds yet another scattering factor to DM particles

trapped in a gravitational potential as in a galactic DM halo. In such a scenario, DM galactic halos

provide the means for holding galaxies intact as observationally seen. This approach is discussed in this

model.

On the other hand, presenting self-anti-gravitational attribute to DM particles necessitates similar

anti-gravitational attribute to baryons opposite to observations. This new physics pushes towards a new

look at the dynamics of baryons. By presenting gravitational properties of normal mass and DM asabove and presenting DM as having opposite sign to that of the mass of normal matter we are

attributing negativemass to both of them. The observational fact that the normal mass seems to have

a self-attractive gravitational properties has always led our thinking to drop a Coulomb-likegravitational option. Here, positive and negative matters are redefined by this new gravitational

interaction to produce positive and negative energy respectively. A composite baryon-DM matter

produces negative gravitational potential energy while DM or baryonic mass standing alone producespositive gravitational potential energy. The dynamics of the universe is solely governed by the

gravitational interaction of baryon-DM matter in the universe.

2. Basis of the ModelIt seems likely that two gravitationally different types of particles existed at the dawn of the universe.

With the successful Big Bang theory, those two types of particles must have contributed significantly tothe evolution of the universe.

By accepting the concept of a negative gravitational interaction and if we treat DM matter and

normal matter (baryonic as a representative matter) as opposite mass components, the followingdifferent scenarios may describe the gravitational nature between them,

1. Self-repulsive DM, self-repulsive baryons, and attractive DM-baryon.2. Self-repulsive DM, self-attractive baryons, and attractive DM-baryon or equivalently, self-

repulsive baryons, self-attractive DM, and attractive DM-baryon.

3. All attractive.4. Self-attractive DM, self-attractive baryons, and repulsive DM-baryon.5. All repulsive.

Here, it is regarded that passive and inertial masses are equal as Newtonian dynamics require.

Of the five above scenarios, choice 3 is widely accepted in the sense that gravity is always

attractive. While possibility 5 is excluded because it doesnt provide any attractive force contrary toobservation, possibility 4may resolve a good number of cosmological problems. For example, flat

galactic rotational curves can be explained by introducing external force emanating from negatively


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gravitating DM source acting on super large cosmological areas with rotational velocity explained in

terms of tidal forces.15

Furthermore, intergalactic space contains DM particles that are widely assumed

to follow possibility number 3 above. With this choice , a number of cosmological problems remainunsolved, such as flat galactic rotation curves, dwarf satellite galaxy problem, cuspy halo problem and

others. Also, DE remains a mystery.

Choice 2basically does not fall under any known category that reserves conservation laws.

Choice 1 could be a possible solution to many cosmological anomalies. It is stemmed fromNewtonian-Coulombic approach where mass is similar to charge; like masses attract and unlike repel. It

however presents a challenge to cosmological observation and currently accepted gravitational laws,

since baryons seem to show self-attractive behavior. In this paper, suggestion 1 is further

investigated.

Although no particles are known to have negative mass, some physicists, such as Hermann Bondi16

described some of the anticipated properties such particles may have. His analysis of the interaction ofa negative mass follows the equivalence of the three types of masses. The conclusion is then, in general

relativity, negative mass repels all masses, and positive mass attracts all.

Quantum physics considers vacuum as consisting of wave excitation modes of quantum fields.

Wave modes can be interpreted as particles that may have been produced in the early universe. This is

in line of the proposed metal-like theory in this paper. Furthermore, metal-like theory proposes thatDM particles are what constitute vacuum. Also, metal-like theory identifies DM-vacuum energy as

very weak in the intergalactic region compared to its value near massive cosmological objects thereby

giving an explanation of cosmological constant problem.

If we consider DM as opposite in sign to baryons, their analysis seems to contradict cosmologicalobservations of hypothesized DM since DM is actually attracted to baryons and not just follow keep-a-distance-mechanism as Bondis analysisseems to imply. On the other hand, with the assumption that

DM particles having the same type of mass as normal mass as widely believed (suggestion 3 above),

many cosmological anomalies are not resolved and a DM particle should not be as elusive as it is;

avoiding detection.

A recent work indicates that rotation curves due to DM halos at intermediate radii in spiral galaxiesare remarkably similar

17which suggests a universal DM mass profile. Furthermore it was reported that

the universality of galactic surface densities within one dark halo scale-length holds for both DM and

luminous matter. This can be interpreted as a close correlation between the enclosed surface densities of

luminous and DM matters in galaxies.18

This relationship can be described adequately under the modelproposed here.

3. Metal-like Attraction MechanismFollowing possibility 1 above, this model proposes a long range gravitational interaction with

baryon-baryon repulsive gravitational interaction suppressed by a metal-like attraction mechanism. At

close range, other forces, e.g., electromagnetic force, are responsible for bonding baryonic material.

Consider two gravitationally interacting baryonic objects; the interaction will be repulsive as

suggested. Only due to the existence of attractive force between a sea of opposite-mass particles (DMparticles) and baryonic objects, the baryonic-baryonic interaction will be seen as attractive. This


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approach seems plausible if it can explain dynamics of general relativity (GR) with Newtonian limits

and complies with particle physics.

4. Composite DM-baryonic MatterDM-particles are proposed to possess much smaller mass than their baryonic counterparts and thereforeform a DM-halo around baryonic objects. Such a DM-baryon composite necessarily requires that DM

doesnt annihilate with the baryonic core. A metal-like bond is a bond that forms between two baryonic

objects when their DM-halos overlap.

To illustrate the metal-like mechanism, figure 1 shows a general system of two repulsive baryonic

objects glued together by a sea of DM particles.

baryonic objects

Sea of DMparticles

Fig. 1. A general system of two self-repulsive baryonic objects glued

by sea of DM particles.

5. Feasibility of Metal-like ForceThe proposed metal-like force should be directional along the line connecting the centers of the two

baryonic objects. This could be seen for an isolated two baryonic objects as the cloud of particles of

opposite type would have highest probability density between the two objects as figure 2 illustrates.This should in general be the case whether DM particles are hot, warm or cold.

Baryonic objects

Higher densityof DMparticles

Fig. 2. Higher density of DM particles between two core objects

The net centered DM-mass between the two baryonic objects can be viewed as an overlapping ofthe DM halos of the two baryonic objects as figure 3 shows.


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Baryonic objects

Overlapping volumeof higher density ofDM particles

Fig. 3. Higher density of DM particles in the overlapping area

of two DM halos.

It is important also to notice that for an isolated two baryonic objects, due to the coulomb force of

inverse square of the distance, the DM mass that ultimately needs to allocate itself in between the

baryonic objects to completely obscure the repulsive baryonic-baryonic force and yet produce apparentattractive force as suggested in a metal-like force is less than the total mass of the two baryonic objects.

The close relationship between the DM halo particles and the baryonic galactic content can be readily

explained by the intimate DM-baryonic attractive relationship as well as the DM self-repulsive natureas presented here.

For cosmological large structures such as galaxies, figure 4 illustrates baryonic core with a baryonic

edge star of a hypothetical spherically symmetrical galaxy. The DM halo particles are included in thevolume between the edge star and the baryonic core.

Repulsiveintergalacticspace

Baryoniccore

Baryonic

edge star

DM halo

Fig. 4. Galactic system showing intergalactic space, an

edge star, the core and the enclosed DM halo

Three gravitationally bound systems can be clearly distinguished employing the DM-baryonicgravitational relationship. First, Newtonian behavior exists within the baryonic galactic inner cores

with a constant metal-like force due to constant DM-density on average. Second, a metal-like varying


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gravitational force exists away from galactic cores due to varying DM halo density. Lastly, a centered

DM halo exists in a cluster of galaxies as illustrated in figure 5.

Baryonic galaxy

High density

of DM particlesLow density ofDM particles

Fig. 5. DM particle distribution in a cluster of galaxies.

6. Metal-like Force Mathematical FormMetal-like force approach is an attempt to explain the dynamics of the universe via modification to

gravity. In a metallic bond, the force that describes ionic interaction can be described as Coulombic andproportional to r

-2. Likewise, the gravitational force that describes the proposed metal-like force can be

described as proportional to r-2

as we see it in Newtonian force. The apparent Newtonian force then

describes the true free gravitational force if multiplied by a scaling factor. Therefore the magnitude of

the gravitational force can be described by the following equation,

= ||

1

Where is the gravitational constant,Fgis the gravitational force, m1and m2are the baryonic and DMmasses, and is a scaling factor that accounts for the DM density.

7. Stability of Cosmic StructuresIn the metal-like model, any stable cosmic structure should be gravitationally bound with DM particles

as the acting bonding agent. In the inner galactic core, the metal-like force results in Newtonian

dynamics while in the galactic outskirts the metal-like force predicts different dynamics. The metal-like model also predicts that the Newtonian force between two baryonic objects within the inner core is

larger than the true DM-baryonic attraction force or pure baryonic-baryonic repulsive force due to

the inverse square of the distance law.


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Baryonic objects

Overlapping area ofhigher density of DMparticles

Baryonic objects

DM centralobject

r

Fig. 6. Left:about2/3 of each baryonic object is shielded by its own halo. The overlapping area in the middle equals 2/3 ofthe baryonic mass. Right: Metal-like force illustrating a centered DM attracting system.

As well known, DM makes up roughly 80 percent of the mass in the universe. For a gravitationally

stable cosmological structure the DM mass should proportionally be at least equal to one-fifth of that of

the baryonic mass within its core on average. This is because, for same mass two baryonic objects, 2/3

of that magnitude will be the central DM as that of the two baryonic objects as illustrated in figure 6

above, the apparent baryon-baryon attractive force is 16/3Gm2/r

2while baryon-baryon repulsive force

is Gm2/r

2. Therefore, for nucleation of any cosmological structure, the DM halo should make available

a centered DM of at least one-fifth of that of the baryonic mass on average to counterbalance the

baryon-baryon repulsive force and remain gravitationally intact. The proposed metal-like force

necessitates apparent force to true force of a maximum ratio of about 5:1.

8. Metal-like Cosmology and Rotation CurvesThe rotation curves (RCs) of spiral galaxies become approximately flat at the largest radii observed.

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This is one of the strongest indications of the need for dynamically dominant DM in the universe. The

inner shape of rotation curves is well predicted by the distribution of observed baryons.

21

There appearsto be though a characteristic acceleration scale at which baryonic material alone can no longer account

for the observed dynamics, hence the need for a DM halo in galaxies.22

The universalityof the RCs in

combination with the invariant

distribution of the luminous

matter

implies a universalDM distribution with

luminosity-dependent scaling properties

23, i.e., luminosity,

dictates the rotational velocity at any radius for any object, so revealing the existence of a universalRC.

It is proposed here that a baryonic edge stars dynamics is mainly determined by the proposed

metal-like gravitational relationship. Just as in the galactic inner core, the metal-like interaction is

responsible for bonding the edge star to the galactic core with the exception that the DM bondingparticles are not distributed evenly throughout the galactic halo and therefore the DM density is not

constant on average.

9. Metal-like Gravity VS MONDModified Newtonian dynamics (MOND) [8] is a theory that describes the rotational velocity of stars faraway from the galactic center without the presence of DM. It proposes a modification of Newtonian

gravity to explain flat galactic rotation curves (RCs) by introducing the function which equals


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one at normal acceleration and equals at very low acceleration; where is the centripetalacceleration of the star and is a constant of about1.2 10/characteristic of MONDslowacceleration. MOND expresses the galactic rotational velocity of stars as

. MONDs empirical

formula is very successful in fitting observational data of galactic flat RCs. A possible physical

interpretation of this functional form is provided by the assumption that gravity is mediated by

gravitons with non-zero mass.

Star

Overlapping volumeof higher density of

DM particles

Galaxy

d

r

Fig. 7. The attractive force between an edge-star and galaxy center comes from the stars

DM halo as well as the Galaxys DM halo.

To estimate flat RC curves for an edge star using metal-like gravity, figure 7 shows that the stars

centripetal force between the DM overlapping volume and the center of the galaxy has two

components, one due to galaxy-DM halo and another due to the stars DM-halo. The edge stars DM-component is the dominating component when the star is far from the galaxy core (edge-star) and the

galaxys DM component can be neglected. Figure 8 implies that the stars DM-component increases

proportional to the distance to the core (r) since the mass increases approximately linearly withthe

radius.

Closeby

edge-star

Galaxy

Non-overlapping

volume

Overlappingvolume

Far away

edge-star

Fig. 8. Effective overlapping DM matter increases proportional to the distance to the galaxy core.

Since the stars DM contribution to the total gravitational force is the dominant component, it

shapes the rotational curves of galaxies as equation (3) shows.

=

2


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Where is the luminous (star and gas) mass of the galaxy computed up to the location of the star, MDis the DM-mass of the overlapping volume in fig 8.

In simple words, the farther away the edge-star is from the host galaxy core, the flatter the galaxys

surface area at the stars site and the larger the overlapping DM-mass that is responsible for the metal-like gravity force and consequently the larger the gravitational attractive force. In figure 8 above, the

farther away the edge-star is from the galactic core the smaller the non-overlapping volume betweenthe galaxys DM-halo and the stars DM-halo. In Newtonian form, this increase in force can effectively

be expressed as an increase in the contributing galaxy mass. In equation (2), increases as a functionof the distance to the edge-star and becomes,

3

Where is the mass of the edge-star.

To estimate the proportionality factor of equation (3) it is noticed that the factor is a function of the

galactic luminous mass at the location of the star. Introducing the factor as = .5

as anempirical fitting factor we can estimate the stars rotational velocity. The fitting parameter hasdimensions as the square root of linear mass per meter ( ).

Equation (3) can be expressed as = , which produces equation (4),

= .5 4

Such an empirical power law of equation (4) that has only one free parameter explains the intimate

relationship between luminous mass of galaxies and DM halo densities obtained from observations.

Current CDM halo models express DM densities as power laws with nearly constant surface densities.For example, theoretical dark matter halos produced in computer simulations are best described by the

Einasto profile = .24

While those models dont seem to explicitly offer a physicalinterpretation of this fine tuning of DM-luminous mass dependency as satisfied by the observed Tully-

Fisher-type relations, this is readily explained in the metal-like model as geometrical as seen in figure

8. This fine tuning of DM distribution in galaxies is very weird indeed and a physical explanation isnear impossible with current proposed DM models.

To compute the rotational velocity of an edge-star, we choose the magnitude of as 1.345 for spiralgalaxies. Equation (4) expresses the rotational velocity curves of galaxies as flat and produces identicalRC curves as MOND for galaxies. It is worthwhile to note that unlike MOND which is DM-free theory,

metal-like cosmology differentiates between the DM-distribution in a galaxy and DM-distribution in acluster of galaxies as shown in figure 5. Equation (4) does not apply to clusters of galaxies. To compare

with MOND, the luminous mass was derived from a perfect fit to the rotation curves of galaxy NGC

22425

by MOND formula. Rotation curves were then generated by metal-like gravity using equation(4), which produced identical rotation curves as seen from figure 9.


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Fig. 9. Identical RC curves for galaxy NGC 224 as fitted by MOND and Metal-like gravity.

Since MOND is widely rejected as a non-DM based theory but yet it is very successful in

explaining RCs for spiral galaxies, one can ask, shouldnt there be DM -based model that explains the

success of MOND? Metal-like gravity is just that model.

MOND and metal-like gravity produce the same galactic RCs, therefore the fitting parameter canbe derived from MOND formula which is found to be .

10.Black Holes and Gravitational SingularitiesCurvature of space-time as described by GR theory should hold for a baryonic structure with the

dynamic mass that results from metal-like gravity is included in Einstein's equations. This leads to ano change of black hole dynamics from current proposed theories.

Metal-like gravity on the other hand sheds light on the interior dynamics of black holes. While GRanalysis of the interior of a black hole introduces gravitational singularity at the core, due to infinite

gravitational collapse of normal matter, metal-like gravity should remove it since DM-baryon

repulsive-attractive gravitational forces eventually balance out, preventing a total collapse to

singularity. It is interesting to see an event horizon made by a gravitational-bond as the end result ofa gravitational collapse.

11.Cosmological Problem, Evolution of the Universe and Cosmological CoincidenceThe ad hoc positive cosmological constant of Einstein can account for the observed accelerated

expansion of the universe and describes the value of the energy density of the vacuum of space. If theuniverse is described by an effective local quantum field theory down to the Planck scale then we

would expect a cosmological constant of the order of

. However, the measured cosmological

constant is smaller than this by a factor of 10120. Moreover, the true nature of such an ad hoc term is a

total mystery. It is usually modeled as a cosmological fluid with a constant density and negativepressure. In this paper, the source of the repulsive nature of such a hypothetical fluid is simply the self-

repulsive DM particles of intergalactic space, and therefore the self-repulsive DM particles that

constitute the DE fluid and drives the universe to accelerate its expansion. The discrepancy of the largefactor between intergalactic vacuum energy and local vacuum energy can be explain by that

gravitational pressure, the cause of local vacuum energy, is completely lacking in intergalactic space.

For example, locally, for planets and moons, hydrostatic equilibrium is reached when the compressiondue to gravity is balanced by a pressure gradient in the opposite direction due to the strength of the


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material, at which point gravitational compression ceases. With self-repulsive DM-particles that defines

vacuum energy; the local vacuum energy is astronomical.

The cosmological coincidence problem may be resolved by unifying DE and DM into a single dark

substance as proposed here. It would be of great importance if we could define DE, DM and the

evolution of the universe under a single conceptual framework. This is achieved under the metal-likemodel where the evolution of the universe should be no different than the accepted Big Bang

cosmology as the proposed metal-like force only describes Newtonian force as an apparent one which

differs than the true force by a proportionality factor as equation (1) describes.

In the metal-like model, the relative galactic space was much larger since the early stages and

throughout the evolution of the universe. While Newtonian cosmology doesnt allow expulsion of

galactic material into intergalactic space as DM collapses the same way as baryons, in the metal-likecosmology self-repulsive DM nature allows that. The non-contributing galactic DM particles to the

metal-like bond in the early evolution of the universe are eventually expelled to intergalactic space.

When galactic space got smaller with the redistribution of DM particles due to virialization of galactic

structures, the net intergalactic DM negative force became proportionally larger until finally it showedup universally at the same time cosmological virialization had completed. This started the era of

accelerated expansion of the universe, hence the cosmic coincidence problem. This era marks the peak

evolution of the cosmos and the existence of mankind which allowed detection of the era.

It is important to mention that for Big Bang event to occur under a metal-like cosmology,

nucleation of the seeds of baryonic objects should be readily available. This might have occurrednaturally under other forces of electroweak and strong interactions as inferred from early universe

Primordial nucleosynthesis of Big Bang cosmology since DM is gravity-only entity.

12.High DM-Density of Dwarf Satellite Galaxies and Cuspy Halo ProblemThe metal-like mechanism is the acting galactic gravitational system. The model presents DM density

in the galactic core region as constant on average, therefore resulting in constant force, which solvesthe core-cusp problem arisen from numerical N-body simulations of DM halos based on the

collisionless cold DM model.26

For example, it is the metal-like gravity that is responsible for the

apparent Newtonian dynamics which is responsible for the baryon-baryon gravitational attraction.

Accordingly, in the cores of galaxies DM does not show up as a cusp.

Satellite dwarf galaxies can be viewed as objects bound to the host galaxy by metal-like force when

their DM halos overlap, with the host galaxys DM halo extends to engulf the dwarf galaxy. Withhigh

host galaxys DM-density within the satellite dwarf galaxy, this increases the satellite galaxys DM halo

to large magnitudes observed in their galactic dynamics. Some dwarf galaxies are observed to contain a

ratio of DM to baryons of 99:1, possibly by the host much larger galaxy contributing to most of thedwarf galaxys DM halo.

Dwarf satellite galaxy problem arises from numerical cosmological simulations that predict theevolution of the distribution of matter in the universe. Cosmological models consider both DM particles

and baryonic matter as self-attractive as well as attractive to each other which allow DM to clump in

pure manner. This scenario is fundamentally different than the proposed self-repulsive DM matter asthe formation of invisibleclumps of DM is prohibited due to its self-repulsive nature. Hierarchical


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formation of the universe under this model is predicted to form less number of satellite galaxies since

self-repulsive DM particles limit their formation and drive them apart.

13.Metal-like Theory and GRRelativistic effects show up near strong gravity fields and high velocities. Although GR equations

cannot produce a negative geometry normally, it is possible to do so using a negative mass.Einsteins equation does not, of itself, rule out the existence of negative mass

If the correct gravitational theory is GR, then Newtonian theory should satisfactorily describe,

astrophysical systems involving small velocities and weak potentials such as galaxies and clusters ofgalaxies. So far we have discussed Metal-like bond with GRs Newtonian limit describing astronomical

systems where GR explains astronomical phenomena only with the introduction of unseen matter and

energy dubbed DM and DE respectively. But GR can only describe the dynamics of the universe by

introducing DM and DE separately. So far there is no known method by which GR can combine thosetwo entities as due to same source. Here, the proposed metal-like gravity introduces a gravitational

scalar field with positive and negative energy components; the positive energy component describes the

self-repelling DM particles in the intergalactic regions while the negative part of this potential energydescribes the attractive force made by the metal-like gravity. Metal-like cosmology then describes the

same source of DM and DE. Simply put, the equations of state possess an energy density that is

algebraically negative with metal-like bond and positive with DM and baryon self-interaction. Here,metal-like cosmology is described within the limits of GR without solving GR equation of motion to

derive any cosmological parameters.

In simple words, GR is a geometrical theory which explains gravity as curvature of space-time

described by Einsteins equation,

=

(5)

Stress, energy and momentum contribute to the energy-momentum tensor and the negative pressure due

to the cosmological constant as represented by the first term in the r.h.s.of the equation. It determinesspace-time curvature, which is represented by Einsteins tensorwhich describes space-time curvature

as in the l.h.s. of the equation, and hence the dynamics of the universe. A cosmological constant term

was added by Einstein to describe a static universe, later dropped by him with the discovery ofthe expansion of the universe but revived again with the discovery of the accelerated expansion of the

universe. A negative energy can be included in the energy-momentum term just like weinclude positive mass-energy. The cosmological constant term is readily explained by metal-like

cosmology and thereby should be dropped from Einsteins equation.

14.Gravitational Ether as an Insensible Background to Inertial Normal MatterIt seems that the only way to equate gravitational mass with inertial mass is to introduce a gravitationalfield that runs in the background. This way a force on an object carrying mass will feel a back ground

gravitational resistance so long the force is acting on the object. This only happens if there is a

gravitational repulsion between the object and the background which is explained according to themetal-like theory.


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Special theory of relativity (SR) describes the equation of motion of an object possesses rest mass

that it will acquire more mass by changing its speed accelerating it through a background. In metal-

like gravity, the added relativistic mass may be described as due to larger relativistic gravitationalresistance by the background. This is a perfect description to SR theory if it can accommodate a rest

frame (the background gravitational field). As described here, the Metal-like theory allows a

background DM-gravitational field that can be described as fit-all inertial frame with no preferred-direction quality. In other words, any inertial object in this background field feels its gravitational

effect relativistically and symmetrically. This relativistic symmetry is broken only when objects are

accelerated through the field. This is achieved by Metal-like theory by describing a DM-high way inwhich an inertial metal-like object feels no background resistance and therefore interacts only with

space-time just as SR requires. The role of the DM-frame then is to construct the gravitational highway

and the metal-like bond. Away from baryonic material where metal-like matter exists such as in the

intergalactic region, DM matter curves space negatively. That is the source of DE.

15.The DM-Ether Background SuperhighwayAs had always been the case prior to the prevailing SR, an absolute reference frame was needed that

any moving object should rely on for inertia. Einstein based the derivation of Lorentz invariance (the

essential core of SR) on just the two basic principles of relativity and light-speed invariance in vacuum.

The introduction of length contraction and time dilation for all phenomena in a preferredframe of

reference, which plays the role of Lorentz's immobile ether, leads to the complete Lorentztransformation. However, in the metal-like gravitational theory presented here, the ether is insensible to

inertial objects by means of a proposed superhighway and therefore no drift contribution to the inertial

objects speeds by the presence of the ether is produced. This way SR preserves its space-time

correlation. As in a super conductor the flow of electrons encounters no electrical resistance as if thematerial is insensible to the electrical current, here we propose that the DM-background constitutes an

insensible superhighway to the flow of DM-baryonic composite matter simply because they carry

neutral mass relative to the background.

16.The Equivalence PrincipleWhile Newtonian dynamics does not explain the observationally confirmed fact that gravitational mass

and inertial mass is the same of all object GR takes this as a basic principle. A gravitational ether

background with gravitational quality as described by metal-like gravity can explain well theequivalence principle. As discussed earlier, relativity theory recognizes such a rest frame if it is

inherently undetectable by inertial objects but yet only felt when an object is accelerated through it.

Figure 10 illustrates the gravitational-free highway that an object travels relative to the inertial DM-gravitational rest frame.


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Geodesicpath

Inertial force Baryon BaryonMetal-likegravitationalforce

Compressed DM-space

Relative movement betweenbaryonic objects

Fig. 10. Gravitational super-highway and the equivalence principle;

inertial force equals background gravitational force.

In the figure above, accelerating a baryonic object against another of inertial state compresses DM-

space elements between them and increases the metal-like gravitational force by increasing the DM

density between them. The gravitational force will increase proportional to the applied inertial force.

The accelerating object then moves at a constant speed as soon as the inertial force is removed feeling

no net force from the background ether as it is mass-neutral with its DM-halo. This process requires arelaxation period which necessarily must be small enough not to alter the state of the DM-background.

This is achieved by the fact that DM-particles are gravitationally repulsive. When the background isrelaxed it will have an invariant density with respect to any inertial object regarding to its relative speed

to the background simply because the background does not feel the inertial object. In other words,

inertial force is a measure of the gravitational force with respect to the background.

It is not a contradiction to GR that a true gravitational force between objects contributes to the

energy-momentum tensor in Einsteins equation of motion. While curvature of space-time as described

by GR is the correct description that determines the dynamics of the universe, true gravitational force

between objects contributes to this curvature and determines it if it is the dominant component of the

energy-momentum tensor in Einsteins equation within Newtonian limit. This can be achieved with abackground DM-frame (an ether that is thought of as not endowed with the quality characteristic of

ponderable media, as consisting of parts which may be tracked through time with the idea of motion notapplied to it: Einstein).

In the realm of GR, the Einsteins equivalence principle postulates that inertial mass must equalpassive gravitational mass; as the law of conservation of momentum requires that active and passive

gravitational mass be identical.

Simply the model leads to positive curvature of DM-space-time around baryons and negative

curvature in the intergalactic region. Accordingly, the intergalactic DM-continuum background does

not feel the galaxies because they are mass-neutral, and therefore the accelerated expansion of theuniverse are due to the negative curvature of space-time due to this background.


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17.ConclusionA model is investigated that describes dark matter and normal matter as two types of mass that followCoulomb law where like particles gravitationally repel and unlike particles attract. Accordingly,

intergalactic dark matter (DM) particles are self-repelling resulting in accelerated expansion of the

universe. DM particles are proposed to permeate all of space. The model describes a metal-like forcethat suppresses baryonic self-repulsive gravitational nature and introduces Newtonian regime within

galactic cores. The model introduces new physics and proposes solutions for many cosmological

mysteries such as flat galactic rotation curves, dwarf satellite galaxy problem, cuspy halo problem, andcosmological coincidence problem and most importantly, the nature of dark matter and dark energy.

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metal like gravity

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