joao c h barcellos

5-Comoving and proper distances (verified) Comoving distance factors out the expansion of the universe, giving a distance that does not change in time due to the expansion of space (though this may change due to other, local factors, such as the motion of a galaxy within a cluster). Comoving distance and proper distance are defined to be equal at the present time. At other times, the Universe's expansion results in the proper distance changing, while the comoving distance remains constant. https://en.wikipedia.org/wiki/Comoving_and_proper_distances "... is the distance between them which would be measured with rulers at the time they are being observed (the proper distance) divided by the ratio of the scale factor of the Universe then to now. In other words the proper distance multiplied by (1 + z)." https://ned.ipac.caltech.edu/level5/Hogg/Hogg4.html From the equation (E10) from my paper, we have : D(t) = D0 * exp(H0*t) ( It is the size measured now as a function of the size that would have been measured at the time of photon emission.) We can then identify as D0 = proper distance. Substituting D(t)=Lambta (=L) (wave length reaching us) and D0 = Lambta0 (=L0) ( wave length emited ) We have: L = L0 * exp(H0*t) So L/L0 = Z + 1 = exp((H0*t) = D / D0 Therefore: D = D0 * ( Z + 1 ) ( deducted from my paper ) B) ALMOST VERIFIED 6-The postulation of dark matter may not be necessary (to be verified) It's in the theory text, but rotation curve of galaxy is not very good yet. C) TO BE VERIFIED (Consequences of the theory) 7- On average, Galaxies at the same distance, the ones with less mass should have higher redshifts and vice versa (NOT verified yet) Because the greater mass increase the contraction rate of the galaxy increasing the frequency of light 8-On average, for aspiral galaxy, the more distant the galaxy, the greater the amount of dark matter. Because the galaxy's radius will appear larger than it actually is.

In resume, I think so. Before Newton created the FORMULA of gravitational attraction, there was first the idea of this attraction. O que do not invalidate his idea. I do not have the calculus of shrink rate in function of the gravitacional field. I was wondering if you could do this calculation from an elevator being accelerated and check the rate of contraction inside the elevator (via the equivalence principle) but I still haven't succeeded in that. But in earth the rate of shrinking is 7% contraction by each 1 bilion of year, No. The horizon event is like the gravitational force: The nucleous can be shrinking but the gravitational force is the same at the same distance of the center . Evidence from Decreasing Universe -------------------------------------- A)-VERIFIED 1-Hubble's law formula can be derived (verified) It's in the theory text. 2-Postulation of dark energy is not necessary (verified) It's in the theory text. 3-Expansion of the universe doubles every 10 billion years (verified) "Universe mysteriously expanding, will double in size in 10 billion years, finds Hubble" https://www.indiatoday.in/science/story/universe-expanding-mysteriously-will-double-in-size-in-10-billion-years-finds-hubble-1951827-2022-05-20 Which was exactly the evidence I was hoping for, that's exactly what my theory predicted: ["...Some Values .... Tj=3.15E17?s = 10 billion years That is, the Jocaxian Time, the time necessary for our space to contract in half, is 10 billion years..."] 4-The Universe is getting hotter (verified) -Unexpectedly, The Universe Is Getting Hotter and Hotter as It Expands https://www.sciencealert.com/the-universe-is-getting-hotter-and-hotter-new-study-finds B) ALMOST VERIFIED 5-The postulation of dark matter may not be necessary (to be verified) It's in the theory text. C)TO BE VERIFIED (Consequences of the theory) 6- On average, Galaxies at the same distance, the ones with less mass should have higher redshifts and vice versa (NOT verified yet) 7-On average, the higher the redshift, the greater the amount of dark matter (not yet verified) 8-On average, the more distant the galaxy, the greater the amount of dark matter. ( not yet verified) ------------------------------------- Do someone now aboute 6, 7, 8 ?

if we were to use the principle of equivalence we should choose the first option, but my intuition thinks that the field (and not the force) is more correct. Although neither of them invalidates the theory. Galaxy M33 = NGC598 X = Radius from the center of galaxy to Star Velocity of star where redshift Z << 1 : Velocity =2.2E-18*3E22*(SQRT(1+X*X/3E22/3E22))+SQRT(1E40*6.7E-11/X) DIST(meters) = DIST(LightY) => Velocity (Km/s) 9.4e19 = 10k yL = 150km/s 1.8E20 = 20K YL = 127km/s 2.3e20 = 24k Yl = 119 km/s 2.8e20 = 30K YL = 115km/s 3.7e20 = 40K YL = 108km/s 4.7e20 = 50k YL = 103km/s Well, it is not so good , but is very better than we have without dark matter, ( but perhaps i forget some parameter , i will think it better after... )

Ok : Suppose an object is between the Earth and the Sun. It is hit by the gravitational pull of the Earth and the gravitational pull of the Sun. At the point where it is (closest to the earth) these two forces can counterbalance each other with zero net force. If the rate of shrinkage depended on the gravitational force and not the gravitational field, this object would not shrink. On the other hand, the object is bathed by the gravitational field of the Earth and also by the gravitational field of the Sun. So if the rate of shrinkage depends on the gravitational FIELD and NOT the gravitational FORCE, then it will shrink at a HIGHER rate than just one of the two fields acting on it. Did you understand? Some one already see inside one black-hole? wrong conclusion. I *DON'T* put in the formula for the rate of shrinkage as a function of the gravitational field. I didn't say it's proportional to the field or the square root of the field or the logarithm of the field or anything like that. I just said that as the field increases, the shrinkage rate should be higher. In addition, all the stars of the milky way contribute in some way to the gravitational field that reaches the earth and not just the mass of the Earth. Another thing: you should also note that as our rulers shrink we can measure the diameter of neutron stars BIGGER than they actually are, for example if they shrink at the same rate as our planet then their radius will seem constant. ANOTHER EVIDENCE: ["The universe is getting hot, hot, hot, a new study suggests Temperature has increased about 10 times over the last 10 billion years"] https://www.sciencedaily.com/releases/2020/11/201110133132.htm when stars or gases schrink the temperature grow up case open

some objects shrink at the same rate others at different rates, depending on the gravitational field. Here on Earth we have a 7% reduction every 1 billion years No, said the oposite, perhaps the tradutor is not good. I said the contration CAN depend from gravitational field and not the gravitational resultant force. I still I am not sure of this. Cancel to zero is difficult but negligible field exists: At far away from the galaxys the field is very very weak. I do not know why, but when i win the Nobel you change your idea :-) I think the objects shrink very very fast , perhaps our gravity is like a black-hole but very very very slow.

I think not: The gravitation field in Jupter is greater than earth, so the rate of shrink is greater yes, both are shrinking. But if the object shrinks at the same rate that we shrink, we don't notice that shrinkage. Even more so the shrinkage is very slow, about 7% for every billion years. Not! The laws of physics are valid including the constants in relation to a sidereal observer (OS), one that does not undergo contraction. From my article: ["Let’s call of “Sidereal Observer” (=“SO”) those observers located in this spatial region. For example, observers in the intergalactic region would be an “OS”. To clarify ideas, we may think that observers in the “OS” (=“SO”) play a role similar to an observer in an inertial frame [5] as opposed to observers located in the “LS” that would play an analogous role to observers in a non-inertial referential."] Note that I used only one hypothesis to explain the dark energy and dark matter effects. By ocam's razor, it would be preferable to post *two* new hypotheses (dark energy+darkmatter). Furthermore, I think it is important to point out that Hubble's law was derived based on this hypothesis, which is not the case in the case of dark energy which remains a mystery. Regarding dark matter I believe this theory can "shed some light", but the upside is that, despite efforts, no evidence of dark matter has been detected, and my theory doesn't need it, although I still can't quite hit it off. observational data, Yes, I agree. I think what's inside the black hole is shrinking much faster, yes. But we don't have access to the inside of the black hole. I believe that the rotation period should increase since the star is contracting and the radius of the star should decrease, and not, as a first approximation, older pulsars should rotate faster. Do you know if this happens? On the other hand, pulsars lose energy due to radiation and this lost energy may be being counterbalanced by their angular momentum, that is, the loss of energy can reduce the rotation speed. So there are two factors that would need to be weighed.

I believe that gravitational forces can cancel each other out but not the gravitational field. If something is between the Sun and the Earth it will experience two gravitational fields and shrink faster than if it has only one of the fields. Well I didn't put the dependence (the formula) of the rate of shrinkage on the gravitational field. I just said that I believe the field makes space (and everything within it) shrink. But the shrinkage function as a function of the field I don't know. Perhaps not greatly, it will depend on the shrinkage rate as a function of the gravitational field. IMPORTANT: With some simplifications, I have derivated the CORRECT GALAXY ROTATION CURVE ( to galaxy Messier 33) : V = H*SQRT(1+R^2/D^2) + SQRT(M*G/R) where: G = 6,7E-11 H = 2,2E-18 M = Mass Sun = 2,0E30 c = 3E8 diameter = 50E3 AL = 4,5E20 R=Radius = 1/2(50E3 AL) = 2,3E20 D=distance= 3E6 AL = 3,0E22 could, please, anyone check if it matches this curve: https://en.wikipedia.org/wiki/Galaxy_rotation_curve Thank You The correct formula is : V = H*D*SQRT(1+R^2/D^2) + SQRT(M*G/R) M= mass galaxy = = 7E9 * Msun = 7E9*2E30= 1E40 Kg

Probably the same process when somethink enter in a black-hole, but too much slower. The theory is new and, as far as I know, no one has looked for this evidence any more than you would need to know where the object comes from. Note that solar system meteors are also subject to gravitational fields from our galaxy. Why not shrink? I don't think anyone has measured the size of a particle at high velocity to know if it compresses in the direction of velocity. But think: In a rocket, space is contracted in the direction of velocity. Wouldn't the particles in there also be contracted? Yes off couse! but remember : the rate of contraction is about 50% every 10 billion years ( here in earth ) Although the moon remains in Earth orbit, it is still bathed in Earth's gravitational field. A measure of the density of these rocks relative to similar ones on Earth could be evidence although my theory does not predict whether matter takes on the size of the matter in which it is found. For example when a rocket stops its speed, what was contracted by relativistic space contraction, returns to normal size. So, as I said, this is an open question for me. Yes! ( if its elements-composition remain the same) But how to know how old is the star? Older stars (or galaxies) should have a lower redshift (ie higher frequency) than younger ones if they are at the same distance from us. The problem is knowing the lifetime of the star or galaxy. Yes, by this theory, galaxies with greater masses must have smaller redsheefts. "At redshifts z < 1 most of the bright (MB < - 20) and massive galaxies (M* > 1010) are normal galaxies, that is ellipticals and spirals" https://ned-ipac-caltech-edu.translate.goog/level5/March04/Conselice/Conselice3_2.html?_x_tr_sl=en&_x_tr_tl=pt&_x_tr_hl=pt-BR&_x_tr_pto=wapp

Well I started think in this because of equivalence principle. If you are inside an accelereted rocket , will anything be shrinking inside the rocket ? See this article : https://www.researchgate.net/publication/313035899_The_Equivalence_Principle_and_the_End_of_the_Dark_Energy All things will be shrunk, including particles. Wouldn't it be the same if they had a rocket accelerated relative to an inertial observer? Surface events on Earth are not attractive hosts because on a scale of half the size every 10 billion years, events lasting a few thousand years will go unnoticed. Goog question ! When a particle arrives from interstellar space, its physical properties like electric charge, spin, mass are not affected. With respect to its volume (and density) it's open-ended, that is, I don't know what would happen to its physical volume and density when it enters the gravity of our galaxy. It's an open question for me. Everything within our galaxy is shrinking, including our Sun and our solar system as a result of the galaxy's gravitational field. This means that the stars must emit a higher and higher frequency of light as the wavelength becomes shorter. Note that on Earth everything decreases too, so we should not perceive anything that decreases along with us. Note that this theory does not say that galaxies cannot be moving. In this way, in principle, they can be moving away or approaching freely. What the theory says is that there doesn't need to be an accelerated departure, the accelerated departure would be a kind of "optical illusion" due to our shrinkage. So it's possible that galaxies are getting closer, and if that approach is faster than the effects of our shrinkage, we'll see them get closer. IMPORTANT: At very long distances few or almost no galaxies should be approaching. That is, if this theory is correct, the number of galaxies approaching CAI with distance. IS THIS CONFIRMED? At very long distances few or almost no galaxies should be approaching. That is, if this theory is correct, the number of galaxies approaching DECREASE with distance from us.

The mass remains the same, but the density, to an outside observer, increases. For the local observer the density remains the same. This shrinkage should not be noticed by our instruments as the distances are not very great and the shrinkage is extremely slow. The force of gravity is not affected. But as greater the gravity is as fast is the shrinkage of space where the gravity is. Note that other galaxies, like ours, must also be shrinking due to gravity, so discounting other factors such as the potential energy lost by the photon to leave the galaxy, the frequency must be higher in the more massive galaxies, the deviation to the red smaller than less massive galaxies like nebulae. (Does this agree with observations?)

Derivation of Hubble's Law and its Relation to Dark Energy and Dark Matter João Carlos Holland de Barcellos, Jan 2019 Abstract: From the "Decreasing Universe" model [01, 02], establishing the contraction of space tissue when exposed to a gravitational field, we derive the Hubble Law and, from there, we will explain the effects "Dark Energy" and "Dark Matter". PassWords: Hubble’s Law, Dark Energy, Dark Matter, Decreasing Universe, Universe Expansion. Introduction We know from observation that galaxies seem to move away in an accelerated way. This observation was synthesized in the famous "Hubble Law" [04]. To explain this accelerated scape an entity was proposed that became known as "Dark Energy"[09]. Subsequently, it was also observed that stars orbit galaxies at a much higher velocity than calculated. As if there was much more matter inside the galaxies than the one observed. To explain this phenomenon was proposed another entity that became known as "Dark Matter" [06]. However, despite many efforts, no other evidence of both "Dark Energy" and "Dark Matter" has been found. So we are proposing a new explanation that replaces these two "dark" entities with another hypothesis: The "Decreasing Universe" Hypothesis [01]. By reducing the number of hypotheses - from two to one - we will be in agreement with the "Ocam Razor", beyond which, as we shall see, we can also derive the "Hubble Law". In the "Decreasing Universe" model [01] it is established that the gravitational field causes a space contraction that can be detected by an observer who is not subjected to such field. In this way, all objects within this space are also contracted, specially instruments of these observers. Particularly our planet is subjected, in a greater or lesser degree, to various fields: The gravitational field of the Earth itself, the Sun, the Moon, the distant galaxies, and on. If, for example, we have a measuring instrument as a scaler with the length "L" (= 1 meter), then, from the point of view of an observer who does not suffer gravitational influence, it will notice that this scaler, with the time, will decrease in size. Of course, for observers subject to these there will be no change, since all space and everything that is immersed in it is contracting at the same time so that it will have no change in the measurements made by them. For example, here on Earth, a table with 2m length, after millions of years, will continue to measure 2m, as the table shrinks in the same proportion as the measuring scaler and, locally, no difference can be observed. Outer Space However, in the intergalactic space the gravitational field is practically null, and, therefore, this space does not suffer the same contraction that we here on Earth are undergoing. Thus, in the absence of a considerable gravitational field in intergalactic space, the space between us and a distant galaxy will not contract in the same proportion as our own terrestrial space is contracting. Consider, for example, the enormous time a photon, emitted by a distant galaxy, takes to reach us. In this long period of time, which may be billions of years from the emission of the photon until it reaches our planet, our space - and our scalers - will be reduced in size compared to the original size they had when this photon was emitted under the view of an observer who is not subject to such a gravitational field. This reduction of our local space and the size of our 'scalers' will cause us to distance ourselves to the star larger than it was at the time the photon was emitted (even if its actual distance did not change in that period). Defining Some Concepts Let's call of "Local Space" (= “LS”) the region of space that is subject to a non-negligible gravitational field and thus suffers spatial contraction. Let's call of "Local Observer" (= “LO”) the observer who belongs to a “LS” and therefore subject - him and his instruments - the spatial contraction. For example, the planet Earth is an “LS” and we are “LO”. Let's call of "Outer Space" (= “OS”) the region of space that is subject to a very weak and despicable gravitational field. Let's call of "Sidereal Observer" (= “SO”) those observers locateds in this spatial region. For example, observers in the intergalactic region would be an “OS”. To clarify ideas, we may think that observers in the “OS” (= “SO”) play a role similar to an observer in an inertial frame [05] as opposed to observers located in the “LS” that would play an analogous role to observers in a non-inertial referential. Exemplifying the Concepts Consider, for example, at an arbitrary initial instant any "t0" in the “LS”, a scaler of length "L0" that an “LO” uses to make its measurements. Suppose that at this moment "t0" an “SO”, in intergalactic space, take this measure of this same “L0” scaler as the standard measure for your own measurements. Then, at time "t0", both observers (“LO” and “SO”) will consider the pattern "L0" of the same size. However, the “LS” will continue to contract in relation to the “OS”. The “LO” will not notice the variation of the scaler "L0" because both its measuring scaler and everything in his “LS” decrease in the same proportion. However, the “SO”, after a time "t" ("t"> “t0") will see the scaler of the "LO” decrease to a smaller size "L". Let us call "TJ" (Jocaxian Time) the time period (Δt = t-t0) necessary for an “SO” see the space (and the scaler) of the OL contracting at half size it had at time t0. That is, to shrink itself to a size L = L0/2 at time t0 + Tj. Before we go on let's make some simplifications. Some Simplifications Before we continue, we will consider that: - If the gravitational field is constant, the time required for the “LS” (and all that is contained in it), to contract to half its size, called TJ, measured by an “SO”, will also be constant. We will also consider that the galaxies, from the point of view of an “SO” are not necessarily rapidly moving away from each other. For simplicity we will calculate the effects of "Dark Energy" and "Dark Matter" only as a result of our gravitational contraction, keeping constant its distances (from the point of view of an “SO”). Also we will not consider the effect of time dilation [03] due to the gravitational force in the “LS” in relation to the “OS”. Local Space Contraction Formula (“LS”) We can mathematically translate the concepts we saw above into the following formula: L(t) = L0/2∆t/Tj ( E1 ) (Formula of space contraction from the point of view of an “SO”) Where: L (t) = Measure of L0 in the “LS” by a "Sidereal Observer". t0 = Initial time (arbitrary) L0 = Length measured in t=t0 Tj = Jocaxian Time ∆t = t – t0 Note that for an “LO”, L = L0 (always!), that is, the size of the scaler does not change with time in the “LS”. At each "TJ" period of time, our space (and our scales) are contracted in half (from the point of view of an "SO"). If we define : Fj(∆t) = 2∆t/Tj ( E1-B ) (Jocaxian Factor). We can rewrite (E1): L = L0/Fj(∆t) ( E2 ) We can also rewrite the same Jocaxian Factor (Fj) in a more friendly way: Fj(∆t) = exp( In(2)*∆t/Tj ) ( E3 ) “Dark Energy” Effect Of course, if intergalactic space does not contract, and if our 'scale of measurement' decrease in size, then this intergalactic space should seem to us larger, in the same proportion as our ‘scale of measurement’ contract itself. If, for example, at t = t0, we measure the distance to a galaxy "X" with our swcale of length L0, as being D0, after a time "Tj" our rule will be measuring half of its initial size L0, and therefore, when we (“LO”) measure the distance to that galaxy, we will measure it as being D = 2 * D0 We should note that a measure within our “LS” sizes do not change, as everything decreases along with our scaler and rulers, but the “OS” does not contract like our “LS”. So we will have this illusion that the galaxy "X" is moving away from us. This is what we can call the "Dark Energy Effect". Apparent Distance Formula The measured distance is inversely proportional to the length of the measurement pattern. We can synthesize this idea mathematically with the following formula (See the Appendix A😞 D(∆t) = D0 * Fj(∆t) ( E4 ) (Distance Formula with the Jocaxian Factor). Where: “t0“is the time at which the photon was emitted by the galaxy. "t" is the time at which Earth received this photon. "D0" is the distance we would measure, from Earth to galaxy at time "t0" "D(∆t)" is the distance we measured from Earth to a galaxy after “∆t”time. "Δt" = t-t0 Time period As Fj(Δt) grows exponentially with time (E3) the Earth's distance from the galaxy will also appear to increase exponentially with time. Hubble’s Law With the formula of the apparent distance (E4) we can calculate the apparent distance speed: V = d[ D(∆t) ] /dt = ( E5-A ) V = d[D0*exp( ln(2)*∆t/Tj ) ] /dt ( E5-B ) V = ( ln(2) / Tj ) * D(∆t) ( E6 ) (Distant galaxies’ apparent distance speed formula.) But Hubble's law is exactly like this: V = H0 * D ( E7 ) (Hubble’s Law) Where (H0 = Hubble’s Constant and D is the distance from the galaxy) As E6 = E7, now we can determine Tj: Tj = ln(2)/H0 ( E8 ) Substituting (E8) into (E3) we will have: Fj(∆t) = exp( H0*∆t) ( E9 ) (Jocaxian Factor in terms of the Hubble constant) What provides us: D(∆t) = D0* exp( H0*∆t) ( E10 ) (Apparent distance formula in terms of the Hubble constant) If we want to calculate the real distance from Earth to the galaxy, using the measurements that our scales had at the time the photon was emitted (at t = t0) then: ∆t = D0/c ( E11 ) (Time for a photon emitted from the galaxy to reach us, where c = speed of light) From (E11) and (E10) we will have: D = D0 exp( D0 *H0/c ) ( E12 ) (Apparent distance of a galaxy depending on the actual distance) Some Values As H0 = 2.2e-18 s-1, we can replace it in (E8) and find Tj Tj = 3.15E17 s = 10 billion years That is, the Jocaxian Time, the time necessary for our space to contract in half, is 10 billion years. We can now find the contraction rate of our space for every billion years: (Tx)10 = 2 => Tx = exp( ln(2)/10 ) = 7% That means: For every 1 billion years our space (and our scalers) are contracted 7% of their original size. It is interesting to note that this value (7%) corresponds exactly to the contraction rate calculated from the "Redshift" of the Galaxy NGC3034 [02]. Currently the apparent distance of the 'NGC3034' is about 11E6 light years, (or 1E23 meters). Applying (E12) to the galaxy NGC3034 and knowing that H0/c = 8E-27 m-1 we will have the following equation for the distance to the galaxy NGC3034: 1E23 = D0 * exp( D0 * 8E-27) ( E13 ) (Equation of the real distance of the Galaxy NGC3034) Using a solver [08] we will obtain for the real distance: D0 = 9E22 that is, this galaxy is about 10% closer to Earth than it appears to be. Dark Matter Dark Matter [06] can also be observed being an effect of our spatial contraction. As nomenclature, we will suppress the subscripts "obs" of the measurements observed here from Earth. So we'll simplify: Vobs = V ; ( Rotation Speed Observed) Dobs = D ; ( Distance Observed) Robs = R ; ( Radius Observed) Wobs= W ; ( Angular Speed Observed) Mobs = M ; ( Mass Observed) Considering the illustration: Star Orbiting a distant Galaxy Fig.1 - From Earth we observe a star rotating a distant galaxy. Suppose that from Earth we now observe a star circling the periphery of a galaxy that is at an observed (apparent) distance "D" from our planet. According to Fig. 1 above, the observed “R” radius of the galaxy will be proportional to this distance: R = sen(α) * D ( E14 ) (Orbit radius as a function of observed distance and angle) As we saw earlier, at the time the photon was emitted, the real distance would be D0, so: R0 = sen(α) * D0 ( E16 ) (Real orbit radius as a function of actual distance and angle) From (E9) and (E11) We can define the Jocaxian Factor of the Galaxy: FJ = exp( D0 *H0/c ) ( E17 ) (Jocaxian Factor of the Galaxy) So, we will have: R0 = R / FJ (E18) (Real Radius as a function of the Jocaxian factor of the Galaxy) If M is the observed mass of the galaxy where the star orbits, and V is its tangential velocity observed from the Earth, and G is the Gravitational constant of the Galaxy, we will have [07]: V2 = M*G/R (E19) (Equation of Velocity as a function of mass and radius) In terms of the angular velocity, we have: V2 = W2 *R2 (E20) (Equation of Velocity as a function of angular velocity and radius) From (E19) and (E20) we derive: W2 = MG/R3 (E21) (Equation of the angular velocity as a function of Mass and Radius) From (E21), at t = t0, we have: W02 = M0G/R03 (E22) (Equation of the angular movement in function of the Real Radius and Real Mass) The angular velocity does not change with the observed distance, since the time interval between two emitted photons is the same interval when they arrive to Earth. So: W = W0 (E23) (The angular speed is the same for an “LO” as for a “SO”) From (E20), E (22), E (23) we find: V2 = (M0G/R03) * R2 (E24) Using (E18): V2 = (M0Fj3) * G/R (E25) (Equation of the tangential velocity as a function of the Barium Mass and Apparent Radius) Comparing (E25) with (E19) we conclude that: M = M0 *FJ3 (E26) (Apparent mass as a function of actual mass) From Earth we observe a mass M for the galaxy larger than the mass at t = t0. Then the effect "Dark matter" will be the difference of M with the real mass M0: Dark Matter = M–M0=M0*( exp(3*D0 *H0/c ) – 1 ) (E27) (Dark matter equation as a function of the Hubble constant and the actual distance) Conclusions If we adopt the "Decreasing Universe" where the gravitational field shrinks the space in which it crosses, we find that the accelerated separation of galaxies, often explained by the so-called "Dark Energy" is a kind of "illusion" resulting from this space contraction and, therefore, unnecessary. The "Dark Matter", on the other hand, can also be explained by the same effect of the gravitational contraction of our space, since the radius of the galaxies is observed as greater than it really is, consequently, the speed of translation of a star is seen as above-expected with the observed baryonic mass, providing the false impression that there is an extra, invisible matter responsible for the effect. Appendix A Derivation of the Distance Formula from the Local Contraction Formula. At t=t0 we will take as the measurement standard for both observers the measure "L0", for example, L0 = 1 meter. Thus, all distances will be taken as a number that multiplies the L0 pattern; Then both observers, sidereal and terrestrial, measure the same distance to a given galaxy: Distance = D0 * L0 ( A1 ) ( D0 is the distance that is measured to the galaxy by taking the measurement pattern L0) After a time t (> t0), from the point of view of a sidereal observer, the terrestrial space shrank, and the rule tablet L0 decreased to L according to E1: L = L0/Fj(∆t) (Spatial contraction formula (E2) ) As in our hypothesis, from the point of view of the Sidereal Observer, the galaxy does not move away, the distance covered must be the same, that is: Distance = D * L ( A2 ) (D is the measured Distance to the galaxy according to the L pattern, by the Terrestrial observer) We must keep in mind that for the local terrestrial observer, L=L0, since he does not perceive his own contraction). From (A1) and (A2 )we have to: D0*L0 = D*L ( A3 ) (From the point of view of the sidereal observer, the distance is not altered) Using (E1), we have finally: D = D0* Fj(∆t) ( E4 ) (Measured distance to the galaxy according to the terrestrial observer, as a function of time) References [01] The Gravitational Field and the Dark Energy https://ijrdo.org/index.php/as/article/view/1311 [02] The Equivalence Principle and the End of the Dark Energy http://www.ijera.com/papers/Vol7_issue1/Part-1/C0701011314.pdf [03] Gravitational time dilation https://en.wikipedia.org/wiki/Gravitational_time_dilation [04] Hubble's law https://en.wikipedia.org/wiki/Hubble%27s_law [05] Inertial frame of reference https://en.wikipedia.org/wiki/Inertial_frame_of_reference [06] Dark Matter https://pt.wikipedia.org/wiki/Dark_Matter [07] Orbital Speed https://en.wikipedia.org/wiki/Orbital_speed [08] Solver for Equations https://www.mathway.com/Algebra [09] Dark Energy https://en.wikipedia.org/wiki/Dark_energy

Hubbe_derivation2.pdfHubbe_derivation2.pdf You can read it here too : https://www.scirp.org/journal/paperinformation.aspx?paperid=91689 Hi ! A few years ago I developed a theory that explained the accelerated receding of galaxies and its rapid movement of rotation of them without the need to postulate the existence of "Dark Energy" and "Dark Matter" respectively. ( The theory link: https://www.scirp.org/journal/paperinformation.aspx?paperid=91689 ) I thought my idea was a good one as I used fewer hypotheses than these two "dark" entities. However, I knew that it could be one of dozens (or hundreds) of theories that try to explain these "dark" elements that, until now, still do not have concrete evidence, in addition to those used to explain the movement of galaxies. Roughly speaking, my article says that if our local space is shrinking (due to gravity) then we will see the distances increasing. For example: If our scale measures 1 meter and, after a long time, it starts to measure half a meter, a galaxy that was X meters away will now be measured as 2X meters away. So, in my article I verify that the rate of "shrinkage" of our space was 50% every 10 billion years. And that would explain the "dark energy" effect. However, without evidence, my article was in danger of being just one among so many other dropouts in cyberspace. Subsequently, searching the web I find something for me quite promising: 1-"Universe mysteriously expanding, will double in size in 10 billion years, finds Hubble" https://www.indiatoday.in/science/story/universe-expanding-mysteriously-will-double-in-size-in-10-billion-years-finds-hubble-1951827-2022-05-20 Which was exactly the evidence I was hoping for, that's exactly what my theory predicted: ["...Some Values ??.... Tj=3.15E17?s = 10 billion years That is, the Jocaxian Time, the time necessary for our space to contract in half, is 10 billion years..."] So, now my theory had another strong evidence in its favor 2-Then I find other one, like increase in temperature due to space shrinkage: Unexpectedly, The Universe Is Getting Hotter and Hotter as It Expands https://www.sciencealert.com/the-universe-is-getting-hotter-and-hotter-new-study-finds Thank you ! Joao Carlos