The expansion of the universe can be explained by General Relativity using the Friedmann-Robertson-Walker metric, which contains a scale factor a(t) that determines the size of cosmos. Upon solving Einstein's field equations for ordinary matter (eg. dust), the scale factor is found to increase as t to the two-thirds power. Thus, GR predicts the universe expands from a point, called the big bang, and its expansion slows down with time. This solution does not involve pressure, as dust is assumed to be pressureless.

However, in the 1990's it was discovered through Supernova Type Ia observations that the expansion of the universe is not slowing down, but is accelerating. Cosmic acceleration at first appeared to contradict GR. A number of modified gravity theories have been proposed to explain it, but none have gained general acceptance. The most favored theory today is the Lamda-Cold-Dark-Matter (LambdaCDM) model, whereby cosmic acceleration is described by adding a cosmological constant Lambda to Eintein's field equations. This constant is often interpreted as "Dark Energy", a phantom substance with pressure equal to minus the mass-energy density. The model has a number of outstanding problems, and is the subject of ongoing research.

Dear P. K. Karmakar ,

Nobody knows the answer to your question, but, I have given a possible detailed answer in the Daon Theory ( see my profile).

JES

Dear P. K. Karmakar,

In my opinion, if the universe has hyperspheric form, its expansion is due to simple centrifugal force

Preprint ALL SPECIAL RELATIVITY EQUATIONS OBTAINED USING GALILEAN TRA...

Besides, it fits perfectly with the difficulty of measuring this expansion (it does not expand equally) and with the latest trends of grouping zones according to their density to calculate the Hubble constant.

The expansion of the universe can be explained by General Relativity using the Friedmann-Robertson-Walker metric, which contains a scale factor a(t) that determines the size of cosmos. Upon solving Einstein's field equations for ordinary matter (eg. dust), the scale factor is found to increase as t to the two-thirds power. Thus, GR predicts the universe expands from a point, called the big bang, and its expansion slows down with time. This solution does not involve pressure, as dust is assumed to be pressureless.

However, in the 1990's it was discovered through Supernova Type Ia observations that the expansion of the universe is not slowing down, but is accelerating. Cosmic acceleration at first appeared to contradict GR. A number of modified gravity theories have been proposed to explain it, but none have gained general acceptance. The most favored theory today is the Lamda-Cold-Dark-Matter (LambdaCDM) model, whereby cosmic acceleration is described by adding a cosmological constant Lambda to Eintein's field equations. This constant is often interpreted as "Dark Energy", a phantom substance with pressure equal to minus the mass-energy density. The model has a number of outstanding problems, and is the subject of ongoing research.

Self-gravity doesn't exist at this scale of cosmos.

Here is a non-technical but an idea based answer that is supported by Hubble's law.

The accelerating expansion of the universe is due to another fundamental force called Dark Gravity. This means variation of space-time field points in such a way that the points are farthest at the center of the universe and getting closer as one moves towards the edges. Consequently, gravitational constant tends to change and a point comes where spacial point and temporal point collapses. Hence, favors the big bang at the center but denies the big crunch near the edges.

Thus, galaxies speed up to faster than the speed of light near the edges and the total expansion theory comes into play causes nothingness of everything near the edges.

This also implies the universe to be more than what we observe.

Dear Khalid Ansari Universe does not act mechanically, the Universe is a Quantum Mechanics phenomenon. Universe like anything in it, it is growing by its nature, as it is growing new galaxies are born. Think of an apple tree, as it is growing new apple produce. Apple tree is getting its nitration from outside of its body, the universe is acting similar to this apple tree.

Space-time of GTR is not working with any solar system neither with ours, and spacetime is just a mechanical theory for one galaxy universe, while our universe has billions of galaxies and it is expanding rapidly.

And Gravity is not mechanical either, a mass can not create any gravity, i.e. if the earth had gravity, do you think the earth would let the mass of water goes up?

We have to think out the box, GTR is not working.

https://www.academia.edu/38373675/Creation_of_a_Quantum_Mechanic_Universe_and_its_Rotation.doc

Article Gravity is an Internal Force

Per the General Theory of Relativity, mass causes space-time to curve in a positive direction, causing what we perceive as gravity (namely, things get closer together in the future than we would expect if there were no force acting on them), while the absence of mass causes space-time to curve in a negative direction, causing what would be called anti-gravity if some thing were causing the effect (namely, things get further apart in the future than we would expect if there were no force acting on them.

In this scenario, some place in empty space will either move toward objects or away from them, depending on the overall ratio of mass to empty space within the region near it. If the mass in a given region is big enough (as it is in planetary systems, stellar systems, galaxies and clusters of galaxies), things will move relative to each other according to what we would consider the force of gravity between them. But if the mass in a given region is too small in comparison with the amount of empty space, then things will move further apart, at a more or less constant rate per unit of space. At the time that Einstein predicted this, the Universe as we know it was not know to exist -- only a part of the Milky Way galaxy was thought to be the whole Universe -- and it is neither collapsing under its own gravitational force, nor expanding, so he presumed that somehow, the ratio of mass to empty space must automatically balance, using the constant capital lambda to account for that result. But once Slipher showed that most galaxies were moving away from us, and Hubble and Humason showed that the further a galaxy was from us the faster it was moving away from us, everyone (especially Einstein) realized that the mass of the Universe must not be large enough to balance the amount of empty space, and so the Universe is expanding at a more or less constant rate (constant in terms of being about the same in every part of space) at a given period of time. As it turns out that rate is NOT constant over time, because early on there wasn't as much empty space as now, so the ratio of mass to space was larger, and mass was actually slowing the rate of expansion for the first 8 billion years or so of the Universe's existence. But about 6 billion years ago the amount of empty space had become so great that the amount of mass was no longer adequate to slow the expansion and as the Universe continued to grow and the ratio of mass to empty space continued to decrease (it is currently only about 27% of the "balance" or "critical" value), the expansion slowly increased. My expectation is that it will asymptotically approach a value not much bigger than now over the next umpteen billion years (not much bigger than now because 27% of the "critical" mass is already far closer to zero than to the "balance" point).

The way this works is that on the average, for every Megaparsec (3.26 million light years), more or less empty space expands at about 70 km/sec (the actual value is somewhere between 67 and 73 km/sec/Mpc, but 70 is the average of that range, and I've been using it ever since I was working on the distribution of galaxies and clusters of galaxies with George Abell back in the 1960's, and have never seen any reason to change the value). Objects that are about 10 megaparsecs (32.6 million light years) away from us have a tendency to move away from us at about 700 km/sec, give or take a few tens or hundreds or km/sec due to their "peculiar velocities" (their motions relative to their neighbors, independent of the overall expansion of space). Within that distance, the peculiar velocities are large enough that the recessional velocity relative to the Cosmic Background Radiation (which is the most fundamental way of determining the rate of expansion) does not necessarily correspond directly to their distance. But once you get to a distance of 100 megaparsecs (about 326 million light years), the Hubble Flow, as it is sometimes called, is about 7000 km/sec, which is far larger than the peculiar velocities of any galaxy, even galaxies inside rich clusters of galaxies, where peculiar velocities of a thousand or so km/sec can be caued by the enormous mass and gravity of the cluster. As a result, at such distances and all distances beyond that, the recessional velocity relative to the CMB is a very good indicator of the distance of a galaxy or cluster of galaxies, and by the time you get to about 4000 Megaparsecs, the recessional velocity due to the cumulative expansion of 70 km/sec/Mpc for every one of those 4000 Mpc is 280 thousand km/sec, or nearly the speed of light; and not much beyond that the cumulative recessional velocity becomes equal to or even larger than the speed of light, so that at some point, no light from such distant regions can reach us.

Note that in this discussion there is absolutely no mention of any kind of force, thermal pressure, or any other method of causing space to expand. It is just "natural" for large amounts of sufficiently empty space to expand, and that is all that the Universe is doing, or will ever do, for the rest of eternity (not that any of us or any of our descendants will be around long enough to see anything significantly different than what is going on at this exact moment in the history of the Universe).

Dear Courtney,

GR does not work like this, if you have 0 in the energy-stress tensor you have 0 in the Einstein tensor, regardless of whether or not you add the cosmological constant. Eliminating that constant causes the universe to expand, as Kathleen points out (with the buts that she mentions) but there is no anti-gravity by mass 0

Dear Sir! Javad Fardaei I'm in support of the quantum mechanical aspect of the universe. But this doesn't mean its classical mechanical aspect is wrong. Indeed, GTR needs to be revised but its space-time field theory can work at quantum foam level. I'll go through the paper you referred to and will try to come up with a better answer.

Thank you, sir.

Dear All,

A bad theory must make ad hoc modifications every time it collides with reality (standart model, LambdaCDM, etc).

A good theory is capable of predicting reality before it is known.

Here is the study that I commented before that points out that the expansion of the universe is not homogeneous

https://doi.org/10.1016/j.physletb.2020.135303

And knowing how the "science" of journals works, we will soon have more publications in that direction and more modifications in bad theories.

Sergio Garcia Chimeno ,

Thank you for sharing the article on "Consistency of the local Hubble constant with the cosmic microwave background," which brings us up-to-date on an important subject.

Dear Nancy Ann Watanabe ,

You are welcome :)

But remember that the only way we have to know the truth is through the scientific method.

And that journals currently do not follow the scientific method and have become a fraud, they should be taken with caution

Dark energy seems to accelerate the expansion of the Universe but only at the inter-galactic scale i.e. only the galaxies are moving further to each other. Within a galaxy, the stars are not moving further apart as gravitation between them seems to counter the effects of dark energy.

The universe, or all that is, is energy, the fastest form being light, to which all else/all other forms are therefore self-similarly relative, or fractal, and which also naturally follows the shortest path at the ultimate rate of the golden ratio: linear in 1D or c=1 (vacuum; dark energy); orthogonally in 2D or c-squared, c²=electromagnetism; and geodesically in 3D. A geodesic (or rugbyball shape; cf. Grigory Perelman's Poincaré conjecture solution) consists self-similarly, transversely of parabolic and longitudinally catenary conics, in turn consisting of spiraling ellipses (2D) per a primes distribution (cf. Ulam spiral; Riemann hypothesis) radii of space.

So as light overall travels its shortest path geodesically, it therefore travels, at its fastest, longitudinally along the major axis, relatively linearly (1D) c=1 before, at h or Big Bang, reaching transversely the minor axis, where light's linear speed c slows to c times c, c-squared (2D area), aka orthogonal electromagnetism, other quanta, atoms, molecules, DNA, brains, planets and galaxies -- all being light c AND c² (matter=stored or minor axis slowed, gravitational energy) at the self-similar or fractal expansion/contraction rate of the prime numbers distribution asymptotic with the golden ratio (continuous fraction) limit, or linear c=1 Black Hole again, following respective entropies at respective minor axis apexes.

The universe either is a ball of energy and matter, subject of gravitational or pressure forces, or it is a hypersphere.

Currently, we did not even reach a common understanding about the energy density of the gravitational field, but nevertheless we are speculating about dark energy.

Here are three basic facts, usually leading to vigorously contradictionary discussions:

1. The gravitational field energy is proportional to the square of the field strength

2. The modification of the energy of the gravitational field around masses is exactly equal to the mechanical energy of the movement of the masses, which caused the modification of the gravitational field.

3. The energy density of the gravitational field around masses is negative.

Energy density is distributed by the fastest (least action) curvilinear path that as mentioned and as is known the fastest energy, light, travels. That path or distribution of energy density is 2D elliptical, or 3D geodesic, and 1D relatively linearly c=1 (dark energy) along the longitudinal major axis before, at h or the Big Bang, transversely along the minor axis, the visible universe, slowing to c² (c times c) aka c-squared or orthogonal electromagnetism, the visible universe, self-similarly (output as input; Riemannian zeta function) forming other matter (slowed, conserved, stored energy), namely quanta, DNA, planets, galaxies, their respective entropies at respective apexes distributed along the parabolic curvature of this geodesical minor axis and returning linearly to c=1 (if not 0, a dimensionless point, the Black Hole) to begin again. Overall therefore, as energy follows such curvature, a fractal (Mandelbrot set) figure 8, Mobius Ulam spiral or primes distribution of the energy density of the universe results, the limit of which goes to phi, c=1, uniting general with special relativity, consistent as well with Grigory Perelman's Poincaré conjecture solution.

Dear Thierry De Mees

You are right that quasar redshift remains a mystery. The renowned observational astronomer Halton Arp has written books on quasar redshifts and their association with active galaxies, in particular the book "Seeing Red", which makes a very good case. Both Margaret and Geoffrey Burbidge , the discoverers of quasars, agreed with Arp. Alas, Geoffrey Burbidge, according to insiders, was fired as Director of Kitt Peak National Observatory in the 1980's because he thought quasars were local, a very unpopular idea at the time. Arp was similarly forbidden to use the Palomar telescope, and had to rely on Margaret Burbidge to do his observations.

I suspect quasar redshift has a different origin from cosmological redshift. I am not sure though that the latter can be explained by intervening hydrogen, as that should cause scattering and therefore blurring of the distant cosmos, which is not observed. As for Dark Energy, I am now writing a paper that proves Dark Energy is impossible according to Einstein's field equations, and that cosmic acceleration is only explained by a cosmological constant LAMBDA. That is, of course, if general relativity is right.

Remaining 'mysteries' make for great research funds.

Dear Stefan Rüster

I have just looked over your paper and it deserves more study. It seems coincidental that I am currently working on a paper to prove dark energy is inconsistent with the Friedmann-Robertson-Walker metric, and that the cosmological constant is necessary to explain dark energy. I have also found, however, that dark energy is consistent with a STATIC cosmological metric, but only for very late times.

Yes, an orange slice is redundant because it's part of the whole orange, not.

Correct me if I'm wrong.

Dear Stefan Rüster ,

Dark energy arose from trying to explain the velocity of stars at the ends of the galaxy since in that case Einstein's equations failed, his introduction to the expansion of the universe is later.

The addition of the cosmological constant was intended to make a static universe (it expands without it, although I think it does not accelerate) interpreted as energy in a vacuum (something that I consider highly debatable) the expansion accelerates, correct? Isn't that constant already considered as dark energy?

Dear Kathleen Rosser ,

The wave equation can have several solutions, but the wave will be triangular, square, sinusoidal, etc., but not all at the same time.

Einstein's equations have several solutions, why is a solution used each time as is convenient for us? shouldn't the universe have just one shape?

See Grigory Perelman's Poincaré conjecture 3D solution for the rugbyball shape of the universe, eliminating singularities by continuously pinching Ricci curvature in GR to dimensionless points (0, 0, 0, 0).

Dear Stefan Rüster

Correction to an error in my statement above, "the cosmological constant is necessary to explain dark energy." I had meant to say "the cosmological constant is necessary to explain cosmic acceleration." Dark energy is redundant, as you point out. A constant "dark energy" density with an equation of state p=-rho plays exactly the same mathematical role as Lambda in Einstein's field equations.

I have also found that "dark energy" contradicts a necessary premise of the FRW metric. To wit: in order to solve the Friedmann equations for an accelerating scale factor a(t), it turns out "dark energy" must expand more slowly than the rest of the universe, or even "stand still". This would mean that a major source of matter-energy in the universe would not be co-moving, and the FRW metric would no longer be valid. It is also contradictory to equate Lambda with energy, for the same reason. So I agree that Lambda should not be considered "vacuum energy", nor any kind of material energy. If it is "energy", it must be the energy due to the structure of spacetime itself. (Lambda must stay on the left side of the equation!)

I'll have to read your paper further to understand your statement, "Lambda is proportional to the total energy density of the metric under consideration."

Dear Sergio Garcia Chimeno

Yes, the universe should have one shape. Unfortunately, Einstien's field equations are difficult to solve in general, and we must make limiting assumptions about symmetries, homogeneity, etc. to get any solutions at all. So the solutions we get tend to be convenient for us, and may not precisely describe the universe. That is one reason cosmological theory is not completely settled. An example of disagreement, some researchers show that dispensing with a homogeneous universe enables us to account for cosmic acceleration without a cosmological constant. Other researchers are looking for new equations beyond Einstein's field equations.

Dear Kathleen Rosser ,

Perfect, and why don't we do it the other way around?

If the wave equation can be obtained with a sine wave, it would be logical to think that only with the form of the universe can the Einstein equations be obtained, right?

And if that form also responds to any "uncomfortable question" such as that it is beyond the universe limits, that it existed before time, etc. To any question you can imagine.

Maybe that's the authentic form then, right?

Dear Stefan Rüster ,

What I meant to say is that Lambda is currently considered as dark energy, so I don't understand using Einstein's equations with Lambda to prove that dark energy is not necessary.

Unfortunately I can not argue better, I do not have the relativistic knowledge from the Lagangrian point of view to follow your preprint, probably you have already taken that into account and I do not see it

Dear Stefan Rüster

I studied your paper Deleted research item The research item mentioned here has been deleted

more closely and enjoyed reading it. The math certainly looks correct, your argument is quite elegant, and your conclusion---that Lambda represents conserved cosmic energy---rather compelling. In a realistic universe, there would be a hierarchy of "embedded" metrics, with the perfect fluid star interior metric joined to an outer Schwarzschild metric (as per solar system observations), which in turn would be embedded in a galactic metric, which then joins the FRW metric at the turnaround radius. The galactic metric remains the unsolved link in astrophysics. To my knowledge, no relativistic metric has been found that describes the galactic rotation curve without dark matter. But that's another story.

The 3D conical (1/2 Minkowski or Hilbert space) galactic curve is also in turn "embedded" self-similarly fractal within Grigory Perelman's Poincaré Conjecture solution (using Ricci curvature in GR) for ultimately overall (non-relativistically) a rugbyball (whole Minkowski or Hilbert space) shape of the universe, the absolute maximal limit (uni-=1) where all astrophysical and other objects live, visible from the outside or at the speed of light c=1 as linear or flat (Einstein imagined), the Black Hole, one and the same with the seemingly elusive dark matter. Missing link found.

"One and the same," thank you for reading.

Dear Stefan Rüster

I'm interested in your superposition method. Metrics in GR can't be superposed per se. However, static concentric metrics of the form g00=1+phi (where phi/2 is sometimes called the "potential") obey a superposition law in that the potential terms from different metrics add. Examples include the Schwarzschild-de Sitter metric and the Reissner-Nordstrom metric. This superposition principle is elegantly proven by VV Kiselev in his article Quintessence and Black Holes (2002, also published in Classical Quantum Gravity 2003). Does this relate at all to your idea? Kiselev's article may be found at

https://arxiv.org/pdf/gr-qc/0210040.pdf

Dear Stefan Rüster

As stated in my paper "Current Conflicts in General Relativity: Is Einstein's Theory Incomplete?" , there are no gravitational potentials in GR, as you say. This is why I was careful to word my reply above as, "where phi/2 is sometimes called the 'potential'", with "potential" in quotes. This term is indeed sometimes called the potential by prominent physicists, a slight misnomer, but simply to make linguistic reference to the term.You had mentioned superposing metrics in a reply above. My last response was an attempt to clarify. Since metrics do not superpose per se, I thought perhaps you meant you were superposing the "potential term" as it were, which is rigorous as shown by Kiselev. Apparently not.

Re galaxies: I have looked at your updated paper, and while it is true that adding an r-squared term gives an approximation to the galactic rotation curve, as various physicists have noted, this does not match the data well enough to have gained general acceptance. See for example the work of Stacy McGaugh.

Dear Stefan Rüster ,

I insist again, it seems to me (although I would have to investigate more) that Lambda is currently considered dark energy, if you show that the universe expands thanks to Lambda you are demonstrating something already known. If you want to demonstrate that dark energy is not necessary, you must remove Lambda

Dear Stefan Rüster ,

Lambda is necessary to explain the accelerated expansion of THE FORM our universe.

We must stop thinking that the universe is flat, it doesn't make any sense.

Without Lambda, without dark energy, Einstein's equations already predict an expansion (not accelerated). But it would be necessary to calculate if that expansion can accelerate the distances on the surface of a hypersphere (the most probable form) and as I said at the beginning of my answers it would be explained by simple centrifugal acceleration.

If Lambda exists it implies a curvature (gravity) in a vacuum and implies that Einstein's equations cannot approximate Newtonian gravity.

The energy density of the entire universe already appears in the Stress-Energy tensor if you use the entire energy density of the universe. Reappearing as a constant multiplied by the metric tensor would imply changes in that Stress-Energy tensor

I add that as I commented in a previous answer, I very much doubt that the universe expands equally (what Lambda does)

Universe is BOTH dark energy, the flat portion of lambda or linear, black hole c=1 AND parabolically-curved lambda c², c times c, or c-squared (orthogonal electromagnetism at h or the big bang), our relatively physically visible universe, which taken together complete a shape of a rugbyball (cf. Grigory Perelman's Poincaré conjecture solution). Arguing past each other for one or the other makes for imperishable publishing, but remains no different than two blinded scientists claiming an elephant is either smooth or rough, or Schrodinger's cat is alive or dead. If you triangulate in 3D or zoom out far enough on any life, dynamic or growth phenomena, you will then see the state to be both alive and dead in THAT scaled timeframe; both smooth and rough; both a flat Gaussian outlier tail and bell-curved lambda; both discrete and continuous; both the train passenger and platform observer; both particle and wave simultaneously.

First of all there is no such thing as “Universe expansion”. The FLRW metric is a tool to demonstrare spatial expansion for comoving observer. The FLRW metric is just comoving form of the SdS metric (in static case). Therefore, the space expansion is the same phenomena as central gravity. Please check the articles by Mitra, also some on my profile..