UPDATE October 11, 2021: our model predicts anisotropy in redshifts on different sides of the sky, because we probably are not at the center of the expanding explosion cloud in the Minkowski space.
Something like that has been observed:
"The supernova data indicate, with a statistical significance of 3.9, a dipole anisotropy in the inferred acceleration (see figure) in the same direction as we are moving locally, which is indicated by a similar, well-known, dipole in the CMB."
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Under less-than-extreme conditions it may be impossible to distinguish our new special relativity & newtonian model from the geometric interpretation of general relativity. It is just a mapping of the Minkowski geometry, under the effect of all fields, to a geometry of general relativity under the effect of all fields except gravity.
Extreme conditions happen in black holes and in cosmology. The predictions of the different models may be distinguishable there.
The FLRW metric is very simple. A spatial slice of the universe is simply the 3-dimensional surface of a 4D sphere. There is a uniform distribution of matter in that spatial slice.
Can we embed something like a part of the FLRW metric into an asymptotically Minkowski space?
We certainly can simulate the expansion of the visible universe with an ordinary newtonian explosion. An observer at the center of an expanding cloud sees a redshift which depends approximately linearly on the distance of the object which is receding.
Dark energy is actually evidence against the FLRW universe. The model has been patched together through speculating a cosmological constant Λ which accelerates the expansion.
In an ordinary newtonian explosion, the far edges of the expanding cloud start to slow down because of gravitation. We should observe a surprisingly small redshift in faraway stars.
That is what we actually are seeing. There is a surprisingly high redshift in near objects closer than some 5 billion light years from us. Or the redshift in faraway objects is surprisingly small.
Could it be that dark energy is evidence for Minkowski cosmology?
One of the weaknesses of general relativity is the singularity at the birth of the universe. In Minkowski cosmology we might be able to avoid such singularity.
Note that the Big Bang is not exactly like a black hole collapse run backwards. Entropy decreases with time if we reverse time. Also, the radiation goes in the wrong direction. The baryonic matter content may be the same, whether we run a collapse or an explosion, but the radiation is different.
The Vaidya metric describes a star which is emitting or absorbing radiation.
Energy non-conservation in the FLRW model
As the universe expands in the FLRW model, photons get redshifted and lose energy. Where does this energy go?
In the Minkowski model, photons lose energy when they climb up from the side of potential well of the exploded matter. There is also an illusion of lost energy, when an observer absorbs a photon which was sent from a faraway galaxy which has a large redshift. But there is no loss of energy if measured by an inertial observer in the asymptotic Minkowski space.
We see that Minkowski cosmology solves the problem of energy non-conservation in general relativity.
A supernova is a mini Big Bang
A large explosion requires a lot of energy which is in a low-entropy state, and can suddenly escape to a higher entropy state.
A supernova is such an object. It can also be regarded as a mini Big Bang, because new stars and planets will form from its explosion cloud of gas and dust.
Scientists living inside the explosion cloud might think that they are inside an expanding FLRW universe. When gravity slows down the outer fringes of the cloud, the scientists might be led to believe that dark energy has created a cosmological constant Λ. Later, very accurate measurements would reveal that the redshift is not the same on different sides of the cloud. That is the result of the scientists not being at the center of the cloud.
Dark energy is a symptom that something is happening to the uniform expansion of the cloud. In the FLRW model, people interpret it as a sign of an accelerated expansion.
If Minkowski cosmology is correct, we are starting to see deceleration at the edges of the explosion cloud. The diameter of the explosion cloud might be only 10 times the diameter of the observable universe.
Expanding balls in an asymptotically Minkowski space, and the cosmic microwave background
An expanding ball of dust in newtonian gravity is an analogue which is used to teach the FLRW universe to students.
Valerio Faraoni and Farah Atieh have written a review article of expanding balls in general relativity. It turns out that some solutions of an expanding ball do have the FLRW metric inside the ball, and the Schwarzschild metric outside the ball.
The Oppenheimer-Snyder collapsing star, time-reversed, is a well-known model of an expanding ball.
What about the cosmic microwave background? We are seeing radiation whose intensity is uniform with a precision 1 / 100,000 in every direction of the sky.
Let us reverse time and treat the expanding ball as a collapse. Let an observer inside the ball point a flashlight at some direction in the sky.
If the ray of light ends up in the final hot and dense state of the collapse, then the observer in the expanding ball at the same point of spacetime would see hot gas in that direction. He would interpret it as the cosmic microwave background.
If the flashlight is inside the Schwarzschild radius in the collapse, then the light will end up in the singularity. However, if the observer is standing on the surface of the collapsing ball, the light might never meet the hot gas state. On what condition the light will meet hot gas?
The FLRW model probably solves this question. In FLRW, the spatial metric of the universe has grown 1,100-fold since the hot gas phase. In the CMB we are seeing a hot gas shell whose radius was around 60 million light years at the time when the light was emitted. If an expanding ball mimics the FLRW metric well enough, then our position at the epoch of the hot gas must have been at least 60 million light years inside the expanding ball.
In the FLRW model, the size of the universe can be arbitrarily large. In the expanding ball model, the ball probably can be arbitrarily large.
Question. Can we make the expanding ball such that the metric explains the redshift measurements that people interpret as "dark energy"?
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