An alternative to the ΛCDM model in modern cosmology is the model of the rotating spase of the Universe :

"ROTATING SPASE OF THE UNIVERSE, AS A SOURCE OF DARK ENERGY AND DARK MATTER."

https://hal.archives-ouvertes.fr/hal-01329145v1

Evidence presented in preprint:

"Analytical evaluation of the numerical values of the Hubble constant and main spatial-energy characteristics of the observable Universe."

https://hal.archives-ouvertes.fr/hal-02045149v2

Main evidences:

1. The vacuum pressure in all points of the Universe is constant. To expand the space required the pressure drop.

2. The source of dark mass is the kinetic energy of rotation of the space of the observable Universe. Elementary particles of dark mass does not exist. Therefore, numerous experiments for several decades in their search did not give a result. Prediction: these particles will not be detected in future experiments at the Large Hadron Collider.

3. The preprint gives an analytical estimate of the Hubble constant based on the characteristics of elementary particles. Consequently, this constant is an immanent property of the observable Universe. It cannot be a characteristic of dark energy.

4. Modules: the forces of Planck, the forces of gravitational compression of the observable Universe and the imaginary forces of dark energy are equal to each other. But there is a red space from distant objects of the observable Universe. This is possible only if its space rotates.

5. The Hubble Sphere, as the observable Universe, is located inside the Schwarzschild Sphere. Hence the observable universe is a black hole.

6. The observable Universe, like an electromagnetic fractal of the Universe, is a slowly rotating black hole in a gravitational fractal of the Universe: "FRACTAL STRUCTURE OF THE UNIVERSE." https://hal.archives-ouvertes.fr/hal-01330337v1

Since the Big Bang, one incomplete rotation of 345 degrees has been made.

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