The XXI century cosmology

The global description of the observable Universe that we have today motivates the review of gravitation (Huterer & Shafer 2018; Debono & Smoot 2016; Genova-Santos 2020; Riess 2019, Trippe 2014) and the postulation of new theoretical alternatives. Particularly interesting could be generalizations consistent with experimental data, astronomical observations, and the well-proven formalism of existing theories. This is the case of the proposed potential U_YF , which is a heuristic construction useful to modify the Newtonian inverse-square law. The origin of this hypothetical U_YF field is only the ordinary baryonic matter and represents the inertia due to the distribution of matter on a large scale, incorporating the Mach principle into the formalism. The proposed potential allows a local variation of gravity depending on the range of the distance as shown in figure (2). It is consistent with the observations and leads to several important consequences:

The inverse square law of Newtonian gravity implicitly assumes a null mass for the graviton and an infinite range of gravitational force, which contradicts the finiteness of the observable universe and the existence of gravitational waves. If local inertia is somehow linked to the large-scale distribution of matter in the Universe (Mach`s Principle), then the inverse square law is insufficient to describe it. Also it´s cannot explain the rotation curves of galaxies, neither the missing mass of Zwichy, and is not enough for to explain the observed baryonic matter density in cosmological scales. So in LFRW cosmological models to appear the paradigmatically concept about non baryonic Dark Matter (cold dark matter).

By other hand, using the Boltzmann distribution, the calculus of the mean energy per nucleon during the surface of last scattering, leads to at complementary contribution to the Newton gravity. This inverse Yukawa-like field (U_YF ) would be caused by distribution at great scale of the baryonic mass, in the sense of Mach's principle. This U_YF -field result: null in very near solar system, slightly attractiveness in ranges of interstellar distances, very attractiveness in distance ranges comparable to galaxies cluster and repulsive to cosmic scales

The consequences of adding a U_YF -field as a large-scale contribution of Newtonian gravity (Falcon 2011, Falcon 2013, Falcon 2021) implies that:

1. All particles with no null rest mass are subject gravitational inverse-square laws, plus an additional force term that varies with distance, caused U_YF -field. At large distances from the sources, the reduction in the Newtonian field would be complemented by an additional interaction component that is grows at much greater distances.

2. This U_YF -field depend of comoving distance: null in the inner solar system, weakly attractive in ranges of interstellar distances, very attractive in distance ranges comparable to the clusters of galaxies and repulsive to cosmic scales.

3. The minimum of the potential energy of the U_YF -field, located at the order of the comoving distance of 10Mpc implies the nullity of the force of gravity, and consequently predicts a graviton mass of at least 10-64 kg.

4. Also the Force (FIY) supplementary to Newtonian gravity would reach a maximum for distances of the order of 1.2 Mpc, favoring the agglutination of matter in galaxy clusters, and would be evidenced as a maximum in the redshift volume density distribution around z = 2 (fig. 3)

5. The inclusion of the large scale term of the gravity, remove the incompatibility between the flatness of the Universe and the density of matter in the Friedmann equation, without invoking the non baryonic dark matter (28).

6. The usual cold dark matter parameter (Wc) would be, the gravitational contribution caused by the large scale distribution of the ordinary baryonic matter thought the U_YF -Field (32).

7. The cold dark matter could be interpreted as the gravitational contribution caused by the large scale distribution of the ordinary baryonic matter:

8. The dark energy would results to be the cosmic acceleration in local frameworks, caused by the large scale distribution of the ordinary baryonic matter, as prescribed the Mach's principle, through of the U_YF proposed (32)

9. The Hubble-Lemaître’s law would be the manifestation on a cosmic scale of the U_YF field, with theoretical expression as in (34). The theoretical upper limit, evaluated for the most distant objects (r>>50 Mpc) would be 86,3 kms-1Mpc-1 .

10. The age of the universe would not be much older than τ ~ 11.42 Gyr, in good agreement with direct WD-Cosmochronology.

11. The Virial theorem and Kepler’s third law now including an additional term (FYF) that solve the Zwicky’s paradox, so the “missing mass” is reinterpreted as the energy of the U_YF -field, and rotation curves of galaxies problem could be modeled similarly to the Milgrom models.

12. The comparison between Newtonian forces and that associated to the U_YF results in: both forces would be comparable in the 15-40 kpc intervals, being able to explain the missing mass in the rotation curves. Inside galaxy clusters, the force is proportional to the inverse of the comoving distance (Fig. 8).

13. The U_YF provides an additional contribution for the gravitational redshift (59) that increase the until an factor of ~8, it´s solvent the Arp’s controversy, and would help understand the problem of AGN at High-redshift and the nature of Quasars.

14. The inclusion of the U_YF -field leads to a reduction in the calculation of the angle of deflection of the gravitational lensing so the deflecting mass at long distances would have been underestimated by a factor of three, without affect the deflection in total eclipses of sun

15. The modification of the Newtonian gravitation on a large scale does not affect the Jean’s length in ranges of comoving distance less than 100 kpc (Fig.11). but the Jean’s length results 40% less at distance ranges of Mpc, which coincides with the agglutination of hot gas in X-rays galaxies clusters.

16. The energy density of the universe must increase due to the graviton's rest mass, which is incorporated through the U_YF field in Friedmann's equation (26). Consequently, the critical density no longer corresponds to the Einstein-de Sitter model, which lacks a material basis.

17. The U_YF reduces the angular diameter distance for all z-values with a maximum in z≈2, in angular diameter distance distribution.

18. In range of comoving distance of the megaparsec, the Jeans Mass decreases then a perturbation will collapse even further when compressed, leading to run-away collapse of the protogalaxies..

19. The large-scale modification of Newtonian gravitation given an identical result for BAO as the paradigm of cold dark matter, by the arithmetic identity: : Ω_m=Ω_b+Ωc= Ω_b(1+Ω_YF) ; but it does not require assuming the existence of non-baryonic exotic particles

20. The CMB and primordial nucleosynthesis remain unchanged by a large-scale modification of Newtonian gravity, such as the U_YF -field discussed here.

Regardless of whether the U_YF -Field is exactly the one proposed here or not, is that, perhaps, to understand the dynamics of the universe, we would have to abandon the assumption about the universal validity of the inverse square law of Newtonian gravity, assumed uncritically, instead of conjecturing unobservable exotic matter.