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We attempt to find new symmetries in the space-time structure,leading to a modified gravitation at large length scales,which provides the foundations of a quantum gravity at very low energies. This search begins by considering a unified model for electrodynamics and gravitation,so that the influence of the gravitational field on the electrodynamics at very large distances leads to a reformulation of our understanding about space-time through the elimination of the classical idea of rest at quantum level. This leads us to a modification of the relativistic theory by introducing the idea of a universal minimum speed related to Planck minimum length. Such a speed,unattainable by the particles,represents a privileged inertial reference frame associated with a universal background field (a vacuum energy),enabling a fundamental understanding of the quantum uncertainties. The structure of space-time becomes extended due to such a vacuum energy density,which leads to a negative pressure at the cosmological length scales as being an anti-gravity,playing the role of the cosmological constant. The tiny values of the vacuum energy density and the cosmological constant are obtained,being in agreement with current observational results. We estimate the very high value of inflationary energy density of vacuum at Planck length scale. After we find the critical radius of the universe,beyond which the accelerated expansion (cosmological anti-gravity) takes place. We show that such a critical radius is Ruc = rg/2,where rg = 2GM/c²,being rg the Shwarzschild radius of a sphere with a mass M representing the total attractive mass contained in our universe. And finally we obtain the radius Ru0 = 3rg/4(> Ruc) where we find the maximum rate of accelerated expansion. For Ru > Ru0,the rate of acceleration decreases to zero at the infinite, avoiding Big Rip.

This research aims to introduce a new principle in the flat space-time geometry through the
elimination of the classical idea of rest and by including a universal minimum limit of speed in the
quantum world. This limit, unattainable by the particles, represents a preferred inertial reference
frame associated with a universal background field that breaks Lorentz symmetry. There emerges
a new relativistic dynamics where a minimum speed forms an inferior energy barrier. One of the
interesting consequences of the existence of such a minimum speed is that it prevents the absolute
zero temperature for an ultracold gas according to the third law of thermodynamics. So we will
be able to provide a fundamental dynamical explanation for the third law through a connection
between such a phenomenological law and the new relativistic dynamics with a minimum speed.

The paper aims to introduce a new symmetry principle in the space-time geometry through the
elimination of the classical idea of rest and by including a universal minimum limit of speed in the
subatomic world. Such a limit, unattainable by particles, represents a preferred reference frame
associated with a universal background field that breaks Lorentz symmetry. Thus the structure of
space-time is extended due to the presence of a vacuum energy density, which leads to a negative
pressure at cosmological scales. The tiny values of the cosmological constant and the vacuum energy
density shall be successfully obtained, being in good agreement with current observational results.

We use a renormalization group method to treat QCD-vacuum behavior specially closer to the regime of asymptotic freedom. QCD-vacuum behaves effectively like a ?paramagnetic system? of a classical theory in the sense that virtual color charges (gluons) emerges in it as a spin effect of a paramagnetic material when a magnetic field aligns their microscopic magnetic dipoles. Due to that strong classical analogy with the paramagnetism of Landau's theory,we will be able to use a certain Landau effective action without temperature and phase transition for just representing QCD-vacuum behavior at higher energies as being magnetization of a paramagnetic material in the presence of a magnetic field H. This reasoning will allow us to apply Thompson's approach to such an action in order to extract an ?effective susceptibility? (χ > 0) of QCD-vacuum. It depends on logarithmic of energy scale u to investigate hadronic matter. Consequently we are able to get an ?effective magnetic permeability? (μ > 1) of such a ?paramagnetic vacuum?. Actually,as QCD-vacuum must obey Lorentz invariance,the attainment of μ > 1 must simply require that the ?effective electrical permissivity? is ǫ < 1 in such a way that μǫ = 1 (c2 = 1). This leads to the anti-screening effect where the asymptotic freedom takes place. We will also be able to extend our investigation to include both the diamagnetic fermionic properties of QED-vacuum (screening) and the paramagnetic bosonic properties of QCD-vacuum (anti-screening) into the same formalism by obtaining a β-function at 1 loop,where both the bosonic and fermionic contributions are considered.

We attempt to find new symmetries in the space-time structure,leading to a modified gravitation at large length scales,which provides the foundations of a quantum gravity at very low energies. This search begins by considering a unified model for electrodynamics and gravitation,so that the influence of the gravitational field on the electrodynamics at very large distances leads to a reformulation of our understanding about space-time through the elimination of the classical idea of rest at quantum level. This leads us to a modification of the relativistic theory by introducing the idea of a universal minimum speed related to Planck minimum length. Such a speed,unattainable by the particles,represents a privileged inertial reference frame associated with a universal background field (a vacuum energy),enabling a fundamental understanding of the quantum uncertainties. The structure of space-time becomes extended due to such a vacuum energy density,which leads to a negative pressure at the cosmological length scales as being an anti-gravity,playing the role of the cosmological constant. The tiny values of the vacuum energy density and the cosmological constant are obtained,being in agreement with current observational results. We estimate the very high value of inflationary energy density of vacuum at Planck length scale. After we find the critical radius of the universe,beyond which the accelerated expansion (cosmological anti-gravity) takes place. We show that such a critical radius is Ruc = rg/2,where rg = 2GM/c²,being rg the Shwarzschild radius of a sphere with a mass M representing the total attractive mass contained in our universe. And finally we obtain the radius Ru0 = 3rg/4(> Ruc) where we find the maximum rate of accelerated expansion. For Ru > Ru0,the rate of acceleration decreases to zero at the infinite, avoiding Big Rip.