It will be introduced a new symmetry principle in the space-time geometry through the elimination of the classical idea of rest, by including a universal minimum limit of speed in the subatomic world. Such a lowest 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 length scales. The tiny values of the cosmological constant and the vacuum energy density will be successfully obtained, being in good agreement with current observational results.
The present work aims to search for an implementation of a new symmetry in the space-time by introducing the idea of an invariant minimum speed scale (V ). Such a lowest limit V , being unattainable by the particles, represents a fundamental and preferred reference frame connected to a universal background field (a vacuum energy) that breaks Lorentz symmetry. So there emerges a new principle of symmetry in the space-time at the subatomic level for very low energies close to the background frame (v ≈ V ), providing a fundamental understanding for the uncertainty principle, i.e., the uncertainty relations should emerge from the space-time with an invariant minimum speed.
In this work we propose an action to describe diffusion limited chemical reactions belonging to various classes of universality. This action is treated through Thompson's approach and can encompass both cases where we have segregation as in the A + B → 0 reaction, as well as the simplest one, namely the A + A → 0 reaction. Our results for long-time and long-wavelength behaviors of the species concentrations and reaction rates agree with exact results of Peliti for A + A → 0 reaction and rigorous results of Bramson and Lebowitz for A + B → 0 reaction, with equal initial concentrations. The different classes of universality are reflected by the obtained upper critical dimensions varying continuously from dc = 2 in the first case to dc = 4 in the last one. Just as at the upper critical dimensions, we find universal logarithmic corrections to the mean field behavior.PACS Number(s): 64.60
The paper aims to provide an explanation for the tiny value of the cosmological constant and the low vacuum energy density to represent the dark energy. To accomplish this, we will search for a fundamental principle of symmetry in space-time by means of the elimination of the classical idea of rest, by including an invariant minimum limit of speed in the subatomic world. Such a minimum speed, unattainable by particles, represents a preferred reference frame associated with a background field that breaks down the Lorentz symmetry. The metric of the flat space-time shall include the presence of a uniform vacuum energy density, which leads to a negative pressure at cosmological length scales. Thus, the equation of state for the cosmological constant [p(pressure)= −ǫ (energy density)] naturally emerges from such a space-time with an energy barrier of a minimum speed.The tiny values of the cosmological constant and the vacuum energy density will be successfully obtained, being in agreement with the observational results of Perlmutter, Schmidt and Riess.
This work presents an experimental test of Lorentz invariance violation in the infrared (IR) regime by means of an invariant minimum speed in the spacetime and its effects on the time when an atomic clock given by a certain radioactive single-atom (e.g.: isotope N a 25 ) is a thermometer for a ultracold gas like the dipolar gas N a 23 K 40 . So, according to a Deformed Special Relativity (DSR) so-called Symmetrical Special Relativity (SSR), where there emerges an invariant minimum speed V in the subatomic world, one expects that the proper time of such a clock moving close to V in thermal equilibrium with the ultracold gas is dilated with respect to the improper time given in lab, i.e., the proper time at ultracold systems elapses faster than the improper one for an observer in lab, thus leading to the so-called proper time dilation so that the atomic decay rate of a ultracold radioactive sample (e.g: N a 25 ) becomes larger than the decay rate of the same sample at room temperature. This means a suppression of the half-life time of a radioactive sample thermalized with a ultracold cloud of dipolar gas to be investigated by NASA in the Cold Atom Lab (CAL).
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