Cosmological Constant, Classical "Vacuum" and Special Relativity (From the Lorentz boost to the Milgrom acceleration)

TL;DR

This paper demonstrates that the Cosmological Constant is inherently necessary in General Relativity due to its connection with Special Relativity, linking classical vacuum concepts to accelerated cosmic expansion and revisiting Einstein's original ideas.

Contribution

It reveals that the Cosmological Constant must be included in GR, deriving it from SR principles and connecting it to classical vacuum and Einstein's 1917 formulation.

Findings

CC is required by SR through minimal acceleration in Lorentz boosts.

Universe exhibits accelerated expansion with negative cosmological parameter.

CC relates to classical Minkowski vacuum, not quantum vacuum.

Abstract

We show that Cosmological Constant (CC) is not optional in GR (General Relativity) because it is required by SR (Special Relativity). This completely unexpected result is obtained by introducing a minimal acceleration (Milgrom), square root of CC, in Einstein boost with Lorentz Transformation (LT). We prove that hyperbolic rotation (LT) is an hyperbolic motion with a centrifugal acceleration. In SR with CC (CSR or CR), the universe is not only in expansion (with the law of Hubble) but even in accelerated expansion (cosmological parameter is minus one). Given that the structure of space-time in Einstein's GR is determined by the presence of matter and CC is associated to the absence of matter, we associate CC not to "quantum" vacuum but to classical "vacuum" of Minkowski's space-time (with a renormalization of Minkowski's metric). Finally we show that 1917 Einstein's CC corresponds to 1906 Poincare's non-electromagnetic negative pressure.