Action Principle for Scale Invariance and Applications (Part I)

Abstract

On the basis of a general action principle, we revisit the scale invariant field equation using the co-tensor relations by Dirac (1973). This action principle also leads to an expression for the scale factor $\lambda$, which corresponds to the one derived from the gauging condition, which assumes that a macroscopic empty space is scale-invariant, homogeneous, and isotropic. These results strengthen the basis of the scale-invariant vacuum (SIV) paradigm. From the field and geodesic equations, we derive, in current time units (years, seconds), the Newton-like equation, the equations of the two-body problem, and its secular variations. In a two-body system, orbits very slightly expand, while the orbital velocity keeps constant during expansion. Interestingly enough, Kepler's third law is a remarkable scale-invariant property.

18 pages, no figures

References in corpus (6)

• Dark Energy and the Accelerating Universe
• An alternative to the LCDM model: the case of scale invariance
• Dynamical effects of the scale invariance of the empty space: The fall of dark matter ?
• Space-time deformations as extended conformal transformations
• Scale Invariance, Horizons, and Inflation
• Scale Invariant Gravity and Black Hole Ringdown

Cited by in corpus (2)

• Elucidating the Dark Energy and Dark Matter Phenomena Within the Scale-Invariant Vacuum (SIV) Paradigm
• Elucidating the z-dependence of the MOND acceleration (a_0) within the Scale Invariant Vacuum (SIV) paradigm