Antigravity mechanism in the theory of dual relativity

Abstract

In the paper, one of the physical consequences of the recently developed theory of dual relativity (TDR) is considered. The general framework of TDR is described and some results previously obtained within this theory are summarized. The total action functional of TDR includes the action functionals of matter fields of two kinds: ordinary and dual. Based on the general equations of the theory, formulas are derived for the effective action functional of a system of point-like massive particles belonging to both kinds of matter, in the Newtonian limit. This functional includes an interaction term, which has the form of the gravitational interaction energy in Newtonian mechanics. It is shown that this energy is positive in the case of interaction between particles of ordinary and dual matter. This result indicates that this interaction has antigravitational nature.

Figures (1)

• Figure 1: Typical forms of the cosmological quasipotential ${\mathcal{U}}_{_{\hbox{\scriptsize c}}}(A)$. The red solid line corresponds to the oscillating solution with $\varepsilon_{\hbox{\scriptsize tot}}<0$ and with parameters fitted in Ref. TDR to the set WM57 of the $H(z)$ data from Ref. Farooq17. The critical points of ${\mathcal{U}}_{_{\hbox{\scriptsize c}}}(A)$, $A_{\hbox{\scriptsize c.L}} = 1$ and $A_{\hbox{\scriptsize c.R}} = \sqrt{3}$, are indicated by the blue filled circles on the $A$-axis. The turning points of the oscillations are indicated by the blue open circles. The black dashed line demonstrates the general character of the function ${\mathcal{U}}_{_{\hbox{\scriptsize c}}}(A)$ calculated with $\varepsilon_{\hbox{\scriptsize tot}}<0$ at not too small value of the mixing parameter $\zeta$. The blue dashed-dotted line corresponds to the stable solution with $\varepsilon_{\hbox{\scriptsize tot}}>0$ at $\zeta \rightarrow +0$.