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.

• The paper presents how antigravitational interactions arise from a tri-metric structure, leading to a repulsive force between ordinary and dual matter.
• It employs quantitative fits to H(z) data, yielding graviton Compton wavelengths of 24.2–64.1 Gpc and mixing parameters around 10⁻⁶².
• The study implies that dual matter and its antigravitational effects could explain cosmic voids without invoking dark energy.

Antigravity Mechanism in the Theory of Dual Relativity: An Expert Synthesis

Theoretical Foundations of Dual Relativity

The Theory of Dual Relativity (TDR) introduces a tri-metric framework, departing from the conventional mono-metric structure of General Relativity (GR). In TDR, spacetime is described as a four-dimensional manifold $\mathcal{M}$ endowed with a nondynamical, flat background metric $\gamma^*_{\mu\nu}$ of signature $-2$. The geometric structure is characterized by two independent vierbeins ($e^a_\mu$, $e^a_\mu$) and the spin connection $\omega^{ab}_\mu$. These vierbeins induce two distinct but interrelated metric tensors ($g_{\mu\nu}$ and $g_{\mu\nu}$), subject to a duality constraint, effectively reducing the independent geometric degrees of freedom to that of GR. The duality links the metrics algebraically via $e^a_\mu \eta^*_{ab} e^b_\nu = \gamma_{\mu\nu}$.

Crucially, the total action of TDR encompasses not only the gravitational sector—constructed analogously to the Utiyama-Kibble approach, supplemented with a graviton mass term and a mixing parameter $\zeta$—but also bifurcates the matter sector into 'ordinary' and 'dual' matter, each coupling to different metrics. Ordinary matter couples to $\gamma^*_{\mu\nu}$0, while dual matter couples to $\gamma^*_{\mu\nu}$1, which itself is algebraically related to $\gamma^*_{\mu\nu}$2 and the background through the duality condition. This partition is central to the phenomenology of TDR, particularly the emergence of antigravitational effects.

Cosmological Implications and Observational Fitting

TDR is explicitly constructed to reproduce the successes of GR on macroscopic scales while allowing for novel cosmological solutions inaccessible to standard GR. In the cosmological limit, TDR accommodates spatially flat, time-dependent metrics for both $\gamma^*_{\mu\nu}$3 and $\gamma^*_{\mu\nu}$4, parameterized by scale factors $\gamma^*_{\mu\nu}$5 and lapse functions $\gamma^*_{\mu\nu}$6. The resulting equations for the scale factor $\gamma^*_{\mu\nu}$7 yield two solution classes, distinguished by the sign of the total energy density:

• $\gamma^*_{\mu\nu}$8: Admits globally stable solutions where the equilibrium metric coincides with the background, contingent on the co-existence of both ordinary and dual matter with matched energy densities and pressures at critical points. Here, TDR achieves parameterizations of $\gamma^*_{\mu\nu}$9 superior (lower $-2$0) to $-2$1CDM fits across multiple datasets, as quantified in (Tselyaev, 2024).
• $-2$2: Gives rise to non-singular, oscillatory scale-factor dynamics, avoiding the initial singularity endemic to most GR-based cosmologies. The 'jump' time for the scale factor between critical values is exceedingly short, $-2$3 s, drastically below nuclear timescales, thereby distinguishing TDR from bouncing cosmologies and typical modifications of early-universe dynamics.

Notably, the effective cosmological constant $-2$4 is set to zero within TDR, resolving the classical cosmological constant problem without resorting to dark energy. Observationally derived graviton Compton wavelengths in the theory are of order $-2$5 Gpc, exceeding the Hubble length, consistent with gravity acting as a long-range force on cosmological scales within TDR.

Newtonian Limit and the Emergence of Antigravity

The Newtonian limit is rigorously derived by considering a domain-based system of point-like, nonrelativistic particles, separately for ordinary and dual matter. The respective action functionals reflect coupling to their associated metrics (ordinary: $-2$6, dual: $-2$7) and yield the kinetic and potential structure:

• Ordinary matter: Retains conventional identification of inertial and gravitational mass ($-2$8).
• Dual matter: Shows positive inertial mass ($-2$9) but negative gravitational mass ($e^a_\mu$0), the latter dependent on the cosmological background through $e^a_\mu$1 and $e^a_\mu$2.

The total interaction energy for the system, eliminating gravitational self-energy divergences via regulated Green’s function techniques, takes the form

$e^a_\mu$3

Repulsive ('antigravitational') forces thus emerge \textbf{exclusively} between ordinary and dual matter due to the sign difference in their gravitational masses. Interactions within each matter sector remain attractive. This antigravity is a robust consequence of the dual metric structure and the allocation of negative gravitational mass to dual matter.

Equivalence Principle and Its Violation

A core theoretical implication is the explicit violation of the strong Equivalence Principle (EP). While the action for ordinary matter respects $e^a_\mu$4, the dual sector does not, except under coordinate rescalings that invert the mass relationships—an explicit realization of a 'principle of alternative equivalences.' This means the EP holds within, but not across, the ordinary and dual sectors. Consequently, a single universal coupling to gravity is replaced by sector-specific couplings, which may have important consequences for experimental tests of EP violations and generally for modifications of post-Newtonian dynamics.

Broader Implications and Future Directions

The existence of antigravitating dual matter—currently a theoretical postulate—has deep implications:

• Cosmology: Dual matter is required for stable, equilibrium cosmological solutions in TDR, and could potentially account for observed cosmic voids through effective repulsive interactions (as an alternative explanation to dark energy or certain dark matter models).
• No Cosmological Constant: The absence of a cosmological constant term in the effective field equations is achieved naturally due to the structure of the dual matter contribution, shifting the interpretation of cosmic acceleration.
• Experimental: If dual matter exists and exhibits the predicted antigravitational behavior, it would alter the formation and evolution of large-scale structure, provide novel candidates for the sources of cosmic voids, and demand reinterpretation of phenomena currently attributed to dark matter/energy.
• Theoretical Development: The framework sets the stage for further investigation into quantum effects in TDR, non-Newtonian corrections, and relativistic tests, as well as the formal structure of the tri-metric interaction. The presence of a finite graviton mass and potential for superluminal propagation in the dual sector are areas warranting further study, both for consistency and observability.

Conclusion

The theory of dual relativity offers a mathematically consistent framework in which two forms of matter—ordinary and dual—interact via gravity, but with the dual matter possessing gravitational mass of opposite sign. In the Newtonian limit, this gives rise to antigravitational force between ordinary and dual matter, a phenomenon derivable directly from the metric structure and action functional of TDR. The framework addresses several outstanding cosmological issues, including non-singular cosmological evolution and the non-necessity of a dark energy component, while yielding strong fits to cosmic expansion data. The primary challenge remains the empirical verification of dual matter and the further theoretical development of the post-Newtonian and quantum aspects of the theory.

Reference: "Antigravity mechanism in the theory of dual relativity" (2603.28356)