A Complex Tension Origin for Dilaton Gravity: Jordan Stiffness and Logarithmic Einstein Dynamics

Area of Science:

• Theoretical Physics
• Quantum Gravity
• Cosmology

Background:

• Dilatonic gravity theories require a microphysical explanation for their scalar sector.
• Existing models lack a fundamental understanding of the dilaton's origin and behavior.
• Scalar-tensor theories are crucial for understanding gravity's fundamental properties.

Purpose of the Study:

• To provide a microphysical completion for the scalar sector of dilatonic gravity.
• To identify the dilaton with a specific physical mode within a discrete relational network.
• To derive the logarithmic scalar-tensor structure from fundamental principles.

Main Methods:

• Identifying the dilaton with the coarse-grained stiffness mode of a complex tension field.
• Applying controlled ordered-regime coarse-graining to a discrete relational network.
• Utilizing a Weyl map to establish the relationship between tension and the canonical scalar.

Main Results:

• The real projection of tension scales as Φ(Θ)=Φ0cosΘ, leading to a phase-dependent Planck mass.
• An emergent logarithmic structure for the Einstein-frame canonical scalar, φ∝ln[Φ(Θ)/Φ0].
• This structure aligns with vacuum models inspired by the Logarithmic Schrödinger Equation (LogSE).

Conclusions:

• A controlled microphysical origin for a specific scalar stiffness law (Φ(Θ)∝cosΘ) is established.
• The derived logarithmic canonical structure provides a foundation for specific scalar-tensor theories.
• The framework offers potential for satisfying Solar-System constraints and suggests avenues for experimental and astrophysical tests.