[Paper Review] Post-Newtonian phenomenology of a massless dilaton

Aurélien Hees, O. Minazzoli|arXiv (Cornell University)|Dec 16, 2015

Cosmology and Gravitation Theories4 references3 citations

TL;DR

This paper extends post-Newtonian phenomenology for a massless dilaton by incorporating a general dilaton-Ricci coupling and non-canonical kinetic term within the microphysical dilaton-matter coupling model of Damour and Donoghue. It derives all necessary equations for analyzing local gravitational observations—equations of motion, light propagation, and proper time evolution—revealing a decoupling scenario that drastically reduces deviations from General Relativity, offering a potential explanation for the non-detection of universality of free fall violations despite theoretical expectations.

ABSTRACT

In this paper, we present extensively the observational consequences of massless dilaton theories at the post-Newtonian level. We extend previous work by considering a general model including a dilaton-Ricci coupling as well as a general dilaton kinetic term while using the microphysical dilaton-matter coupling model proposed in [Damour and Donoghue, PRD 2010]. We derive all the expressions needed to analyze local gravitational observations in a dilaton framework, which is useful to derive constraints on the dilaton theories. In particular, we present the equations of motion of celestial bodies (in barycentric and planetocentric reference frames), the equation of propagation of light and the evolution of proper time as measured by specific clocks. Particular care is taken in order to derive properly the observables. The resulting equations can be used to analyse a large numbers of observations: universality of free fall tests, planetary ephemerides analysis, analysis of satellites motion, Very Long Baseline Interferometry, tracking of spacecraft, gravitational redshift tests, ...

Motivation & Objective

• To extend post-Newtonian phenomenology of massless dilaton theories beyond previous works by including a general dilaton-Ricci coupling and non-canonical kinetic term.
• To incorporate the microphysical dilaton-matter coupling model proposed by Damour and Donoghue, which links the dilaton to QCD scale, fermion masses, and fine structure constant.
• To derive all necessary equations for analyzing local gravitational observations—equations of motion, light propagation, and proper time evolution—within the dilaton framework.
• To identify and analyze a decoupling scenario that significantly reduces deviations from General Relativity, particularly in universality of free fall tests.
• To provide a comprehensive theoretical toolkit for constraining dilaton theories using diverse observational data, including planetary ephemerides, spacecraft tracking, and clock comparisons.

Proposed method

• Derives the effective action in the string frame with a general dilaton-Ricci coupling and non-canonical kinetic term, consistent with string loop expansions.
• Applies the microphysical dilaton-matter coupling model where the dilaton couples to the QCD trace anomaly, electron mass, and fine structure constant via five coupling parameters.
• Uses the parametrized post-Newtonian (PPN) formalism to express metric perturbations and deviations from General Relativity, including EEP-violating effects.
• Derives equations of motion for celestial bodies in both barycentric and planetocentric reference frames, essential for planetary and satellite dynamics.
• Derives light propagation equations to model range, Doppler, and astrometric observables, crucial for VLBI and spacecraft tracking experiments.
• Derives the evolution of proper time for atomic clocks to enable gravitational redshift and equivalence principle tests.

Experimental results

Research questions

• RQ1 How do non-minimal dilaton-Ricci and non-canonical kinetic terms affect post-Newtonian observables in dilaton theories?
• RQ2 What are the implications of the Damour-Donoghue microphysical dilaton-matter coupling for local gravitational tests?
• RQ3 Can a specific combination of couplings lead to a decoupling scenario that suppresses deviations from General Relativity?
• RQ4 How do different types of experiments (e.g., UFF tests vs. clock comparisons) constrain different dilaton coupling parameters?
• RQ5 What are the precise equations of motion and light propagation needed to analyze modern gravitational data in dilaton frameworks?

Key findings

• A specific combination of couplings leads to a decoupling scenario where the PPN parameters exactly match those of General Relativity, significantly reducing observable deviations.
• In the decoupling scenario, the universality of free fall (UFF) violation parameter η_dec is strongly reduced, scaling as |η_dec| ≈ |α̃_E0(α̃_B0 − α̃_C0)|, with α̃_A0 defined by the dilaton couplings to matter.
• The decoupling mechanism explains the non-detection of UFF violations in experiments despite theoretical expectations, offering a resolution to a long-standing puzzle.
• Clock comparison experiments are most sensitive to the dilaton coupling with the electron mass (d_me) and fine structure constant (d_e), while UFF tests are most sensitive to couplings with quark masses (d_mu, d_md) and QCD scale (d_g).
• The derived equations of motion in barycentric and planetocentric frames are suitable for analyzing planetary ephemerides, asteroid dynamics, and artificial satellite orbits.
• The full set of equations for light propagation and proper time evolution enables precise modeling of range, Doppler, astrometry, and gravitational redshift measurements in dilaton gravity.