Constraints on a Scalar-Dependent Gravitational Coupling from Gravitational Wave Observations
Abstract
We investigate a minimal extension of the standard cosmological model in which the gravitational coupling is not constant but depends on a scalar field. This modification introduces small deviations in gravitational interactions while remaining consistent with existing observations. We derive the framework and show that gravitational waves provide a promising way to test this model.
1. Introduction
The ΛCDM model explains many cosmological observations but relies on unknown components such as dark energy.
Instead of introducing new components, we consider modifying gravity slightly by allowing the gravitational constant to vary.
2. Theoretical Framework
We introduce a scalar field φ and define:
G(φ) ≈ G0 * (1 + αφ)
Action
S = ∫ d^4x √(-g) [ (1 / (16πG(φ))) R - 1/2 (∂φ)^2 - V(φ)]Potential
V(φ) = (1/2) m^2 φ^2
This ensures:
- Early evolution possible
- Late-time stability
3. Observational Signatures
3.1 Gravitational Waves
f ∝ (G(φ) M)^(5/3)
Approximation:
f_obs = f_GR * (1 + ε)
Mass shift:
M_obs = M_true * (1 + ε)^(-5/3)
3.2 Distance Dependence
ε(r) = ε0 * (r / R)
Prediction:
- Mass correlates with distance
3.3 Cosmological Constraints
- CMB: ΔG/G < 10%
- Solar system: almost no variation
- Structure formation: sensitive to G
4. Parameter Constraints
ε < 10^-3
(dG/dt)/G < 10^-13 per year
m ≥ H0
5. Results
- Mass shift: ~0.1%
- Frequency deviation: very small
- Currently unobservable
- Detectable in future experiments
6. Discussion
This model:
- Does NOT replace ΛCDM
- Adds small corrections
- Is testable via gravitational waves
7. Conclusion
We constructed a scalar-dependent gravity model that:
- Matches current observations
- Predicts small measurable deviations
- Can be tested with future detectors
Keywords
gravity, cosmology, scalar field, gravitational waves, modified gravity