Temporal Theory of Gravitation (TTG) v1.1

Extended Core with Screening and Phenomenology

Abstract

TTG v1.1 extends the minimal anchor core (v1.0) by introducing nonlinear, even-parity coupling functions A()A() that enable environmental screening. This preserves the falsifiable predictions of v1.0 on cosmological and galactic scales while automatically satisfying stringent Solar System constraints through suppression of fifth forces in high-density regions. The core formalism remains unchanged; the extension lies solely in the functional form of A()A() and its derivative ()(), ensuring full backward compatibility.

1. Introduction: From Anchor to Adaptation

• Recap of TTG v1.0: Minimality, falsifiability, and universal linear coupling.
• Motivation for v1.1: Reconciling theory with tight Solar System tests (e.g., MICROSCOPE, Cassini) without sacrificing cosmological signatures.
• Strategy: Introduce nonlinear A()A() to enable density-dependent screening a natural extension preserving the EFT framework.
• Preview: New phenomenological windows (galactic rotation curves, asymmetric GW binaries) and hierarchical falsifiability.

2. Screening Mechanism: Coupling Functions and ()()

• Generalized coupling:
  A()=cosh()A()=cosh() or A()=exp(22M2)A()=exp(2M22)
• Derivative: ()=dlnAd()=ddlnA
• Screening principle:
  • High density  -0-0  ()-0()-0  suppressed fifth force (Solar System safe)
  • Low density  0=0  ()0()=0  observable effects (galactic/cosmological scales)

3. Field Equations and Dynamics

• Einstein equations: Unchanged from v1.0.
• Scalar field equation:
  V()=()TV()=()T
• Energy-momentum exchange:
  T=()TT=()T
• Note: All v1.0 equations hold with ()().

4. Newtonian and Post-Newtonian Limits

• Yukawa correction:
  (r)=()2GMremr(r)=r()2GMemr
• Screening in Solar System:
  ()-0PPN-1,PPN-1()-0PPN-1,PPN-1
• Fifth force: Suppressed in high-density environments; active in galactic halos.

5. Cosmology and Large-Scale Dynamics

• Scalar evolution with nonlinear A()A().
• Late-time activation of   dynamical dark energy (w(z)1w(z)=1).
• Example potential: V()=V0eV()=V0e (quintessence-like).
• Screening ensures compatibility with BBN and CMB constraints.

6. Gravitational Waves and Dipole Radiation

• Tensor sector: Unmodified  cgw=ccgw=c.
• Dipole term:
  (f)=GR(f)+dip(AB)2(Mf)7/3(f)=GR(f)+dip(AB)2(Mf)7/3
• Screening reduces A,BA,B in neutron stars/BHs suppressed in symmetric systems.
• Observable in asymmetric binaries (e.g., NS-BH).

7. Falsifiable Predictions and Signal Table

8. Parameter Space and Priors

• Parameters: {,,M}{,,M}, plus V()V() form.
• Priors: ()() small in Solar System, significant at galactic scales.
• Constraints: MCMC fits to combined datasets (Planck + BAO + SN + galactic RCs).

9. Conclusion: TTG as a Living Framework

• TTG v1.0: Fixed, minimal, falsifiable anchor.
• TTG v1.1: Adaptive, screened, and phenomenologically viable.
• Future directions: v1.2+ (quantum corrections, entropy gradients, coupling to matter sectors).

Appendix A. Comparison with TTG v1.0