Timeless Quantum Field (TQF): A Scale-Invariant Unified Model of Gravity, Inflation, and Particle Physics

We introduce the Timeless Quantum Field Framework (TQF), a classically scale invariant quantum field theory coupled to quadratic gravity in which all physical mass scales arise dynamically. The central principle of the framework is that the fundamental laws of physics contain no intrinsic mass parameters; instead, scales such as the Planck scale, the grand unification scale, and the electroweak scale emerge through quantum effects via dimensional transmutation. The gravitational sector contains quadratic curvature invariants, including R2 and the Weyl tensor squared, which render the theory perturbatively renormalizable and introduce a scalar degree of freedom (the scalaron). This scalaron naturally drives cosmic inflation with a Starobinsky type potential consistent with current cosmological observations. The particle sector extends the Standard Model with additional scalar and fermionic fields while preserving classical scale invariance. Radiative symmetry breaking generates a hierarchy of scales, linking Planck-scale physics to grand-unified symmetry breaking and electroweak symmetry breaking. Gauge couplings unify near 10^16 GeV, while the scalar sector provides viable dark matter candidates in the form of a TeV-scale scalar and an axion-like particle. Within this framework, gravity, particle physics, cosmology, and dark matter emerge from a single scale-invariant quantum field theory. The Timeless Quantum Field Framework therefore offers a unified perspective in which the observed structure of physical scales arises dynamically from classically scale-free laws under fundamental quantum laws.