Covarying Coupling Constants (CCC)

• CCC is a framework where multiple fundamental constants such as G, c, and h dynamically evolve in concert under strict symmetry and scaling laws.
• The approach employs complex action, scalar–tensor models, and renormalization techniques to establish linked evolution of coupling constants.
• Observational and experimental applications of CCC span cosmology, astrophysics, quantum systems, and dense matter to constrain dynamic constant evolution.

Covarying Coupling Constants (CCC) refers to frameworks and physical theories where multiple fundamental coupling constants—such as the gravitational constant ($G$), the speed of light ($c$), the Planck constant ($h$), the Boltzmann constant ($k$), and others—are dynamically interrelated rather than strictly constant. Instead of varying independently, these constants “covary”: their temporal, spatial, or background-field-dependent evolution is constrained by theoretical, dynamical, or symmetry principles such that their ratios or scaling laws are fixed throughout cosmic or physical evolution. The CCC concept thus provides an organizing principle for diverse phenomena spanning high-energy particle theory, quantum field theory, cosmology, and astrophysical systems.

1. Theoretical Mechanisms for CCC

Complex Action in Path Integrals

In the complex action approach (Nielsen, 2011), the standard path integral is generalized to use a complex action $S = S_R + i S_I$, so the dominating physical histories minimize the imaginary part $S_I$. A critical assertion is that some coupling constants themselves are adjusted—not fixed a priori—so as to minimize $S_I$ across all cosmic history. For example, the bare Higgs mass parameter “slides” to minimize the spacetime integral $\int |H(x)|^2 d^4x$. This fine-tuning principle enforces a dynamical correlation among couplings, manifesting as covariation driven by a global selection principle.

Scalar–Tensor and Volume–Time Gravity Models

In scalar–tensor gravity (Cuzinatto et al., 2022), $G$ and $c$ are promoted to functions of spacetime and unified via a scalar field $\phi = c^3/G$. Dynamical phase-space analysis reveals that evolution enforces $\dot{G}/G = 3\,\dot{c}/c$, locking the ratios such that $G/G_0 = (c/c_0)^3$ after the scalar field relaxes to equilibrium. Similarly, canonical Hamiltonian approaches to general relativity with a global time choice (e.g., spatial volume as clock) induce explicit time dependence of matter couplings (Hassan et al., 2018), e.g., $m(t) = m/t$, $\lambda(t) = \lambda/t^4$, so couplings run in tandem as the universe expands.

Renormalization and Varying UV Cutoff

An alternative approach interprets CCC as a consequence of the effective field theory's physical cutoff varying with cosmic time (Lee, 2023). If the UV cutoff $\Lambda_\mathrm{UV}(t)$ is a function of the scale factor $a(t)$, then via the renormalization group,

$\frac{da_i}{dt} = k \beta_i H,$

where $a_i$ are dimensionless coupling constants, $\beta_i$ are beta functions, $k$ encodes the cutoff scaling, and $H$ is the Hubble parameter. Thus, all couplings’ variations are linked, their rates determined by their beta functions and cosmic expansion.

2. Observational and Astrophysical Manifestations

Cosmological Relationships and Empirical Constraints

Frameworks based on CCC have been utilized and constrained by various observational phenomena:

• The empirical relation $G \sim c^3 \sim h^3 \sim k^{3/2}$ (Gupta, 2022, Gupta, 2022, Gupta, 2023) is derived from dimensional and energetic links in stellar and high-energy processes, such as core-collapse supernova chain conversions (mass $\to$ thermal $\to$ photon energy).
• Observational data sets such as SNe Ia, quasar, and GRB Hubble diagrams are accurately described in CCC models, with all constant variations parameterized by a single function $g(z)$, typically yielding constraints like $(\dot{G}/G)_0 = 5.4 H_0$, i.e., $G$, $c$, $h$, and $k$ all run at proportional rates set by the Hubble time (Gupta, 2023, Gupta, 2022).
• In scalar–tensor and CCC+TL (tired light) cosmologies (Gupta, 2023, Gupta, 15 Jan 2024, Gupta, 15 Sep 2025), the function $f(t)$ or $f(z)$ that governs coupling variation enables simultaneous fits to supernovae luminosity distances, galaxy angular sizes at cosmic dawn, BAO features, and the CMB sound horizon, without requiring \emph{ad hoc} dark energy or exotic dark matter.
• Analysis of galaxy rotation curves in the CCC+TL paradigm shows that the apparent “missing mass” can arise due to local variations of the CCC parameter $\alpha$, controlled by baryonic density, eliminating the need for particle dark matter. The resulting “$\alpha$-matter” and “$\alpha$-energy” components mimic dark matter and energy, adapting locally as $X = -\alpha/H_X$ changes (Gupta, 15 Sep 2025).

Laboratory and Metrology Implications

Laboratory measurements, for example via the Kibble balance (watt balance) or XRCD methods, face fundamental limitations in detecting variations of individual constants when such variations are interrelated through CCC scaling, as in $h \sim c$ (Gupta, 2022). Observed drifts in kilogram standards become ambiguous: variations in $h$ are offset by concurrent variation in $c$, challenging single-constant interpretations.

3. CCC in Quantum Systems and Field Theory

Envelope Theory and Critical Couplings in Many-Body Quantum Systems

The envelope theory (Tourbez et al., 4 Feb 2025) demonstrates that in quantum nonrelativistic $N$-body systems with short-range interactions, the threshold (critical) coupling constants for binding are intrinsically linked. For a mixed system (identical particles plus a different one), the critical $g_{aa}$ and $g_{ab}$ are determined by transcendental equations whose solution space is contour lines of constant threshold: increasing one coupling compensates for a weaker value of the other, an explicit realization of the CCC principle at the quantum binding threshold level.

Generalized Anomalies and Conformal Field Theory

In the context of QFT, coupling constants are promoted to background fields, and generalized 't Hooft anomalies can be formulated in this parameter space (Cordova et al., 2019). These anomalies are encoded as invertible field theories and differential cohomology classes, with their structure imposing global dynamical constraints on the space of couplings. In conformal field theory, marginal couplings define a conformal manifold, and the Wess–Zumino consistency condition compels Type-B Weyl anomaly coefficients to be covariantly constant ($\nabla G = 0$) across the manifold, demonstrating a geometric realization of CCC in the anomaly structure (Andriolo et al., 2022).

4. CCC in Relativistic Mean Field (RMF) Models and Dense Matter

In point-coupling RMF models for dense nuclear matter, the nucleon–nucleon couplings $\alpha_S$, $\alpha_V$, and $\alpha_{TV}$ are allowed to depend explicitly on baryon density. Bayesian analyses with neutron star mass/radius data, stability, and causality priors reveal that realistic equations of state require these couplings to covary with density—decreasing as density increases, with strong correlations (notably between isoscalar scalar and vector channels) at saturation and slightly above (Xia et al., 11 Nov 2024). The covariation among these coupling constants is crucial in matching empirical constraints and generating credible equations of state for neutron stars.

5. Cosmological and Phenomenological Implications

Dynamical Cosmological Constant and Early Galaxy Formation

In CCC cosmologies, the constant usually interpreted as dark energy is promoted to a dynamical effect stemming from varying couplings (Gupta, 2023, Gupta, 15 Jan 2024). The effective “cosmological constant” is replaced by the $\alpha$ parameter, which evolves cosmologically (and locally) and adjusts the expansion history. This mechanism addresses the “impossible early galaxy problem” revealed by JWST by stretching the cosmic timeline (e.g., a universe age of 26.7 Gyr at $z=0$), allowing sufficient time for massive galaxy assembly at high $z$, which is not compatible with standard $\Lambda$CDM assumptions.

Galaxy Dynamics and Modified Gravity Effects

Locally, variation of the CCC parameter in galactic environments generates $\alpha$-matter effects, capable of reproducing flat rotation curves and the baryonic Tully–Fisher relation with a low parameter count. The critical value of the turn-off acceleration is found to be comparable to the phenomenological critical acceleration of MOND, suggesting that such alternative gravity effects may be implicit realizations of CCC-induced modifications (Gupta, 15 Sep 2025).

6. Limitations and Open Challenges

• The freedom in parameterizing the time evolution function $f(t)$ (or $g(z)$, $\alpha(t)$) introduces degeneracy and requires external theoretical or observational constraints.
• Current laboratory measurements (e.g., Kibble balance, XRCD) cannot directly separate out individual constant variations because CCC enforces interdependence, challenging “null result” interpretations.
• High-density constraints on covarying nucleonic couplings, in RMF models, remain limited by the precision of neutron star data for supranuclear densities, particularly for the isovector channel.
• Comprehensive validation of CCC cosmologies against the full suite of cosmological observables (detailed CMB power spectrum, BBN element ratios, high-$z$ galaxy counts, lensing) remains an open and active area of research.

Table: Core Scaling Laws in CCC Cosmologies

Constant	Scaling Law	Empirical Constraint
$G$	$G \sim f^3$	$$(\dot{G}/G)_0 = 3.90 \times 10^{-10}~\mathrm{yr}^{-1}$$
$c$	$c \sim f$	$$(\dot{c}/c)_0 = 1.30 \times 10^{-10}~\mathrm{yr}^{-1}$$
$h$	$h \sim f$ or $h \sim f^2$ (model dep.)	$-$
$k$	$k \sim f^{3/2}$ or $f^2$	$-$

Outlook

CCC frameworks enable unification of diverse astrophysical and cosmological phenomena under the principle that the fundamental constants—previously assumed immutable—can evolve but only in tightly correlated, physically prescribed ways. This has profound implications for observational cosmology, astrophysics, high-precision metrology, and even the interpretation of quantum field theories, suggesting that the invariance of physical law may itself be a dynamical consequence of deeper principles. Further theoretical refinement and multi-messenger observational programs will be decisive in delineating the scope and consequences of covarying coupling constants across domains.