Baryonic Vacuum Fluctuations

• Baryonic vacuum fluctuations are quantum or statistical variations in the baryonic fields of the vacuum that influence gravitational dynamics and mimic dark matter profiles.
• They are modeled as a pressureless fluid with time-regenerated density perturbations responding to baryonic mass, effectively reproducing galaxy rotation curves.
• Their impact spans cosmic baryon asymmetry and the phase structure of dense QCD matter, offering novel insights into both cosmology and nuclear physics.

Baryonic vacuum fluctuations refer to quantum or statistical variations associated with baryonic degrees of freedom in the vacuum, encompassing both microscopic zero-point effects and macroscopic statistical realizations. These fluctuations are central to understanding multiple open questions in cosmology and nuclear physics, including the emergence of dark-matter-like phenomena, baryon asymmetry, and the nonlinear phase structure of nuclear matter.

1. Gravitational Effects of Baryonic Quantum Vacuum Fluctuations

The gravitational manifestation of baryonic vacuum fluctuations is embodied by models in which the quantum vacuum, viewed as a pressureless fluid, interacts gravitationally with baryonic mass distributions. A key formalism models the vacuum as having a uniform background density $\rho_0$ perturbed by $\delta\rho(\mathbf{r})$ in response to the Newtonian potential $\Phi(\mathbf{r})$. The essential assumptions are:

• The fluid has a local flow velocity $\mathbf{v}(\mathbf{r})$ such that $\|\mathbf{v}\| \ll c$ and $\mathbf{v}^2 = -2\Phi(\mathbf{r})$.
• Vacuum fluctuations are continually 'renewed' over a microscopic timescale $\tau_0$, leading (in the stationary limit) to

$$\delta\rho(\mathbf{r}) = - \rho_0 \tau_0 \nabla \cdot \mathbf{v}(\mathbf{r})\,.$$

• The full Poisson equation for the potential,

$$\nabla^2\Phi(\mathbf{r}) = 4\pi G_N[\rho^b(\mathbf{r}) + \delta\rho(\mathbf{r})],$$

incorporates both baryon density and vacuum response.

This formalism introduces a new macroscopic time constant:

$T = \left[4\pi G_N \rho_0 \tau_0\right]^{-1}$

that controls the temporal regeneration of vacuum density. The additional gravitational acceleration induced by the vacuum is then $\delta\mathbf{g} = \mathbf{v}/T$.

Analytically, the derived halo profile for a point mass $M_0$ yields a cuspy density asymptote

$$\delta\rho(r) \simeq \frac{3}{4\pi G_N T} \sqrt{\frac{G_N M_0}{2 r^3}}\,,$$

which, for small $r$, gives $r^{-3/2}$ scaling. The total vacuum-induced halo is entirely determined by the baryonic mass configuration and is generally non-spherical, departing from ad hoc dark matter profiles.

Notably, successful application to spiral galaxy rotation curves requires $T\sim 7\times10^{15}$ s, and rotation curve fits across a broad sample of disk galaxies are comparable in quality to conventional dark matter models, with substantially fewer phenomenological parameters (Couchot et al., 2023).

2. Quantum Fluctuations as the Origin of Baryon Asymmetry

A distinct but related role for baryonic vacuum fluctuations arises in the context of cosmological matter-antimatter asymmetry. In this paradigm, the observed baryon excess within the observable universe is interpreted not as a result of explicit C or CP violation, but as a realization of large-scale quantum fluctuations in an originally baryon-symmetric vacuum during cosmic inflation.

A field-theoretic setup based on a complex scalar field $\phi$ carrying baryon number, evolving in a de Sitter background, leads to stochastic amplification of baryon number density via inflationary quantum fluctuations. The key statistical observable is the smoothed rms fluctuation of the baryon number,

$$|\delta N_B| \simeq \frac{\sqrt{\kappa}}{4\sqrt{2}\pi^2} a_{\text{inf}} H_{\text{inf}}/\ell^2,$$

where $\ell$ is the comoving scale corresponding to the present Hubble radius and $H_{\text{inf}}$ is the inflationary Hubble parameter.

The resulting baryon-to-entropy ratio,

$$\eta_B \simeq 10^{-10} \bigg(\frac{H_{\mathrm{inf}}}{2\times 10^{11}~\mathrm{GeV}}\bigg) \bigg(\frac{T_{\mathrm{rh}}}{2\times 10^{11}~\mathrm{GeV}}\bigg)^{-1},$$

matches observational constraints for generic (high-scale) inflationary parameters. By construction, this mechanism produces vanishing global $\langle n_B \rangle$, but a non-zero realized value in each Hubble-volume patch, consistent with the absence of observable antimatter domains (Kobakhidze et al., 2015).

3. Impact of Baryonic Vacuum Fluctuations on Dense Matter Phases

In nuclear and dense baryonic matter, vacuum fluctuations—especially from fermionic zero-point motion—play a crucial role in the phase structure of QCD matter. Model calculations employing the chiral nucleon-meson Lagrangian demonstrate that inclusion of one-loop vacuum contributions alters the effective potential to

$$U_B(\sigma, v, w) = \sum_{n=1}^4 \frac{a_n}{2^n n!} (\sigma^2 - f_\pi^2)^n - m_\pi^2 f_\pi (\sigma-f_\pi) - \frac{(g\sigma)^4}{4\pi^2} \ln\left(\frac{g\sigma}{\Lambda}\right) - \frac{1}{2} m_v^2 (v^2+w^2),$$

with the vacuum logarithm stiffening the potential at small $\sigma$, thus resisting the restoration of chiral symmetry at moderate densities.

Implementation of functional renormalization group methods further enhances this stabilizing effect:

• The naive mean-field (MF) approach yields a first-order chiral transition at $n\sim1.5n_0$.
• Including the vacuum term (extended mean-field, EMF) removes this transition up to $n\sim 5n_0$ (smooth crossover).
• Dynamical fluctuations (full FRG) push partial restoration to $n>6n_0$, even at densities beyond those in neutron star cores.

The implication is that vacuum fluctuations stabilize hadronic (chirally broken) phases well beyond standard MF predictions (Brandes et al., 2021).

4. Baryonic Vacuum Polarization and Gravitational Dipole Models

Alternative interpretations posit that quantum vacuum fluctuations exhibit gravitational polarization under the presence of baryonic sources. In these models, if antimatter is assigned gravitational mass opposite to ordinary matter, then virtual particle–antiparticle pairs act as gravitational dipoles. For example:

• The dipole density is $P_g = N_0 p_g$, with number density $N_0 \simeq \lambda_m^{-3}$ (Compton wavelength $\lambda_m = \hbar / (mc)$).
• Polarization induces an effective mass density

$$\rho_{\text{vac}}(r) = -\nabla \cdot P_g(r) = -\frac{1}{r^2} \frac{d}{dr}\left[ r^2 P_g(r) \right]$$

which, under full dipole alignment, generates a constant anomalous acceleration matching the "Pioneer anomaly".

• At larger distances, when dipole alignment weakens, the model predicts $\rho_{\text{vac}}(r) \propto 1/r^2$—the empirical scaling of dark matter halos.

This approach enables an interpretation wherein MOND-like behaviors and galactic dynamics emerge from baryonic vacuum polarization, sidestepping invocation of nonbaryonic dark matter (Hajdukovic, 2010).

5. Observational Consequences and Testable Predictions

Baryonic vacuum fluctuation models produce distinctive, testable predictions:

• Quantum vacuum halos are fully determined by the shape and distribution of baryonic mass, leading to non-spherical, correlated dark-matter-like profiles in galaxies. This contrasts with empirical NFW or Burkert profiles, which are typically spherically averaged (Couchot et al., 2023).
• The Tully-Fisher relation, $v \propto M_b^{1/4}$, emerges naturally in the inner regions.
• There is no requirement for modifications to Newtonian gravity or new particle species; purely gravitational responses suffice.
• Extensions to pressure-supported systems and gravitational lensing maps may require three-dimensional simulation and further model development.
• Laboratory detection could, in principle, constrain vacuum fluctuation parameters ($\tau_0, \rho_0$) via gravitational Casimir effect measurements or experiments such as ARCHIMEDES.

A plausible implication is that if vacuum gravitational responses can mimic dark matter in galaxies, then complementary cosmological and laboratory tests must be carefully designed to distinguish between dark matter and baryonic vacuum fluctuation scenarios (Couchot et al., 2023, Hajdukovic, 2010).

6. Distinctions, Limitations, and Theoretical Challenges

The outlined mechanisms are consistent with observed galactic phenomenology and net baryon asymmetry under specific parametric regimes but entail key caveats:

• The successful reproduction of rotation curves using a single new parameter $T$ is notable but further cosmological embedding is required to assess consistency with large-scale structure and CMB measurements (Couchot et al., 2023).
• The inflationary quantum fluctuation baryogenesis paradigm predicts a vanishing global baryon asymmetry, implying that any observational detection of isocurvature baryon fluctuations or antimatter domains would falsify the mechanism (Kobakhidze et al., 2015).
• Gravity-induced vacuum polarization models rest on unverified assumptions about antimatter gravitational mass; direct experimental evidence for or against negative gravitational mass for antimatter remains lacking.

Across all scenarios, embedding baryonic vacuum fluctuation mechanisms within a fully relativistic, quantum field-theoretic and cosmological framework is necessary for deeper theoretical understanding and for alignment with the full suite of astrophysical and laboratory data.