arXiv subjects

Martin Drobczyk

Publications and source records attributed to Martin Drobczyk.

4 recordsLinked to original sources

arXiv2026

A cross-epoch endpoint-consistency test of a single effective scaling from dark energy to inflation

A cross-epoch endpoint-consistency test is formulated for a single power-law effective scaling, $M_U(\mu)=\beta^{1/4}\,M_P(\mu/M_P)^\gamma$, connecting late-time cosmic acceleration to the inflationary energy scale. The normalization is anchored at $\mu=H_0$ by the late-time dark energy closure relations of the density-responsive gravity (DRG) framework and extrapolated to the inflationary Hubble rate $\mu=H_*$. Comparison with the CMB-normalized Starobinsky plateau defines the residual matching factor $C_{\rm infl}\equiv V_0^{A_s}/V_0^{\rm RG}$. The novelty is the formulation of the inflation - dark-energy connection as a quantitative endpoint test between two empirically anchored energy scales. The lever arm $H_*/H_0\sim 10^{55}$ compresses endpoint uncertainties into $\delta\gamma\propto [p\ln(H_*/H_0)]^{-1}\delta\ln X$, so requiring $C_{\rm infl}=\mathcal{O}(1)$ selects a narrow consistency band. For the benchmark $V_0\propto M_U^4$ with $c_4=\mathcal{O}(1)$, matching requires $\gamma\simeq 0.491$ and $\beta\simeq 0.68$, both $\mathcal{O}(1)$. Varying $p\in[2,8]$ shifts $\gamma$ only mildly (approximately $0.45$--$0.52$), with natural matching favoring $p\simeq 3$--$4$. We present the full uncertainty budget, including cumulative threshold effects ($\Xi$) and observational errors on the late-time anchor ($w_0$, $A_s$, $H_*$). A secondary consequence is that the effective vacuum sector dilutes as $\rho_\Phi\propto a^{-6\gamma}$ at late times, faster than spatial curvature for $\gamma>1/3$. In a closed universe, this permits a cosmological turnaround at $|\Omega_K|\sim\mathcal{O}(10^{-4})$, testable with Stage-IV surveys and qualitatively distinct from $\Lambda$CDM.

astro-ph.CO↗

arXiv2026

Tidal Deformation Bounds and Perturbation Transfer in Bounded Curvature Spacetimes

We derive two model-independent results for spacetimes with globally bounded tidal fields. These are operational resolution scales of the local-inertial approximation and tidal dynamics; no spacetime discreteness is implied. Given an invariant bound $\lambda_{\max}\le\lambda_{\rm bound}$ on the electric Riemann eigenvalues $E_{ij}\equiv R_{\hat{0}i\hat{0}j}$ along freely falling worldlines, we prove (i)~a rigorous upper bound on accumulated geodesic deviation through any bounded curvature interior, controlled by $\tau_*\equiv\lambda_{\max}^{-1/2}$, and (ii)~the existence of a critical wavenumber $k_*\sim\tau_*^{-1}$ separating adiabatic from non-adiabatic perturbation transfer through high-curvature epochs, with Bogoliubov coefficients exponentially suppressed for $k\,\tau_*\gg 1$. Both results depend only on the tidal bound (and, for mode transfer, on a mild timescale assumption for the curvature-driven effective potential) and are otherwise insensitive to metric details. For preparation, we collect the standard operational consequences of bounded curvature, including the accuracy-dependent local-inertial domain $L_{\rm LI}(\varepsilon)\sim\sqrt{\varepsilon}\, \lambda_{\max}^{-1/2}$ and, for conformally flat cores in four dimensions, the benchmark ratio $\tau_*/L_*=24^{1/4}$ with $L_*\equiv K_{\max}^{-1/4}$. We quantify the robustness of this coefficient under departures from maximal symmetry via the Weyl-to-Kretschmann ratio $\epsilon_C$. The general framework is validated numerically in the extremal Hayward geometry.

gr-qc↗

arXiv2025

Naturally resonant two-mediator model of self-interacting dark matter with decoupled relic abundance

We propose a minimal, fully thermal mechanism that resolves the long-standing tension between achieving the observed dark-matter relic abundance and explaining the astrophysical signatures of self-interactions. The framework introduces two mediators: a light scalar $\phi$ (MeV scale) that yields the required, velocity-dependent self-interactions, and a heavy scalar resonance $\Phi_h$ (TeV scale) with mass $m_{\Phi_h}\!\approx\!2m_\chi$ that opens an $s$-channel resonant annihilation during freeze-out. This clearly decouples early-universe annihilation from late-time halo dynamics. A detailed numerical analysis identified a narrow predictive island of viability. A representative benchmark with $m_\chi\!=\!600$~GeV, $m_\phi\!=\!15$~MeV, and $m_{\Phi_h}\!\simeq\!1.2$~TeV reproduces the relic density and yields $\sigma_T/m_\chi\sim 0.1$--$1~\mathrm{cm}^2\!/\mathrm{g}$ at dwarf-galaxy velocities while satisfying cluster bounds. The model makes sharp, testable predictions: a narrow $t\bar t$ resonance near $1.2$~TeV within HL-LHC reach, and a spin-independent direct-detection signal $\sigma_{\rm SI}\!\sim\!7\times10^{-48}\,\mathrm{cm}^2$ within next-generation sensitivity. As an optional UV completion, we show that walking $\mathrm{SU}(3)_H$ gauge theory with $N_f=10$ naturally realizes the near-threshold relation $m_{\Phi_h}\!\approx\!2m_\chi$ and can furnish an effective anomalous dimension $\gamma\!\approx\!0.5$ which underlies a density-responsive dark-energy sector, suggesting a unified origin for the dark sector.

hep-ph↗

arXiv2025

A density-responsive scalar-field framework for singularity regularization and dynamical dark energy

We present a covariant scalar-field framework that unifies the space-time singularity regularization with dynamical dark energy. The theory extends general relativity by introducing a scalar field $\Phi$ whose potential couples to the Lorentz-invariant quantity $X \equiv u_{\alpha} u_{\beta} T^{\alpha\beta}_{\mathrm{matter}}$, ensuring manifest covariance. The resulting density-responsive scalar energy $\rho_\Phi$ exhibits dual behavior: (i) in high-density regimes, it saturates at $\rho_\Phi \leq AM_P^4/2$, providing a Planck-scale upper bound on the total energy density that regularizes classical singularities; (ii) in low-density regimes, it approaches a constant $\rho_\Phi \to AM_U^4$, driving cosmic acceleration as dynamical dark energy. A natural renormalization group evolution with an anomalous dimension $\gamma \approx 0.501$ connects the Planck scale to the meV dark energy scale without fine-tuning. The model makes distinctive, testable predictions: $w_0 \approx -0.99$ and $w_a \approx +0.03$, where the positive $w_a$ distinguishes it from $\Lambda$CDM and standard quintessence models. Despite the novel interaction terms, the fifth forces are suppressed by $\beta_{\rm eff} \propto 1/\rho_m^2$, yielding factors below $10^{-58}$ in laboratory environments, and ensuring compatibility with all precision gravity tests. This framework demonstrates how a single quantum field theory mechanism can simultaneously address UV singularities and IR dark energy, providing concrete predictions for future Stage-IV cosmological surveys.

gr-qc↗