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

Abstract

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 $\mu =H_{\ast }$. Comparison with the CMB-normalized Starobinsky plateau defines the residual matching factor $C_{\mathrm{infl}}\equiv V_0^{A_s}/V_0^{\mathrm{RG}}$. 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 $H_{\ast }/H_0\sim 10^{55}$ compresses endpoint uncertainties into $\delta \gamma \propto [p\ln (H_{\ast }/H_0){]}^{-1}\delta \ln X$, so requiring $C_{\mathrm{infl}}=\mathcal{O}(1)$ 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 ($w_0$, $A_s$, $H_{\ast }$). 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.

Published in New Astronomy, 32 pages, 3 figures

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