标量-张量引力中 Quintessence 势的宇宙学重建
Cosmographic Reconstruction of the Quintessence Potential in Scalar-Tensor Gravity
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中文总结 AI 辅助
本文将宇宙学重建方案推广到标量-张量引力，推导了势斜率等的可观测表达式，结合 DESI DR2 等数据重建 Quintessence 势，发现非最小耦合可打开幻影区域，且框架假设 $\alpha_M$ 当前过零。
中文摘要 AI 辅助
我们将 Chakraborty、Dunsby 和 Scherrer 的宇宙学重建方案推广到标量-张量引力中。在具有一般非最小耦合 $F(\Phi)$ 的 Jordan 框架下，我们根据宇宙学参数 $(q,j,s)$、普朗克质量跑动 $\alpha_M = d\ln F/d\ln a$ 及其导数，推导出势斜率 $\lambda_U$、耦合斜率 $\lambda_F$ 及其曲率参数 $\Gamma_U$ 和 $\Gamma_F$ 的精确闭式表达式。我们将 $\alpha_M$ 及其导数表示为一组描述引力常数 $G\propto F^{-1}$ 时间变化的系数 $g_n$，将这四个量全部转化为完全可观测的形式。随后，我们针对当前数据（包括 DESI DR2 重子声学振荡测量和月球激光测距对 $\dot{G}/G$ 的约束）评估重建结果，将宇宙学不确定性传递到重建势中。所有表达式在最小耦合极限下可解析地简化为 Chakraborty、Dunsby 和 Scherrer 的结果，我们通过符号计算验证了这一点。我们发现势斜率 $\lambda_U$ 的恢复精度为十分之几的水平，而曲率 $\Gamma_U$ 基本不受约束。我们进一步证明标量动能项的正性等价于 $w_{\rm eff,0}\ge-1$，因此对最小耦合 Quintessence 封闭的宇宙学参数空间区域恰好是幻影区域，而非最小耦合通过引力塔的单个系数 $g_2$ 重新打开该区域。由于月球激光测距迫使 $|g_1|\lesssim2\times10^{-4}$，而重建对 $g_2\sim O(0.1)$ 敏感，该框架假设 $\alpha_M$ 在当前 epoch 经过零值，这与 Damour-Nordtvedt 最小耦合吸引子的预期一致。
英文摘要
We generalise the cosmographic reconstruction programme of Chakraborty, Dunsby & Scherrer to scalar-tensor gravity. Working in the Jordan frame with a general non-minimal coupling $F(Φ)$, we derive exact closed-form expressions for the potential slope $λ_U$, the coupling slope $λ_F$, and their curvature parameters $Γ_U$ and $Γ_F$ in terms of the cosmographic parameters $(q,j,s)$, the Planck-mass running $α_M = d\ln F/d\ln a$ and its derivatives. We express $α_M$ and its derivatives in terms of a set of coefficients $g_n$ describing the time variation of the gravitational constant $G\propto F^{-1}$, casting all four quantities in fully observable form. We then evaluate the reconstruction against current data, including DESI~DR2 baryon acoustic oscillation measurements and Lunar Laser Ranging constraints on $\dot G/G$, propagating the cosmographic uncertainties through to the reconstructed potential. All expressions reduce analytically to those of Chakraborty, Dunsby & Scherrer in the minimally-coupled limit, which we verify symbolically. We find that the potential slope $λ_U$ is recovered at the few-tenths level while the curvature $Γ_U$ is essentially unconstrained. We further show that the positivity of the scalar kinetic term is equivalent to $w_{\rm eff,0}\ge-1$, so that the region of cosmographic parameter space closed to minimally-coupled quintessence is exactly the phantom region, and that the non-minimal coupling reopens it through a single coefficient $g_2$ of the gravitational tower. Because Lunar Laser Ranging forces $|g_1|\lesssim2\times10^{-4}$ while the reconstruction is sensitive to $g_2\sim O(0.1)$, the framework presupposes that $α_M$ is passing through zero at the present epoch, as expected on the Damour--Nordtvedt least-coupling attractor.
