Modern precision measurements on Hubble expansion $H(z)$ introduce two integral constraints on background models derived from early and late-time cosmology, based on Planck observations of the BAO and, respectively, $H_0$, here normalized to ΛCDM. For $H(z)$ coupled to $\mathrm{\Lambda }=(1-q)H^2$ of zero wave-number modes of cosmological spacetime with deceleration parameter $q(z)$, we infer a coupling constant $g<1$ for $H_0$ in tension with ΛCDM. Results from the Local Distance Ladder give $g\simeq 1-\xi \alpha$ with $\xi =0.49\pm 0.10$. This result appears natural upon identifying $H_0$-tension with breaking of T-duality in the Friedmann scale factor $a(t)$ to the same order.

哈勃膨胀的现代精密测量 $H(z)$ 基于对 BAO 的普朗克观测，分别对源自早期和晚期宇宙学的背景模型引入两个积分约束， $H_0$，这里归一化为ΛCDM。为了$H(z)$ 耦合到 $\mathrm{\Lambda }=(1-q)H^2$ 带减速参数的宇宙时空零波数模态 $q(z)$，我们推断耦合常数 $G<1$ 为了 $H_0$与ΛCDM紧张。局部距离阶梯的结果给出$G\simeq 1-\xi \alpha$ 和 $\xi =0.49\pm 0.10$. 这个结果在识别时显得很自然$H_0$- 在弗里德曼比例因子中打破 T 对偶的张力 $\mathrm{一种}(吨)$ 到相同的顺序。