We discuss that it is quite possible to realize the smooth transition of the universe between a matter/radiation-dominated deceleration and a dark-energy-dominated acceleration, even with a variation of proton-to-electron mass ratio μ. The variation is incorporated into the theory of gravity using a cosmological Higgs scalar field with a non-trivial and self-interaction potential, leading to a varying Higgs vacuum expectation value (VEV). This matches well with the data from molecular absorption spectra of a series of Quasars. In comparison with late-time cosmology, an observational consistency is reached using a Markov chain Monte Carlo simulation and JLA + OHD + BAO data sets. We find that the the pattern of variation is embedded within the evolving equation of state (EOS) of the scalar Dark Energy/Matter components, but leaves negligible trace on the effective EOS of the system. We discuss three cases of scalar extended theory of gravity, (a) a minimally coupled scalar, (b) a non-minimally coupled scalar, and (c) a generalized Brans–Dicke set-up. We also give a toy model of a unified cosmic history from inflation to the present era and discuss how the Higg VEV might have changed as a function of look-back time.

中文翻译：

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质子与电子质量比的宇宙变化与相互作用的希格斯标量场

我们讨论了，即使质子与电子的质量比 μ 发生变化，也很有可能实现宇宙在物质/辐射主导的减速和暗能量主导的加速之间的平滑过渡。使用具有非平凡和自相互作用势的宇宙学希格斯标量场将该变化纳入引力理论，从而产生变化的希格斯真空期望值 (VEV)。这与一系列类星体的分子吸收光谱数据非常吻合。与晚期宇宙学相比，使用马尔可夫链蒙特卡罗模拟和 JLA + OHD + BAO 数据集达到了观测一致性。我们发现变化模式嵌入在标量暗能量/物质分量的演化状态方程 (EOS) 中，但在系统的有效 EOS 上留下的痕迹可以忽略不计。我们讨论了标量扩展引力理论的三种情况，(a) 最小耦合标量，(b) 非最小耦合标量，和 (c) 广义 Brans-Dicke 设置。我们还给出了一个从暴胀到现在的统一宇宙历史的玩具模型，并讨论了 Higg VEV 作为回溯时间的函数可能如何变化。