涌现引力中希格斯真空期望值的宇宙学演化
Cosmological Evolution of the Higgs Vacuum Expectation Value in Emergent Gravity
AI总结：
该研究在涌现引力框架下引入新标量场，使希格斯真空期望值成为动力学量，证明对称性破缺谷为稳定解，重现标准模型关系，还实现辐射主导大爆炸及辐射到暗能量的演化序列。
AI中文摘要：
在拉格朗日密度不含度规导数的广义协变理论中，时空几何由标量场代数地确定，已知最简二次势会产生指数膨胀、再坍缩和大撕裂宇宙学。我们将该涌现引力希格斯宇宙学扩展为一个新的类空标量场——真空期望值产生场，其通过标准模型势与希格斯粒子耦合，使电弱真空期望值成为随宇宙学时间演化的动力学量。我们证明势的对称性破缺谷是完整非线性系统的精确稳定解，背景可通过单个守恒荷以闭式求解；该守恒荷为弗里德曼方程提供纯几何起源的类辐射组分，随尺度因子四次方的倒数稀释，尽管不存在辐射流体，因此宇宙在有限宇宙学时间以辐射主导的大爆炸诞生，且当势的常数项为零时，膨胀历史实现自发的辐射到暗能量序列。希格斯动能项的符号并非模型假设：要求破缺相为物理真空可动态确定该符号，稳定选择重现标准模型中希格斯质量、自耦合与真空期望值的关系，且无可调参数。围绕该谷的振荡描述希格斯凝聚体，其在早期冻结，通过错位机制开始振荡，遵循无参数的绝热振幅定律，并作为背景常数的确定重整化对膨胀历史产生反作用，为类辐射组分提供输入。
英文摘要：
In a generally covariant theory whose Lagrangian density contains no derivatives of the metric, the spacetime geometry is fixed algebraically by the scalar fields, and the simplest quadratic potential is known to generate exponentially expanding, recollapsing and big-rip cosmologies. We extend this emergent-gravity Higgs cosmology by one new spacelike scalar field - the vacuum-expectation-value generating field - coupled to the Higgs particle through the Standard Model potential, so that the electroweak vacuum expectation value becomes a dynamical quantity evolving with cosmological time. We show that the broken-symmetry valley of the potential is an exact and stable solution of the full nonlinear system, on which the background is solved in closed form in terms of a single conserved charge. The charge feeds the Friedmann equation with a radiation-like component of purely geometric origin, diluting with the inverse fourth power of the scale factor although no radiation fluid is present; as a consequence the universe is born at a finite cosmological time in a radiation-dominated big bang, and for vanishing constant term in the potential the expansion history realizes a spontaneous radiation-to-dark-energy sequence. The sign of the Higgs kinetic term is not an assumption of the model: the requirement that the broken phase be the physical vacuum fixes it dynamically, and the stable choice reproduces the Standard Model relation between the Higgs mass, the self-coupling and the vacuum expectation value with no adjustable parameter. Oscillations about the valley describe a Higgs condensate which is frozen at early times, begins to oscillate through a misalignment mechanism, obeys a parameter-free adiabatic amplitude law, and backreacts on the expansion history as a definite renormalization of the background constants that feeds the radiation-like component.
