Axion domain wall network evolution in the early universe

一个有吸引力的候选暗物质(DM)粒子是轴子。这是Peccei&Quinn为了解决“强CP”问题而引入的手性U(1)_Pq的自发对称性破缺产生的伪Nambu-Goldstone玻色子。标准模型(SM)中的强相互作用不违反CP对称性，这一点从中子电偶极矩的消失得到了证明。虽然在弱电标度上对应于PQ对称性破缺的原始‘Weinberg-Wilczek’轴子从未被发现，但人们很快意识到相关的标度可以高得多，从而产生一个‘看不见的轴子’，它与SM场的(导数)耦合非常受抑制。然而，遗迹轴子场的集体振荡与非相对论粒子具有相同的状态方程，因此遗迹轴子可以解释PQ标度约为10^{10-11}GeV的宇宙的Dm。这种轴子的宇宙学演化很有趣，因为对称破缺序列会产生潜在的稳定拓扑缺陷。在Peccei-Quinn标度f_pq以下，真空歧管不是简单连通的。这意味着物理空间中存在闭合路径，这些路径被映射到绕原点缠绕的场空间中的非平凡路径上。这样的场结构对应于宇宙弦。当温度下降到A_QCD~300 MeV时，非微扰QCD效应为轴子产生质量，打破对称性为Z(N)，N为U(1)_pq下带电的夸克数。Z(N)的真空流形是不连通的，这意味着物理空间中存在路径，这些路径映射到场空间中两个真空态之间的路径上。这样的路径必然离开真空流形，由此产生的结构是磁区壁。从拓扑上讲，一旦轴子获得质量，每根弦必须由N个磁区壁连接。由于磁区壁面能的作用，N=1的弦和磁区壁网络将会失稳和崩溃。然而，带有N&GT；1的网络原则上是稳定的，如果它们在形成后开始主导宇宙的能量密度，可能会导致宇宙学灾难[。当N&gt；1引用反映量子引力效应的不可重正的Plank-Scale抑制算符时，标准的论点是避免“磁区壁问题”，该算符显式破坏初始U(1)PQ并提升真空态的简并性，从而导致有效的压力项导致真真空区域的增长。然而，U(1)Pq的这种显式破缺在实验上是受限的，因为它重新引入了CP破坏，这是实验上对中子电磁偶极矩(EDM)上限所要求的可以忽略不计的小破坏。通过要求轴子域壁及时消失以避免宇宙灾难，人们可以由此推断出中子电火花加工的下限。因此，磁区壁问题的“倾斜”解决方案有可能在未来的中子电火花实验中得到验证。我们提出了一种替代机制，通过在真空态的布居中引入统计的‘偏向’来使域壁不稳定。这种偏差是由轴子场在膨胀过程中的演化自然产生的，假设膨胀持续的时间足够长，使宇宙在膨胀期间冷却到A_QCD以下，从而轴子获得质量。这种可能性最近被用来打开以前被排除的轴子参数空间。结果表明，对于Z(2)模型，这种偏置会导致共移区壁能密度的指数衰减。这对轴子最有可能组成暗物质的质量的影响将被研究，因为这与正在进行的轴子搜索特别相关，包括英国的“隐藏部门量子传感器”计划。

An attractive candidate dark matter (DM) particle is the axion. This is the pseudo Nambu-Goldstone boson from the spontaneous symmetry breaking of a chiral U(1)_PQ introduced by Peccei & Quinn to solve the 'strong CP' problem, viz. that the strong interactions in the Standard Model (SM) do not violate CP symmetry as is evidenced by the vanishing electric dipole moment of the neutron. While the original 'Weinberg-Wilczek' axion corresponding to PQ symmetry breaking at the electroweak scale was never found, it was soon realised that the relevant scale can be much higher, thus yielding an 'invisible axion' with very suppressed (derivative) couplings to SM fields. Nevertheless collective oscillations of the relic axion field has the same equation of state as non-relativistic particles so relic axions can account for the DM of the universe for a PQ scale around 10^{10-11} GeV. The cosmological evolution of such an axion is interesting because of a sequence of symmetry breaking which produces potentially stable topological defects. Below the Peccei-Quinn scale f_PQ the vacuum manifold is not simply connected. This implies the existence of closed paths in physical space which get mapped onto non-trivial paths in field space winding around the origin. Such field configurations correspond to cosmic strings. When the temperature drops to A_QCD ~ 300 MeV, non-perturbative QCD effects generate a mass for the axion which breaks the symmetry to a Z(N) with N the number of quarks charged under U(1)_PQ. The vacuum manifold of Z(N) is disconnected which implies the existence of paths in physical space which map onto paths interpolating between two vacuum states in field space. Such paths necessarily leave the vacuum manifold and the resulting structure is a domain wall.Topologically each string must be connected by N domain walls once the axion gets a mass. Due to the surface energy of domain walls, a network of strings and domain walls with N= 1 would be unstable and collapse. However networks with N >1 are stable in principle and can lead to a cosmological catastrophe if they come to dominate the energy density of the universe after they form [. The standard argument for evading the 'domain wall problem' when N >1 is to invoke non-renormalisable Plank-scale suppressed operators reflecting quantum gravity effects which explicitly break the initial U(1)PQ and lift the degeneracy of the vacuum states, resulting in an effective pressure term which causes the domain of true vacuum to grow. Such explicit breaking of U(1)PQ is however experimentally constrained as it reintroduces the CP violation which is required by experimental upper limits on the neutron electromagnetic dipole moment (EDM) to be negligibly small. By requiring axion domain walls to disappear in time to avoid cosmological catastrophe one can thus infer a lower bound on the neutron EDM. Therefore the `tilt' solution to the domain wall problem is potentially testable by future neutron EDM experiments. We propose an alternative mechanism to render domain walls unstable by instead introducing a statistical `bias' in the population of the vacuum states. Such bias is naturally generated by the evolution of the axion field during inflation, under the assumption that inflation lasts long enough for the universe to cool down below A_QCD during inflation so the axion acquires a mass. This possibility has recently been exploited to open up previously excluded axion parameter space. It has been demonstrated that such bias leads for Z(2) models to exponential decay of the co-moving domain wall energy density. The impact of this on the most likely mass for axions to make up dark matter will be studied, as this is particularly relevant to ongoing searches for axions including in the UK 'Quantum Sensors for the Hidden Sector' programme.