Non-Abelian discrete symmetries have been widely used to explain the patterns of lepton masses and flavor mixing. In these models, a given symmetry is assumed at a high scale and then is spontaneously broken by scalars (the flavons), which acquire vacuum expectation values. Typically, the resulting leading order predictions for the oscillation parameters require corrections in order to comply with neutrino oscillation data. We introduce such corrections through an explicit small breaking of the symmetry. This has the advantage of solving the cosmological problems of these models without resorting to inflation. The explicit breaking induces an energy difference or “bias” between different vacua and drives the evolution of the domain walls, unavoidably produced after the symmetry breaking, towards their annihilation. Importantly, the wall annihilation leads to gravitational waves which may be observed in current and/or future experiments. We show that a distinctive pattern of gravitational waves with multiple overlapped peaks is generated when walls annihilate, which is within the reach of future detectors. We also show that cosmic walls from discrete flavor symmetries can be cosmologically safe for any spontaneous breaking scale between 1 and 10¹⁸ GeV, if the bias is chosen adequately, without the need to inflate the walls away. We use as an example a particular A₄ model in which an explicit breaking is included in right-handed neutrino mass terms.

非阿贝尔离散对称已被广泛用于解释轻质物质质量和风味混合的模式。在这些模型中，假定给定的对称性是大规模的，然后被标量（黄酮）自发破坏，标量获得了真空期望值。通常，为了符合中微子振荡数据，需要对振荡参数的最终前导预测进行校正。我们通过明显的对称性小破坏来介绍这种校正。这具有解决这些模型的宇宙学问题而无需求助于通货膨胀的优点。显性破坏在不同真空之间引起能量差或“偏见”，并驱使对称破坏后不可避免地产生的畴壁向an灭。重要的，墙的ni灭会导致重力波，这可以在当前和/或将来的实验中观察到。我们显示出，当墙壁被歼灭时，会产生引力波具有多个重叠峰的独特模式，这在未来的探测器范围之内。我们还显示，对于任何介于1到1之间的自发破坏尺度，来自离散风味对称性的宇宙壁对于宇宙学而言都是安全的。10 ¹⁸GeV，如果选择了适当的偏差，则无需将壁膨胀。我们以一个特定的例子为例A ₄ 右旋中微子质量项中包含显式破坏的模型。