Gravitational waves (GWs) are produced by colliding particles through the gravitational analogue of electromagnetic bremsstrahlung. We calculate the contribution of free-free emission in the radiation-dominated Universe to the stochastic GW background. We find that the energy density of the resulting GW radiation is heavily dependent on the number of elementary particles, N_tot, and the maximum initial temperature, T_max. We rule out N_tot ≳ 10² × N_SM for T_max ∼ T_Planck ≈ 10¹⁹ GeV and N_tot ≳ 10¹⁶ × N_SM for T_max ∼ 10¹⁶ GeV, where N_SM is the number of particles in the Standard Model. In the case of inflation, existing cosmological data constrain T_max ≲ 10¹⁶ GeV . However, alternative models to inflation such as bouncing cosmologies allow for T_max near T_Planck. At the energy scales we are considering, the extra number of particles arise naturally in models of extra dimensions.

引力波（GWs）是通过电磁致引力的碰撞模拟碰撞粒子而产生的。我们计算了辐射主导的宇宙中自由自由发射对随机GW背景的贡献。我们发现，产生的GW辐射的能量密度在很大程度上取决于基本粒子的数量，ñ _TOT，以及最高初始温度， Ť_最大。我们排除N _tot  ＆gtrsim; 10 ²  ×  N _SM 为了 Ť_最大 〜  Ť_普朗克 ＆约; 10 ¹⁹ GeV和 N _tot  ＆gtrsim; 10 ¹⁶  ×  N _SM 为了 Ť_最大 〜10 ¹⁶ GeV，哪里 N _SM是标准模型中的粒子数。在通货膨胀的情况下，现有的宇宙学数据会受到限制Ť_最大值 ＆lesssim; 10 ¹⁶GeV。但是，通货膨胀的替代模型（例如反弹宇宙学）允许Ť_最大 靠近 Ť_普朗克。在我们正在考虑的能量尺度上，额外的粒子自然会在额外尺寸的模型中自然产生。