We study the bootstrapped Newtonian potential generated by a localised source in one and two spatial dimensions, and show that both cases naturally lead to finite spatial extensions of the outer vacuum. We speculate that this implies the necessary existence of a cosmological (particle) horizon associated with compact sources. In view of the possible dimensional reduction occurring in ultra-high energy processes—like scatterings at Planckian energies, the gravitational collapse of compact objects or the end-point of black hole evaporation—one can consider such lower-dimensional ‘bubbles’ immersed in our Universe as describing (typically Planckian size) baby Universes relevant to those dynamics.

我们研究了在一个和两个空间维度上由局部源生成的自举牛顿势，并表明这两种情况自然会导致外部真空的有限空间扩展。我们推测这暗示着与紧凑源相关的宇宙（粒子）视界的必要存在。鉴于超高能量过程中可能发生的尺寸减小（例如普朗克能量的散射，致密物体的重力坍塌或黑洞蒸发的终点），我们可以考虑将这种低尺寸的“气泡”浸入我们的宇宙（描述（通常是普朗克大小）婴儿）与这些动力学相关的宇宙。