February 2010
聲聞乘 cosmic sound transducers: Cosmic sound - curvature and the microwave background radiation →
Sound waves travel at the speed of sound cs. For ordinary sound waves in air, this amounts to around 300 meters per second. In contrast, for the plasma sound waves in the early universe, the speed of sound amounts to roughly 60% of the speed of light. The speed of sound tells us how fast existing density perturbations travel through space. But it also tells us how long it takes to excite specific oscillations: It takes a region of spatial extension L a time L/cs to settle into a coherent state of oscillation in which the plasma density increases and decreases in the same way throughout the whole region. This leads to an upper limit for the spatial extent of any acoustic oscillation in the early universe. The reason is that there was only a limited time, the aforementioned 400,000 years, for these oscillations to be excited in the cosmic plasma. After that period of time, the plasma particles combined to form stable atoms. Since the strong electromagnetic coupling between photons and matter depended on the presence of free electric charges (photons are constantly being absorbed and re-emitted by charged particles), the formation of atoms meant that the strong coupling of photons and matter came to an end. There was an abrupt drop in pressure, and the oscillations ceased. At the close of those 400,000 years, the largest possible coherent oscillations had a spatial extent of 230,000 lightyears (or 70,000 parsec). There was simply no time for more: With the speed of sound at 60% light speed and a time of roughly 400,000 years, the largest regions in which coherent oscillations could develop had a spatial extent of 0.6·400,000 = 240,000 lightyears; with the more precise value of 380,000 years for the cosmic time when atoms formed, the result is 230,000 lightyears. This upper limit is called the “sound horizon”. — EINSTEIN ONLINE
