Kaiser-Stebbins Effect

A moving cosmic string can cause a red shift or blue shift of photons passing by it. When a segment of cosmic string is moving to the right, a photon moving in front of the segment perpendicularly (to the plane that contains the comic string) is red shifted, while a photon moving behind the segment is blue shifted.

Figure 6. The Kaiser-Stebbins effect is originated from conic space-time around the cosmic string, which is a filamentary form of vacuum energy. A moving cosmic string induces relative speed between the light source and observer and causes a Doppler shift of photons. In the figure, represents the effective deficit angle viewed from observer.

The height of temperature step caused by a moving cosmic string is given by
 
where = Lorentz factor for string segment, vs = string segment velocity, s = orientation of segment unit vector and k = line of sight unit vector.
  
Figure 7. (a) A rectangular patch of real CMB anisotropy map (WMAP 1st-year W-band), . (b) A straight cosmic string with moving to the right is input. The dotted vertical line indicates the string. It is hard to recognize the temperature step produced by the cosmic string. (c) A more powerful string is input, . Now it clearly shows the temperature contrast caused by the cosmic strings. In this simulation, we set .

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