Relativistic Corrections to the Thermal Sunyaev-Zel'dovich Power Spectrum

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We present a quantitative estimate of the relativistic corrections to the thermal SZ power spectrum produced by the energetic electrons in massive clusters. The corrections are well within 10% for current experiments with working frequencies below v 350 GHz. Moreover, the corrections appear to be slightly smaller at higher l or smaller angular scales. We conclude that there is no need to include the relativistic corrections in the theoretical study of the SZ power spectrum especially at low frequencies unless the SZ power spectrum is used for precision cosmology.