https://doi.org/10.1140/epjc/s10052-022-10742-x
Regular Article - Theoretical Physics
Impact of the free-streaming neutrinos to the second order induced gravitational waves
1
Institute of High Energy Physics, Chinese Academy of Sciences, 100049, Beijing, China
2
University of Chinese Academy of Sciences, 100049, Beijing, China
Received:
14
December
2021
Accepted:
22
August
2022
Published online:
2
September
2022
The damping effect of the free-streaming neutrinos on the second order gravitational waves is investigated in detail. We solve the Boltzmann equation and give the anisotropic stress induced by neutrinos to second order. The first order tensor and its coupling with scalar perturbations induced gravitational waves are considered. We give the analytic equations of the damping kernel functions and finally obtain the energy density spectrum. The results show that the free-streaming neutrinos suppress the density spectrum significantly for low frequency gravitational waves and enlarge the logarithmic slope n in the infrared region (
) of the spectrum. For the spectrum of 
, the damping effect in the range of 
is significant. The combined effect of the first and second order could reduce the amplitude by 
and make n jump from 1.54 to 1.63 at 
, which may be probed by the pulsar timing arrays (PTA) in the future.
© The Author(s) 2022
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