https://doi.org/10.1140/epjc/s10052-024-13564-1
Regular Article - Theoretical Physics
Gravitational wave luminosity distance for Starobinsky gravity in viscous cosmological models
1
Department of Physics, Liaoning Normal University, 116029, Dalian, People’s Republic of China
2
College of Physical Science and Technology, Yangzhou University, 225009, Yangzhou, People’s Republic of China
3
School of Liberal Arts and Sciences, North China Institute of Aerospace Engineering, 06500, Langfang, People’s Republic of China
a ybwu@lnnu.edu.cn, ybwu61@163.com
Received:
20
September
2024
Accepted:
1
November
2024
Published online:
15
January
2025
In this paper, in the Starobinsky gravity (SG) model, the gravitational wave (GW) luminosity distance is analytically and numerically investigated by considering the dark matter as the two different kinds of shear viscous fluids in universe. Concretely, on the basis of the propagation equation of the metric perturbation derived by using transverse-traceless gauge for the linear perturbation of the metric in FRW background, we obtain the analytical expressions of the modified friction term
and the ratio
of GW to electromagnetic (EM) wave luminosity distance, and find that they only depend on the SG model parameter
and the shear viscous coefficient
, regardless of the bulk viscous coefficient
. Evidently, both of them are affected by
and
. It worth stressing that the results given by us can reduce to ones in documents [13, 22, 30]. It follows that we can extend the previous results as the special cases in our model. Furthermore, by combining the latest observational data, we more tightly constrain the values of related parameters and numerically analyze the influence of both
and
on
and
. We observe that, in the range of
, the evolutionary curves of
and
exhibit that
(
) monotonically decrease (increase) as redshift rises, moreover there are always
and
, specially
in the limit of
, which means that detecting GW signals might represent a more efficient tool than detecting EM signals to test modified gravity model on the given scale of cosmic distances. It is worth noting that the numerical analyses to
and
illustrate once again that the GW luminosity distance
is indeed influenced by
and
, in particular more sensitive to
than
in our model. In addition, by comparing the GW and EM luminosity distances of SG model with
of Einstein GR, we find that the GW and EM signals in SG1 and SG2 change from stronger to weaker than the ones in GR as redshift increases and more difficultly to be detected in the same distance and detection sensitivity. Meanwhile, the EM signals change from strong to weak earlier than GW signals do. Finally, we confirm that
and
of our model meet the constraints imposed by the standard siren GW170817 and its electromagnetic companion GRB170817A.
© The Author(s) 2025
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