Catálogo de publicaciones - revistas

<jats:title>Abstract</jats:title> <jats:p>In this contribution, the <jats:inline-formula> <jats:tex-math><?CDATA $\alpha$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_014110_M1.jpg" xlink:type="simple" /> </jats:inline-formula> preformation factors of 606 nuclei are extracted within the framework of the generalized liquid drop model (GLDM). Through the systematic analysis of the <jats:inline-formula> <jats:tex-math><?CDATA $\alpha$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_014110_M2.jpg" xlink:type="simple" /> </jats:inline-formula> preformation factors of even-even Po-U isotopes, we found that there is a significant weakening of influence of <jats:inline-formula> <jats:tex-math><?CDATA $N=126$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_014110_M3.jpg" xlink:type="simple" /> </jats:inline-formula> shell closure in uranium, which is consistent with the results of a recent experiment [J. Khuyagbaatar <jats:italic>et al</jats:italic>., Phys. Rev. Lett. <jats:bold>115</jats:bold>, 242502 (2015)], implying that <jats:inline-formula> <jats:tex-math><?CDATA $N=126$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_014110_M4.jpg" xlink:type="simple" /> </jats:inline-formula> may not be the magic number for U isotopes. Furthermore, we propose an improved formula with only 7 parameters to calculate <jats:inline-formula> <jats:tex-math><?CDATA $\alpha$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_014110_M5.jpg" xlink:type="simple" /> </jats:inline-formula> preformation factors suitable for all types of <jats:inline-formula> <jats:tex-math><?CDATA $\alpha$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_014110_M6.jpg" xlink:type="simple" /> </jats:inline-formula>-decay; it has fewer parameters than the original formula proposed by Zhang <jats:italic>et al</jats:italic>. [H. F. Zhang <jats:italic>et al</jats:italic>., Phys. Rev. C <jats:bold>80</jats:bold>, 057301 (2009)] with higher precision. The standard deviation of the <jats:inline-formula> <jats:tex-math><?CDATA $\alpha$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_014110_M7.jpg" xlink:type="simple" /> </jats:inline-formula> preformation factors calculated by our formula with extracted values for all 606 nuclei is 0.365 with a factor of 2.3, indicating that our improved formula can accurately reproduce the <jats:inline-formula> <jats:tex-math><?CDATA $\alpha$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_014110_M8.jpg" xlink:type="simple" /> </jats:inline-formula> preformation factors. Encouraged by this, the <jats:inline-formula> <jats:tex-math><?CDATA $\alpha$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_014110_M9.jpg" xlink:type="simple" /> </jats:inline-formula>-decay half-lives of actinide elements are predicted, which could be useful in future experiments. Notably, the predicted <jats:inline-formula> <jats:tex-math><?CDATA $\alpha$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_014110_M10.jpg" xlink:type="simple" /> </jats:inline-formula>-decay half-lives of two new isotopes <jats:inline-formula> <jats:tex-math><?CDATA $^{220}$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_014110_M11.jpg" xlink:type="simple" /> </jats:inline-formula>Np [Z. Y. Zhang, <jats:italic>et al</jats:italic>., Phys. Rev. Lett. <jats:bold>122</jats:bold>, 192503 (2019)] and <jats:inline-formula> <jats:tex-math><?CDATA $^{219}$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_014110_M12.jpg" xlink:type="simple" /> </jats:inline-formula>Np [H. B. Yang <jats:italic>et al</jats:italic>., Phys. Lett. B <jats:bold>777</jats:bold>, 212 (2018)] are in good agreement with the experimental <jats:inline-formula> <jats:tex-math><?CDATA $\alpha$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_014110_M13.jpg" xlink:type="simple" /> </jats:inline-formula>-decay half-lives. </jats:p>

<jats:title>Abstract</jats:title> <jats:p>We investigate the evolution of abundance of the asymmetric thermal Dark Matter when its annihilation rate at chemical decoupling is boosted by the Sommerfeld enhancement. Next, we discuss the effect of kinetic decoupling on the relic abundance of asymmetric Dark Matter when the interaction rate depends on velocity. Usually, the relic density of asymmetric Dark Matter is analyzed in the frame of chemical decoupling. Indeed, after decoupling from chemical equilibrium, asymmetric Dark Matter particles and anti-particles are still in kinetic equilibrium for a while. This has no effect for the case of <jats:italic>s-</jats:italic>wave annihilation since there is no temperature dependence in this case. However, kinetic decoupling has impacts for the case of <jats:italic>p-</jats:italic>wave annihilation and Sommerfeld enhanced <jats:italic>s-</jats:italic> and <jats:italic>p-</jats:italic>wave annihilations. We investigate in detail the extent to which kinetic decoupling affects the relic abundance of asymmetric Dark Matter particles and anti-particles. We find the constraints on the cross section and asymmetry factor using observational data of the relic density of Dark Matter. </jats:p>

<jats:title>Abstract</jats:title> <jats:p>The transonic phenomenon of black hole accretion and the existence of the photon sphere characterize strong gravitational fields near a black hole horizon. Here, we study the spherical accretion flow onto general parametrized spherically symmetric black hole spacetimes. We analyze the accretion process for various perfect fluids, such as the isothermal fluids of ultra-stiff, ultra-relativistic, and sub-relativistic types, and the polytropic fluid. The influences of additional parameters, beyond the Schwarzschild black hole in the framework of general parameterized spherically symmetric black holes, on the flow behavior of the above-mentioned test fluids are studied in detail. In addition, by studying the accretion of the ideal photon gas, we further discuss the correspondence between the sonic radius of the accreting photon gas and the photon sphere for general parameterized spherically symmetric black holes. Possible extensions of our analysis are also discussed.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>We investigate the bulk viscosity of strange quark matter in the framework of the equivparticle model, where analytical formulae are obtained for certain temperature ranges, which can be readily applied to those with various quark mass scalings. In the case of adopting a quark mass scaling with both linear confinement and perturbative interactions, the obtained bulk viscosity increases by <jats:inline-formula> <jats:tex-math><?CDATA $1 \sim 2$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_015103_M1.jpg" xlink:type="simple" /> </jats:inline-formula> orders of magnitude compared with those in bag model scenarios. Such an enhancement is mainly due to the large quark equivalent masses adopted in the equivparticle model, which are essentially attributed to the strong interquark interactions and are related to the dynamical chiral symmetry breaking. Due to the high bulk viscosity, the predicted damping time of oscillations for a canonical 1.4 <jats:inline-formula> <jats:tex-math><?CDATA ${\rm M}_\odot$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_015103_M2.jpg" xlink:type="simple" /> </jats:inline-formula> strange star is less than one millisecond, which is shorter than previous findings. Consequently, the obtained <jats:inline-formula> <jats:tex-math><?CDATA $r$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_015103_M3.jpg" xlink:type="simple" /> </jats:inline-formula>-mode instability window for the canonical strange stars well accommodates the observational frequencies and temperatures for pulsars in low-mass X-ray binaries (LMXBs). </jats:p>

<jats:title>Abstract</jats:title> <jats:p>Hawking-Page phase transitions between the thermal anti-de Sitter vacuum and charged black holes surrounded by quintessence are studied in the extended phase space. The quintessence field, with the state parameter <jats:inline-formula> <jats:tex-math><?CDATA $-1 \lt w \lt -1/3$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_015104_M1.jpg" xlink:type="simple" /> </jats:inline-formula>, modifies the temperature and the Gibbs free energy of a black hole. The phase transition temperature <jats:inline-formula> <jats:tex-math><?CDATA $T_{\rm{HP}}$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_015104_M2.jpg" xlink:type="simple" /> </jats:inline-formula> and the Gibbs free energy <jats:inline-formula> <jats:tex-math><?CDATA $G$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_015104_M3.jpg" xlink:type="simple" /> </jats:inline-formula> are first analytically investigated for the special case of <jats:inline-formula> <jats:tex-math><?CDATA $w=-2/3$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_015104_M4.jpg" xlink:type="simple" /> </jats:inline-formula>, and then, the results of numerical simulations are shown for general <jats:inline-formula> <jats:tex-math><?CDATA $w$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_015104_M5.jpg" xlink:type="simple" /> </jats:inline-formula>. The phase transition temperature <jats:inline-formula> <jats:tex-math><?CDATA $T_{\rm{HP}}$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_015104_M6.jpg" xlink:type="simple" /> </jats:inline-formula> increases with pressure and decreases with electric potential. In addition, <jats:inline-formula> <jats:tex-math><?CDATA $T_{\rm{HP}}$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_015104_M7.jpg" xlink:type="simple" /> </jats:inline-formula> significantly decreases owing to the quintessence field, which generates negative pressure around the black hole. </jats:p>

<jats:title>Abstract</jats:title> <jats:p>Recently, a novel four-dimensional Einstein-Gauss-Bonnet (4EGB) theory of gravity was proposed by Glavan and Lin [D. Glavan and C. Lin, Phys. Rev. Lett. 124, 081301 (2020)], which includes a regularized Gauss-Bonnet term using the re-scalaring of the Gauss-Bonnet coupling constant <jats:inline-formula> <jats:tex-math><?CDATA $\alpha \to \alpha/(D-4)$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_015105_M1.jpg" xlink:type="simple" /> </jats:inline-formula> in the limit <jats:inline-formula> <jats:tex-math><?CDATA $D\to 4$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_015105_M2.jpg" xlink:type="simple" /> </jats:inline-formula>. This theory has also been reformulated to a specific class of the Horndeski theory with an additional scalar degree of freedom and to a spatial covariant version with a Lagrangian multiplier, which can eliminate the scalar mode. Here, we study the physical properties of the electromagnetic radiation emitted from a thin accretion disk around a static spherically symmetric black hole in 4EGB gravity. For this purpose, we assume the disk is in a steady-state and in hydrodynamic and thermodynamic equilibrium, so that the emitted electromagnetic radiation is a black body spectrum. We study in detail the effects of the Gauss-Bonnet coupling constant <jats:inline-formula> <jats:tex-math><?CDATA $\alpha$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_015105_M3.jpg" xlink:type="simple" /> </jats:inline-formula> in 4EGB gravity on the energy flux, temperature distribution, and electromagnetic spectrum of the disk. With an increase in the parameter <jats:inline-formula> <jats:tex-math><?CDATA $\alpha$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_015105_M4.jpg" xlink:type="simple" /> </jats:inline-formula>, the energy flux, temperature distribution, and electromagnetic spectrum of the accretion disk all increase. We also show that the accretion efficiency increases with the growth of the parameter <jats:inline-formula> <jats:tex-math><?CDATA $\alpha$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_015105_M5.jpg" xlink:type="simple" /> </jats:inline-formula>. Our results indicate that the thin accretion disk around a static spherically symmetric black hole in 4EGB gravity is hotter, more luminous, and more efficient than that around a Schwarzschild black hole with the same mass for positive <jats:inline-formula> <jats:tex-math><?CDATA $\alpha$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_015105_M6.jpg" xlink:type="simple" /> </jats:inline-formula>, while it is cooler, less luminous, and less efficient for negative <jats:inline-formula> <jats:tex-math><?CDATA $\alpha$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_015105_M7.jpg" xlink:type="simple" /> </jats:inline-formula>. </jats:p>

<jats:title>Abstract</jats:title> <jats:p>Inspired by the hypothesis of the black hole molecule, with the help of the Hawking temperature, entropy, and the thermodynamic curvature of black holes, we propose a new measure of the relation between the interaction and the thermal motion of molecules of the AdS black hole as a preliminary and coarse-grained description. The proposed measure introduces a dimensionless ratio to characterize this relation and shows that there is indeed competition between the interactions of black hole molecules and their thermal motion. For a charged AdS black hole, below the critical dimensionless pressure, there are three transitions between the interaction and thermal motion states. In contrast, above the critical dimensionless pressure, only one transition takes place. For the Schwarzschild-AdS and five-dimensional Gauss-Bonnet AdS black holes, a transition always occurs between the interaction and thermal motion states.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>It was previously claimed by the author that black holes can be considered as topological insulators. Both black holes and topological insulators have boundary modes, and the boundary modes can be described by an effective BF theory. In this paper, the boundary modes on the horizons of black holes are analyzed using methods developed for topological insulators. BTZ black holes are analyzed first, and the results are found to be compatible with previous works. The results are then generalized to Kerr black holes, for which new results are obtained: dimensionless right- and left-temperatures can be defined and have well behavior in both the Schwarzschild limit <jats:inline-formula> <jats:tex-math><?CDATA $a\rightarrow 0$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_015107_M1.jpg" xlink:type="simple" /> </jats:inline-formula> and the extremal limit <jats:inline-formula> <jats:tex-math><?CDATA $a\rightarrow M$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_015107_M2.jpg" xlink:type="simple" /> </jats:inline-formula>. Upon the Kerr/CFT correspondence, a central charge <jats:inline-formula> <jats:tex-math><?CDATA $c=12 M r_+$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_015107_M3.jpg" xlink:type="simple" /> </jats:inline-formula> can be associated with an arbitrary Kerr black hole. Moreover, the microstates of the Kerr black hole can be identified with the quantum states of this scalar field. From this identification, the number of microstates of the Kerr black hole can be counted, yielding the Bekenstein-Hawking area law for the entropy. </jats:p>

<jats:title>Abstract</jats:title> <jats:p>Recent low-redshift observations have yielded the present-time Hubble parameter value <jats:inline-formula> <jats:tex-math><?CDATA $H_{0}\simeq 74\;\rm{km s}^{-1} \rm{Mpc}^{-1}$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_015108_M1.jpg" xlink:type="simple" /> </jats:inline-formula>. This value is approximately 10% higher than the predicted value of <jats:inline-formula> <jats:tex-math><?CDATA $H_{0}=67.4\;\rm{km s}^{-1}\rm{Mpc}^{-1}$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_015108_M2.jpg" xlink:type="simple" /> </jats:inline-formula>, based on Planck's observations of the Cosmic Microwave Background radiation (CMB) and the <jats:inline-formula> <jats:tex-math><?CDATA $\Lambda$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_015108_M3.jpg" xlink:type="simple" /> </jats:inline-formula>CDM model. Phenomenologically, we show that, by adding an extra component, <jats:italic>X,</jats:italic> with negative density to the Friedmann equation, it can address the Hubble tension without changing the Planck's constraint on the matter and dark energy densities. To achieve a sufficiently small extra negative density, its equation-of-state parameter must satisfy <jats:inline-formula> <jats:tex-math><?CDATA $1/3\leqslant w_{X}\leqslant 1$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_015108_M4.jpg" xlink:type="simple" /> </jats:inline-formula>. We propose a quintom model of two scalar fields that realizes this condition and potentially alleviate the Hubble tension. One scalar field acts as a quintessence, while another “phantom” scalar conformally couples to matter such that a viable cosmological scenario is achieved. The model only depends on two parameters, <jats:inline-formula> <jats:tex-math><?CDATA $\lambda_{\phi}$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_015108_M5.jpg" xlink:type="simple" /> </jats:inline-formula> and <jats:inline-formula> <jats:tex-math><?CDATA $\delta$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_015108_M6.jpg" xlink:type="simple" /> </jats:inline-formula> , which represent the rolling tendency of the self-interacting potential of the quintessence and the strength of the conformal phantom-matter coupling, respectively. The toy quintom model with <jats:inline-formula> <jats:tex-math><?CDATA $H_{0}=73.4\;\rm{km s}^{-1}\rm{Mpc}^{-1}$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_015108_M7.jpg" xlink:type="simple" /> </jats:inline-formula> (Quintom I) yields a good Supernovae-Ia luminosity fit and acceptable <jats:inline-formula> <jats:tex-math><?CDATA $r_{\rm BAO}$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_015108_M8.jpg" xlink:type="simple" /> </jats:inline-formula> fit but slightly small acoustic multipole <jats:inline-formula> <jats:tex-math><?CDATA $\ell_{A}=285.54$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_015108_M9.jpg" xlink:type="simple" /> </jats:inline-formula>. A full parameter scan revealed that the quintom model was superior to the <jats:inline-formula> <jats:tex-math><?CDATA $\Lambda$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_015108_M10.jpg" xlink:type="simple" /> </jats:inline-formula>CDM model in certain regions of the parameter space, <jats:inline-formula> <jats:tex-math><?CDATA $0.02 \lt\delta \lt0.10, \Omega_{m}^{(0)} \lt0.31$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_015108_M11.jpg" xlink:type="simple" /> </jats:inline-formula>, while significantly alleviating the Hubble tension, although it is not completely resolved. A benchmark quintom model, Quintom II, is presented as an example. </jats:p>

<jats:title>Abstract</jats:title> <jats:p>The cosmic distance relation (DDR) associates the angular diameters distance ( <jats:inline-formula> <jats:tex-math><?CDATA $ D_A $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_015109_M1.jpg" xlink:type="simple" /> </jats:inline-formula>) and luminosity distance ( <jats:inline-formula> <jats:tex-math><?CDATA $ D_L $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_015109_M2.jpg" xlink:type="simple" /> </jats:inline-formula>) by a simple formula, i.e., <jats:inline-formula> <jats:tex-math><?CDATA $ D_L = (1+z)^2D_A $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_015109_M3.jpg" xlink:type="simple" /> </jats:inline-formula>. The strongly lensed gravitational waves (GWs) provide a unique way to measure <jats:inline-formula> <jats:tex-math><?CDATA $ D_A $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_015109_M4.jpg" xlink:type="simple" /> </jats:inline-formula> and <jats:inline-formula> <jats:tex-math><?CDATA $ D_L $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_015109_M5.jpg" xlink:type="simple" /> </jats:inline-formula> simultaneously to the GW source, hence they can be used as probes to test DDR. In this study, we investigated the use of strongly lensed GW events from the future Einstein Telescope to test DDR. We assumed the possible deviation of DDR as <jats:inline-formula> <jats:tex-math><?CDATA $ (1+z)^2D_A/D_L = \eta(z) $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_015109_M6.jpg" xlink:type="simple" /> </jats:inline-formula>, and considered two different parametrizations of <jats:inline-formula> <jats:tex-math><?CDATA $ \eta(z) $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_015109_M7.jpg" xlink:type="simple" /> </jats:inline-formula>, namely, <jats:inline-formula> <jats:tex-math><?CDATA $ \eta_1(z) = 1+\eta_0 z $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_015109_M8.jpg" xlink:type="simple" /> </jats:inline-formula> and <jats:inline-formula> <jats:tex-math><?CDATA $ \eta_2(z) = 1+\eta_0 z/(1+z) $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_015109_M9.jpg" xlink:type="simple" /> </jats:inline-formula>. Numerical simulations showed that, with about 100 strongly lensed GW events observed by ET, the parameter <jats:inline-formula> <jats:tex-math><?CDATA $ \eta_0 $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_015109_M10.jpg" xlink:type="simple" /> </jats:inline-formula> was constrained at 1.3% and 3% levels for the first and second parametrizations, respectively. </jats:p>