COSMOGRAFIA COM ONDAS GRAVITACIONAIS”

Abstract

In this work, we investigate the potential of gravitational-wave standard sirens to constrain cosmographic parameters independently of a specific cosmological model. We consider simulated catalogs of \textit{bright sirens}, assuming the identification of electromagnetic counterparts and, therefore, an independent determination of the source redshifts. The analysis is performed for three observational configurations: Advanced LIGO, Einstein Telescope, and DECIGO, allowing us to compare the performance of current and future detectors in reconstructing the luminosity distance--redshift relation. To describe the cosmic expansion, we use the Taylor cosmographic expansion up to $\mathcal{O}(z^3)$ and the Padé approximants $P_{2,1}$ and $P_{3,2}$, evaluating their convergence properties and their impact on the constraints of the parameters $H_0$, $q_0$, and $j_0$, as well as the higher-order parameters $s_0$ and $l_0$ in the case of Padé $P_{3,2}$. We study two complementary scenarios: an analysis as a function of the signal-to-noise ratio of the events and an analysis as a function of the total number of detections. The results show that Advanced LIGO is mainly sensitive to the determination of $H_0$, reaching relative precisions of about $2\%$ in the SNR-based analysis and approximately $1.1\%$ in the most optimistic scenarios based on the number of events. The Einstein Telescope significantly improves the constraints, reaching subpercent precision for $H_0$, of about $0.5\%$--$0.6\%$, and constraining $q_0$ with relative precision of approximately $16\%$--$19\%$. DECIGO provides the best overall performance, reaching precisions of about $0.25\%$--$0.30\%$ for $H_0$, $6\%$--$10\%$ for $q_0$, and making the jerk parameter $j_0$ observationally informative, with relative precision of approximately $16\%$ in the most favorable scenario. In general, the Taylor expansion provides the best precision for the common set of parameters within its domain of validity, while the Padé approximants are important for assessing the stability of the cosmographic reconstruction over wider redshift intervals. We conclude that gravitational-wave standard sirens constitute a promising and complementary tool for investigating the expansion history of the Universe and testing possible deviations from the standard cosmological model.