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Register a new userCosmological Parameter Estimation from the Two-Dimensional Genus Topology -- Measuring the Expansion History using the Genus Amplitude as a Standard Ruler
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We measure the genus of the galaxy distribution in two-dimensional slices of the SDSS-III BOSS catalog to constrain the cosmological parameters governing the expansion history of the Universe. The BOSS catalogs are divided into twelve concentric shells over the redshift range $0.25 < z < 0.6$ and we repeatedly measure the genus from the two-dimensional galaxy density fields, each time varying the cosmological parameters used to infer the distance-redshift relation to the shells. We also indirectly reconstruct the two-dimensional genus amplitude using the three-dimensional genus measured from SDSS Main Galaxy Sample with galaxies at low redshift $z < 0.12$. We combine the low- and high-redshift measurements, finding the cosmological model which minimizes the redshift evolution of the genus amplitude, using the fact that this quantity should be conserved. Being a distance measure, the test is sensitive to the matter density parameter ($Omega_{rm m}$) and equation of state of dark energy ($w_{rm de}$). We find a constraint of $w_{rm de} = -1.05^{+0.13}_{-0.12}$, $Omega_{rm m} = 0.303 pm 0.036$ after combining the high- and low-redshift measurements and combining with Planck CMB data. Higher redshift data and combining data sets at low redshift will allow for stronger constraints.
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We present measurements of the two-dimensional genus of the SDSS-III BOSS catalogs to constrain cosmological parameters governing the shape of the matter power spectrum. The BOSS data are divided into twelve concentric shells over the redshift range $0.2 < z < 0.6$, and we extract the genus from the projected two-dimensional galaxy density fields. We compare the genus amplitudes to their Gaussian expectation values, exploiting the fact that this quantity is relatively insensitive to non-linear gravitational collapse. The genus amplitude provides a measure of the shape of the linear matter power spectrum, and is principally sensitive to $Omega_{rm c}h^{2}$ and scalar spectral index $n_{rm s}$. A strong negative degeneracy between $Omega_{rm c}h^{2}$ and $n_{rm s}$ is observed, as both can increase small scale power by shifting the peak and tilting the power spectrum respectively. We place a constraint on the particular combination $n_{rm s}^{3/2} Omega_{rm c}h^{2}$ -- we find $n_{rm s}^{3/2} Omega_{rm c}h^{2} = 0.1121 pm 0.0043$ after combining the LOWZ and CMASS data sets, assuming a flat $Lambda$CDM cosmology. This result is practically insensitive to reasonable variations of the power spectrum amplitude and linear galaxy bias. Our results are consistent with the Planck best fit $n_{rm s}^{3/2}Omega_{rm c}h^{2} = 0.1139 pm 0.0009$.
We study the topology of the matter density field in two dimensional slices, and consider how we can use the amplitude $A$ of the genus for cosmological parameter estimation. Using the latest Horizon Run 4 simulation data, we calculate the genus of the smoothed density field constructed from lightcone mock galaxy catalogs. Information can be extracted from the amplitude of the genus by considering both its redshift evolution and magnitude. The constancy of the genus amplitude with redshift can be used as a standard population, from which we derive constraints on the equation of state of dark energy $w_{rm de}$ - by measuring $A$ at $z sim 0.1$ and $z sim 1$, we can place an order $Delta w_{rm de} sim {cal O}(15%)$ constraint on $w_{rm de}$. By comparing $A$ to its Gaussian expectation value we can potentially derive an additional stringent constraint on the matter density $Delta Omega_{rm mat} sim 0.01$. We discuss the primary sources of contamination associated with the two measurements - redshift space distortion and shot noise. With accurate knowledge of galaxy bias, we can successfully remove the effect of redshift space distortion, and the combined effect of shot noise and non-linear gravitational evolution is suppressed by smoothing over suitably large scales $R_{rm G} ge 15 {rm Mpc}/h$. Without knowledge of the bias, we discuss how joint measurements of the two and three dimensional genus can be used to constrain the growth factor $beta = f/b$. The method can be applied optimally to redshift slices of a galaxy distribution generated using the drop-off technique.
In this work, we use the simulated gravitational wave (GW) standard siren data from the future observation of the Einstein Telescope (ET) to constrain various dark energy cosmological models, including the $Lambda$CDM, $w$CDM, CPL, $alpha$DE, GCG, and NGCG models. We also use the current mainstream cosmological electromagnetic observations, i.e., the cosmic microwave background anisotropies data, the baryon acoustic oscillations data, and the type Ia supernovae data, to constrain these models. We find that the GW standard siren data could tremendously improve the constraints on the cosmological parameters for all these dark energy models. For all the cases, the GW standard siren data can be used to break the parameter degeneracies generated by the current cosmological electromagnetic observational data. Therefore, it is expected that the future GW standard siren observation from the ET would play a crucial role in the cosmological parameter estimation in the future. The conclusion of this work is quite solid because it is based on the analysis for various dark energy models.
The third-generation ground-based gravitational-wave (GW) detector, Cosmic Explorer (CE), is scheduled to start its observation in the 2030s. In this paper, we make a forecast for cosmological parameter estimation with gravitational-wave standard siren observation from the CE. We use the simulated GW standard siren data of CE to constrain the $Lambda$CDM, $w$CDM and CPL models. We combine the simulated GW data with the current cosmological electromagnetic observations including the latest cosmic microwave background anisotropies data from Planck, the optical baryon acoustic oscillation measurements, and the type Ia supernovae observation (Pantheon compilation) to do the analysis. We find that the future standard siren observation from CE will improve the cosmological parameter estimation to a great extent, since the future GW standard siren data can well break the degeneracies generated by the optical observations between various cosmological parameters. We also find that the CEs constraining capability on the cosmological parameters is slightly better than that of the same-type GW detector, the Einstein Telescope. In addition, the synergy between the GW standard siren observation from CE and the 21 cm emission observation from SKA is also discussed.
We study the topology of cosmic large-scale structure through the genus statistics, using galaxy catalogues generated from the Millennium Simulation and observational data from the latest Sloan Digital Sky Survey Data Release (SDSS DR7). We introduce a new method for constructing galaxy density fields and for measuring the genus statistics of its isodensity surfaces. It is based on a Delaunay tessellation field estimation (DTFE) technique that allows the definition of a piece-wise continuous density field and the exact computation of the topology of its polygonal isodensity contours, without introducing any free numerical parameter. Besides this new approach, we also employ the traditional approaches of smoothing the galaxy distribution with a Gaussian of fixed width, or by adaptively smoothing with a kernel that encloses a constant number of neighboring galaxies. Our results show that the Delaunay-based method extracts the largest amount of topological information. Unlike the traditional approach for genus statistics, it is able to discriminate between the different theoretical galaxy catalogues analyzed here, both in real space and in redshift space, even though they are based on the same underlying simulation model. In particular, the DTFE approach detects with high confidence a discrepancy of one of the semi-analytic models studied here compared with the SDSS data, while the other models are found to be consistent.
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