ESTRUTURAS EM GRANDES ESCALAS - UMA NOVA METODOLOGIA PARA CALCULAR A TAXA DE CRESCIMENTO DE ESTRUTURAS CÓSMICAS

Abstract

The cosmic growth rate, $f(z)$, presents great potential to discriminate alternative models to $\Lambda$CDM, considered the standard model of cosmology. With its simple parametrization, $f(z)=\Omega_{\text{m}}^\gamma$, the growth rate is able to discriminate alternative models to RG, measure cosmological parameters and test parametrizations for the equation of state of dark energy. This is possible from a robust measurement of $\gamma$. In this work we develop two studies on the growth rate: (i) Using the ALFALFA survey of HI emission line, we select a sample in the Local Universe~($\leq85$ Mpc), to measure the gravitational dipole in the Local Universe. We calculate the Local Group velocity due to the HI distribution in the ALFALFA catalogue and compare it with the Local Group velocity in the CMB frame of reference to obtain the velocity scale parameter, $\beta$. Using Monte Carlo realizations and lognormal simulations, our methodology quantifies the errors introduced by shot noise and partial sky coverage. Measuring the velocity scale parameter $\beta$, and calculating the matter fluctuation of the cosmological tracer, $\sigma_{8,\text{tr}}$, leads us to $f \sigma_{8} = 0.46 \pm 0.06$ at $\bar{z} = 0.013$, at $1 \sigma$, with the expected value in the $\Lambda$CDM model. Furthermore, our analyses of the ALFALFA sample also provide a measurement of the growth rate $f= 0.56 \pm 0.07$, at $\bar{z} = 0. 013$; and (ii) From our experiment with the transition scale to homogeneity, $ R_{\text{H}}(z) $ and its angular version, $\theta_{\text{H}}(z)$, we could observe that it is possible to relate $ R_{\text{H}}(z) $ to the growth rate, $f(z)$. Using fractal methodology, we derive a relationship between the two quantities from $\mathcal{N}(<r,z)$, the scaled counts-in-spheres, and the correlation dimension, $\mathcal{D}_2(r,z)$. We performed the model test from measurements on $ R_{\text{H}}(z) $ collected in the literature. Due to the low number of measurements, we decided to reconstruct the function with the Gaussian Process method. Using the DPL approximation, together with the reconstruction of $R_{\text{H}}(z_i)$ we were able to obtain $f(z)$ from the homogeneity scale. We compared our result with the $\Lambda$CDM model and with measurements of $f(z)$ collected in the literature. For much of the range in $z$, our result is consistent with $\Lambda$CDM, as well as with the $f(z)$ measurements.