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Register a new userNon-parametric reconstruction of cosmological matter perturbations
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Added by
Javier E Gonz\\'alez S\\'anchez
Publication date
2016
fields
Physics
and research's language is
English
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Perturbative quantities, such as the growth rate ($f$) and index ($gamma$), are powerful tools to distinguish different dark energy models or modified gravity theories even if they produce the same cosmic expansion history. In this work, without any assumption about the dynamics of the Universe, we apply a non-parametric method to current measurements of the expansion rate $H(z)$ from cosmic chronometers and high-$z$ quasar data and reconstruct the growth factor and rate of linearised density perturbations in the non-relativistic matter component. Assuming realistic values for the matter density parameter $Omega_{m0}$, as provided by current CMB experiments, we also reconstruct the evolution of the growth index $gamma$ with redshift. We show that the reconstruction of current $H(z)$ data constrains the growth index to $gamma=0.56 pm 0.12$ (2$sigma$) at $z = 0.09$, which is in full agreement with the prediction of the $Lambda$CDM model and some of its extensions.
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The cosmological jerk parameter $j$ is reconstructed in a non-parametric way from observational data independent of a fiducial cosmological model. From this kinematical quantity, the equation of state parameter for composite matter distribution is also found out. The result shows that there is a deviation from the $Lambda$CDM model close to $z=1.5$, at the $3sigma$ confidence level.
The existing degeneracy between different dark energy and modified gravity cosmologies at the background level may be broken by analysing quantities at the perturbative level. In this work, we apply a non-parametric smoothing (NPS) method to reconstruct the expansion history of the Universe ($H(z)$) from model-independent cosmic chronometers and high-$z$ quasar data. Assuming a homogeneous and isotropic flat universe and general relativity (GR) as the gravity theory, we calculate the non-relativistic matter perturbations in the linear regime using the $H(z)$ reconstruction and realistic values of $Omega_{m0}$ and $sigma_8$ from Planck and WMAP-9 collaborations. We find a good agreement between the measurements of the growth rate and $fsigma_8(z)$ from current large-scale structure observations and the estimates obtained from the reconstruction of the cosmic expansion history. Considering a recently proposed null test for GR using matter perturbations, we also apply the NPS method to reconstruct $fsigma_8(z)$. For this case, we find a $sim 2sigma$ tension (good agreement) with the standard relativistic cosmology when the Planck (WMAP-9) priors are used.
In the context of a Hubble tension problem that is growing in its statistical significance, we reconsider the effectiveness of non-parametric reconstruction techniques which are independent of prescriptive cosmological models. By taking cosmic chronometers, Type Ia Supernovae and baryonic acoustic oscillation data, we compare and contrast two important reconstruction approaches, namely Gaussian processes (GP) and the Locally weighted Scatterplot Smoothing together with Simulation and extrapolation method (LOESS-Simex or LS). We firstly show how both GP and LOESS-Simex can be used to successively reconstruct various data sets to a high level of precision. We then directly compare both approaches in a quantitative manner by considering several factors, such as how well the reconstructions approximate the data sets themselves to how their respective uncertainties evolve. In light of the puzzling Hubble tension, it is important to consider how the uncertain regions evolve over redshift and the methods compare for estimating cosmological parameters at current times. For cosmic chronometers and baryonic acoustic oscillation compiled data sets, we find that GP generically produce smaller variances for the reconstructed data with a minimum value of $sigma_{rm GP-min} = 1.1$, while the situation for LS is totally different with a minimum of $sigma_{rm LS-min} = 50.8$. Moreover, some of these characteristics can be alliviate at low $z$, where LS presents less underestimation in comparison to GP.
Inferring high-fidelity constraints on the spatial curvature parameter, $Omega_{rm K}$, under as few assumptions as possible, is of fundamental importance in cosmology. We propose a method to non-parametrically infer $Omega_{rm K}$ from late-Universe probes alone. Using Gaussian Processes (GP) to reconstruct the expansion history, we combine Cosmic Chronometers (CC) and Type Ia Supernovae (SNe~Ia) data to infer constraints on curvature, marginalized over the expansion history, calibration of the CC and SNe~Ia data, and the GP hyper-parameters. The obtained constraints on $Omega_{rm K}$ are free from parametric model assumptions for the expansion history, and are insensitive to the overall calibration of both the CC and SNe~Ia data (being sensitive only to relative distances and expansion rates). Applying this method to textit{Pantheon} SNe~Ia and the latest compilation of CCs, we find $Omega_{rm K} = -0.03 pm 0.26$, consistent with spatial flatness at the $mathcal{O}(10^{-1})$ level, and independent of any early-Universe probes. Applying our methodology to future Baryon Acoustic Oscillations and SNe~Ia data from upcoming Stage IV surveys, we forecast the ability to constrain $Omega_{rm K}$ at the $mathcal{O}(10^{-2})$ level.
A non-parametric reconstruction of the deceleration parameter $q$ is carried out. The observational datasets are so chosen that they are model independent as much as possible. The present acceleration and the epoch at which the cosmic acceleration sets in is quite as expected, but beyond a certain redshift ($z sim 2$), a negative value of $q$ appears to be in the allowed region. A survey of existing literature is given and compared with the results obtained in the present work.
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