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Register a new userReconstructing Cosmological Matter Perturbations using Standard Candles and Rulers
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For a large class of dark energy (DE) models, for which the effective gravitational constant is a constant and there is no direct exchange of energy between DE and dark matter (DM), knowledge of the expansion history suffices to reconstruct the growth factor of linearized density perturbations in the non-relativistic matter component on scales much smaller than the Hubble distance. In this paper we develop a non-parametric method for extracting information about the perturbative growth factor from data pertaining to the luminosity or angular size distances. A comparison of the reconstructed density contrast with observations of large scale structure and gravitational lensing can help distinguish DE models such as the cosmological constant and quintessence from models based on modified gravity theories as well as models in which DE and DM are either unified, or interact directly. We show that for current SNe data, the linear growth factor at z = 0.3 can be constrained to 5%, and the linear growth rate to 6%. With future SNe data, such as expected from the JDEM mission, we may be able to constrain the growth factor to 2-3% and the growth rate to 3-4% at z = 0.3 with this unbiased, model-independent reconstruction method. For future BAO data which would deliver measurements of both the angular diameter distance and Hubble parameter, it should be possible to constrain the growth factor at z = 2.5 to 9%. These constraints grow tighter with the errors on the datasets. With a large quantity of data expected in the next few years, this method can emerge as a competitive tool for distinguishing between different models of dark energy.
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Gravitational waves detected from well-localized inspiraling binaries would allow to determine, directly and independently, both binary luminosity and redshift. In this case, such systems could behave as standard candles providing an excellent probe of cosmic distances up to $z <0.1$ and thus complementing other indicators of cosmological distance ladder.
A decomposed generalised Chaplygin gas (gCg) with energy flux from dark energy to dark matter, represented by a negative value for the gas parameter $alpha$, is shown to alleviate the tension between EDGES data and the cosmological standard model. Using EDGES data and employing a Bayesian statistical analysis, the agreement with the standard model is only marginal. However, if $alpha$ is negative enough the gCg fits remarkably well the data, even in combination with SNe Ia datasets. On the other hand, when the CMB and BAO acoustic scales are included the preferred value for $alpha$ is near zero, implying that a small deviation from $Lambda$CDM is predicted.
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.
Calculations of the evolution of cosmological perturbations generally involve solution of a large number of coupled differential equations to describe the evolution of the multipole moments of the distribution of photon intensities and polarization. However, this Boltzmann hierarchy communicates with the rest of the system of equations for the other perturbation variables only through the photon-intensity quadrupole moment. Here I develop an alternative formulation wherein this photon-intensity quadrupole is obtained via solution of two coupled integral equations -- one for the intensity quadrupole and another for the linear-polarization quadrupole -- rather than the full Boltzmann hierarchy. This alternative method of calculation provides some physical insight and a cross-check for the traditional approach. I describe a simple and efficient iterative numerical solution that converges fairly quickly. I surmise that this may allow current state-of-the-art cosmological-perturbation codes to be accelerated.
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.
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