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ModelIndependent Determination of the Cosmic Growth Factor
by Sophia Haude, Shabnam Salehi, Sofía Vidal, Matteo Maturi, Matthias Bartelmann
Submission summary
As Contributors:  Matthias Bartelmann · Matteo Maturi 
Arxiv Link:  https://arxiv.org/abs/1912.04560v1 (pdf) 
Date submitted:  20191211 01:00 
Submitted by:  Bartelmann, Matthias 
Submitted to:  SciPost Astronomy 
Academic field:  Astronomy 
Specialties: 

Approaches:  Theoretical, Observational 
Abstract
Since the discovery of the accelerated cosmic expansion, one of the most important tasks in observational cosmology is to determine the nature of the dark energy. We should build our understanding on a minimum of assumptions in order to avoid biases from assumed cosmological models. The two most important functions describing the evolution of the universe and its structures are the expansion function E(a) and the linear growth factor D_+(a). The expansion function has been determined in previous papers in a modelindependent way using distance moduli to typeIa supernovae and assuming only a metric theory of gravity, spatial isotropy and homogeneity. Here, we extend this analysis in three ways: (1) We extend the data sample by combining the Pantheon measurements of typeIa supernovae with measurements of baryonic acoustic oscillations; (2) we substantially simplify and generalise our method for reconstructing the expansion function; and (3) we use the reconstructed expansion function to determine the linear growth factor of cosmic structures, equally independent of specific assumptions on an underlying cosmological model other than the usual spatial symmetries. We show that the result is quite insensitive to the initial conditions for solving the growth equation, leaving the presentday matterdensity parameter {\Omega}_m0 as the only relevant parameter for an otherwise purely empirical and accurate determination of the growth factor.
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Anonymous Report 1 on 2020326 Invited Report
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In the paper "ModelIndependent Determination of the Cosmic Growth Factor" (arxiv: 1912.04560) the authors reconstructed expansion function and the linear growth function using Pantheon and SNBAO samples. Authors argue that the results can be parameterized by a single number (presentday matterdensity parameter).
Before the paper can be accepted for a publication I suggest authors to address the following points:
1. Pantheon sample has been criticized by M. Rameez et al in arxiv:1911.06456. I recommend the authors to address and/or account for points presented in this paper
2. Eq. 18 looks for me as a simplified form of Eq. 1 in which radiation and curvature terms are neglected. If this is the case it is trivial that the expansion function and any derived quantities are characterized by a matter density parameter only; I recommend authors to clarify this point.
I am not sure that in this case the uncertainty on $\Omega_{m0}$ has physical meaning. It is formally correct, but seems to rely on neglecting of radiation/curvature densities which are by an order of magnitude comparable to the reported uncertainty.
3. I suggest authors to consider replace Fig.12 with loglog scale versions to make uncertainty region a bit more clear. Please also refer in Fig.3 to eq. 22 which provides the definition of "dark energy evolution". Please change also ylabel in this Fig. accordingly.