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Model-independent tests of cosmic gravity.
The Royal Society 2011 Philosophical transactions. Series A, Mathematical Vol.369 No.1957
<P>Gravitation governs the expansion and fate of the universe, and the growth of large-scale structure within it, but has not been tested in detail on these cosmic scales. The observed acceleration of the expansion may provide signs of gravitational laws beyond general relativity (GR). Since the form of any such extension is not clear, from either theory or data, we adopt a model-independent approach to parametrizing deviations to the Einstein framework. We explore the phase space dynamics of two key post-GR functions and derive a classification scheme, and an absolute criterion on accuracy necessary for distinguishing classes of gravity models. Future surveys will be able to constrain the post-GR functions' amplitudes and forms to the required precision, and hence reveal new aspects of gravitation.</P>
Model independent expansion history from supernovae: Cosmology versus systematics
L’Huillier, Benjamin,Shafieloo, Arman,Linder, Eric V,Kim, Alex G Oxford University Press 2019 MONTHLY NOTICES- ROYAL ASTRONOMICAL SOCIETY Vol.485 No.2
<B>Abstract</B><P>We examine the Pantheon supernovae distance data compilation in a model independent analysis to test the validity of cosmic history reconstructions beyond the concordance ΛCDM cosmology. Strong deviations are allowed by the data at z ≳ 1 in the reconstructed Hubble parameter, Om diagnostic, and dark energy equation of state. We explore three interpretations: 1) possibility of the true cosmology being far from ΛCDM, 2) supernovae property evolution, and 3) survey selection effects. The strong (and theoretically problematic) deviations at z ≳ 1 vanish and good consistency with ΛCDM is found with a simple Malmquist-like linear correction. The adjusted data is robust against the model independent iterative smoothing reconstruction. However, we caution that while by eye the original deviation from ΛCDM is striking, χ2 tests do not show the extra linear correction parameter is statistically significant, and a model-independent Gaussian Process regression does not find significant evidence for the need for correction at high-redshifts.</P>
MAPPING GROWTH AND GRAVITY WITH ROBUST REDSHIFT SPACE DISTORTIONS
Kwan, Juliana,Lewis, Geraint F.,Linder, Eric V. IOP Publishing 2012 The Astrophysical journal Vol.748 No.2
<P>Redshift space distortions (RSDs) caused by galaxy peculiar velocities provide a window onto the growth rate of large-scale structure and a method for testing general relativity. We investigate through a comparison of N-body simulations to various extensions of perturbation theory beyond the linear regime, the robustness of cosmological parameter extraction, including the gravitational growth index gamma. We find that the Kaiser formula and some perturbation theory approaches bias the growth rate by 1 sigma or more relative to the fiducial at scales as large as k > 0.07 h Mpc(-1). This bias propagates to estimates of the gravitational growth index as well as Omega(m) and the equation-of-state parameter and presents a significant challenge to modeling RSDs. We also determine an accurate fitting function for a combination of line-of-sight damping and higher order angular dependence that allows robust modeling of the redshift space power spectrum to substantially higher k.</P>
Huang, Yisong,Samawi, Hani M.,Vogel, Robert,Yin, Jingjing,Gato, Worlanyo Eric,Linder, Daniel F. The Korean Statistical Society 2016 Communications for statistical applications and me Vol.23 No.6
The validity of statistical inference depends on proper randomization methods. However, even with proper randomization, we can have imbalanced with respect to important characteristics. In this paper, we introduce a method based on ranked auxiliary variables for treatment allocation in crossover designs using Latin squares models. We evaluate the improvement of the efficiency in treatment comparisons using the proposed method. Our simulation study reveals that our proposed method provides a more powerful test compared to simple randomization with the same sample size. The proposed method is illustrated by conducting an experiment to compare two different concentrations of titanium dioxide nanofiber (TDNF) on rats for the purpose of comparing weight gain.