Related papers: Cosmological tests of General Relativity: a princi…
Functional data typically contains amplitude and phase variation. In many data situations, phase variation is treated as a nuisance effect and is removed during preprocessing, although it may contain valuable information. In this note, we…
The current standard cosmological model is constructed within the framework of general relativity with a cosmological constant $\Lambda$, which is often associated with dark energy, and phenomenologically explains the accelerated cosmic…
Cosmic Microwave Background (CMB) is a powerful probe to study the early universe and various cosmological models. Weak gravitational lensing affects the CMB by changing its power spectrum, but meanwhile, it also carries information about…
Principal component analysis (PCA) for binary data, known as logistic PCA, has become a popular alternative to dimensionality reduction of binary data. It is motivated as an extension of ordinary PCA by means of a matrix factorization, akin…
Principal Components Analysis (PCA) and Independent Component Analysis (ICA) are used to identify global patterns in solar and space data. PCA seeks orthogonal modes of the two-point correlation matrix constructed from a data set. It…
Viable models of modified gravity designed to produce cosmic acceleration at the current epoch, closely mimic the $\Lambda$CDM model at the level of background cosmology. However, this degeneracy is generically broken at the level of linear…
We explore the physical implications of applying principal component analysis (PCA) to translationally invariant classical systems defined on a $d$-dimensional hypercubic lattice. Using Rayleigh-Schr\"odinger perturbation theory, we…
We present a tomographic cosmological weak lensing analysis of the HST COSMOS Survey. Applying our lensing-optimized data reduction, principal component interpolation for the ACS PSF, and improved modelling of charge-transfer inefficiency,…
We consider estimation of large approximate factor models in high-dimensional panels of stationary time series using Principal Component Analysis (PCA). We review the key results establishing the necessary and sufficient conditions for…
Optical weak lensing surveys have become a powerful tool for precision cosmology, but remain subject to systematic effects that can severely bias cosmological parameter estimates if not carefully removed. We discuss the possibility of…
We present some useful ways to visualize the nature of dark energy and the effects of the accelerating expansion on cosmological quantities. Expansion probes such as Type Ia supernovae distances and growth probes such as weak gravitational…
In this paper, we study the degeneracies among several cosmological parameters in detail and discuss their impacts on the determinations of these parameters from the current and future observations. By combining the latest data sets,…
The next generation of large scale surveys will not only measure cosmological parameters within the framework of General Relativity, but will also allow for precision tests of the framework itself. At the order of linear perturbations,…
We study the effect of modifications to General Relativity on large scale weak lensing observables. In particular, we consider three modified gravity scenarios: f(R) gravity, the DGP model, and TeVeS theory. Weak lensing is sensitive to the…
Over the past decades, more and more methods gain a giant development due to the development of technology. Evolutionary Algorithms are widely used as a heuristic method. However, the budget of computation increases exponentially when the…
In the search for the nature of dark energy most cosmological probes measure simple functions of the expansion rate. While powerful, these all involve roughly the same dependence on the dark energy equation of state parameters, with…
In the era of big data, reducing data dimensionality is critical in many areas of science. Widely used Principal Component Analysis (PCA) addresses this problem by computing a low dimensional data embedding that maximally explain variance…
Dark matter cannot be observed directly, but its weak gravitational lensing slightly distorts the apparent shapes of background galaxies, making weak lensing one of the most promising probes of cosmology. Several observational studies have…
Extensions to the $\Lambda\textrm{CDM}$ model prior to recombination can modify the growth of perturbations around radiation-matter equality, leaving a distinct signature in the matter power spectrum. Upcoming large-scale structure surveys…
In this work we investigate the Principal Component Analysis (PCA) sensitivity to the velocity power spectrum in high opacity regimes of the interstellar medium (ISM). For our analysis we use synthetic Position-Position-Velocity (PPV) cubes…