Two-point Correlation Functions in Inhomogeneous and Anisotropic Cosmologies

Abstract

Two-point correlation functions are ubiquitous tools of modern cosmology, appearing in disparate topics ranging from cosmological inflation to late-time astrophysics. When the background spacetime is maximally symmetric, invariance arguments can be used to fix the functional dependence of this function as the invariant distance between any two points. In this paper we introduce a novel formalism which fixes this functional dependence directly from the isometries of the background metric, thus allowing one to quickly assess the overall features of Gaussian correlators without resorting to the full machinery of perturbation theory. As an application we construct the CMB temperature correlation function in one inhomogeneous (namely, an off-center LTB model) and two spatially flat and anisotropic (Bianchi) universes, and derive their covariance matrices in the limit of almost Friedmannian symmetry. We show how the method can be extended to arbitrary N -point correlation functions and illustrate its use by constructing three-point correlation functions in some simple geometries.

arXiv comment23 pages, 3 figures. This version matches the published one

References in corpus (32)

• The motion of point particles in curved spacetime
• Planck 2013 results. XXIII. Isotropy and statistics of the CMB
• Beyond $\Lambda$CDM: Problems, solutions, and the road ahead
• Planck 2015 results. XVI. Isotropy and statistics of the CMB
• Theory of cosmological perturbations in an anisotropic universe
• Measuring Statistical isotropy of the CMB anisotropy
• Cosmic Microwave Background Statistics for a Direction-Dependent Primordial Power Spectrum
• Scalar-Scalar, Scalar-Tensor, and Tensor-Tensor Correlators from Anisotropic Inflation
• How isotropic is the Universe?
• Predictions from an anisotropic inflationary era
• Inflationary perturbations in anisotropic backgrounds and their imprint on the CMB
• Conformal Invariance, Dark Energy, and CMB Non-Gaussianity
• Conformal Invariance and Cosmic Background Radiation
• Perturbation Theory in Lemaitre-Tolman-Bondi Cosmology
• CMB Power Asymmetry from Non-Gaussian Modulation
• The intrinsic bispectrum of the Cosmic Microwave Background [PhD thesis]
• Translational Invariance and the Anisotropy of the Cosmic Microwave Background
• Testing gaussianity, homogeneity and isotropy with the cosmic microwave background
• Weak-lensing by the large scale structure in a spatially anisotropic universe: theory and predictions
• Linearization of homogeneous, nearly-isotropic cosmological models
• Isotropization of the universe during inflation
• The Cold Spot as a Large Void: Lensing Effect on CMB Two and Three Point Correlation Functions
• The Cosmic Microwave Background Bipolar Power Spectrum: Basic Formalism and Applications
• CMB in a box: causal structure and the Fourier-Bessel expansion
• Weak-lensing $B$-modes as a probe of the isotropy of the universe
• Are we living near the center of a local void?
• Inflationary Perturbations in Anisotropic, Shear-Free Universes
• Searching for planar signatures in WMAP
• Cosmological Signatures of Anisotropic Spatial Curvature
• Angular-planar CMB power spectrum
• Detecting the Cold Spot as a Void with the Non-Diagonal Two-Point Function
• New Geometric Representations of the CMB 2pcf

Cited by in corpus (7)

• Quantum Correlators in Friedmann Spacetimes -The omnipresent de Sitter and the invariant vacuum noise
• Structure formation in an anisotropic universe: Eulerian perturbation theory
• Correlation functions of sourced gravitational waves in inflationary scalar vector models. A symmetry based approach
• de Sitter symmetries and inflationary correlators in parity violating scalar-vector models
• Late-Time Anisotropy Sourced by a 2-Form Field Non-Minimally Coupled to Cold Dark Matter
• Breaking degeneracies with the Sunyaev-Zeldovich full bispectrum
• Entanglement Entropy and Complexity of Multicomponent Universe from Holography