Cosmological information contents on the light-cone

Abstract

We develop a theoretical framework to describe the cosmological observables on the past light cone such as the luminosity distance, weak lensing, galaxy clustering, and the cosmic microwave background anisotropies. We consider that all the cosmological observables include not only the background quantity, but also the perturbation quantity, and they are subject to cosmic variance, which sets the fundamental limits on the cosmological information that can be derived from such observables, even in an idealized survey with an infinite number of observations. To quantify the maximum cosmological information content, we apply the Fisher information matrix formalism and spherical harmonic analysis to cosmological observations, in which the angular and the radial positions of the observables on the light cone carry different information. We discuss the maximum cosmological information that can be derived from five different observables: (1) type Ia supernovae, (2) cosmic microwave background anisotropies, (3) weak gravitational lensing, (4) local baryon density, and (5) galaxy clustering. We compare our results with the cosmic variance obtained in the standard approaches, which treat the light cone volume as a cubic box of simultaneity. We discuss implications of our formalism and ways to overcome the fundamental limit. Discussion and Summary 30A Spherical Fourier analysis with the observed redshift as a dimensionless radial distance 31 B Spherical power spectrum on the light cone 33

Monopole fluctuation of the CMB and its gauge invariance

“…Note that the exact value of our reference ηo (or its theoretical prediction) depends on our choice of cosmological parameters, but it is independent of our choice of coordinate system to describe the observed universe. Furthermore, it was noted [18,21] that the background CMB temperature T (η o ), not T (η o ), is really the CMB temperature today in a homogeneous universe, corresponding to the cosmological parameter ω γ , or the radiation density parameter. For later convenience we define…”

Monopole Fluctuation of the CMB and its Gauge Invariance

“…Note that the exact value of our reference ηo (or its theoretical prediction) depends on our choice of cosmological parameters, but it is independent of our choice of coordinate system to describe the observed universe. Furthermore, it was noted [18,21] that the background CMB temperature T (η o ), not T (η o ), is really the CMB temperature today in a homogeneous universe, corresponding to the cosmological parameter ω γ , or the radiation density parameter.…”

Background photon temperature T¯ : A new cosmological Parameter?

“…For CMB, the observables are T obs lm and D obs l , and the Fisher matrix is then obtained in Ref. [13] as…”