# Cosmological Information Contents on the Light-Cone

## TL;DR

This paper develops a theoretical framework to quantify the maximum cosmological information obtainable from light-cone observations, considering cosmic variance and perturbations, across various cosmological probes.

## Contribution

It introduces a formalism combining Fisher analysis and spherical harmonics to assess information limits from light-cone observables, extending beyond standard volume-based approaches.

## Key findings

- Quantifies maximum information content for five key cosmological observables.
- Highlights the impact of cosmic variance on information limits.
- Provides a comparison with traditional cubic volume approaches.

## 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.