[Paper Review] Lectures on Modern Cosmology and Structure Formation

O. J. P. Éboli, V. Ribelles|arXiv (Cornell University)|May 22, 1993

History and Developments in Astronomy3 citations

TL;DR

This paper presents a comprehensive review of three leading cosmological models—inflationary universe, cosmic strings, and global texture—that explain the origin of large-scale structure in the universe through quantum fluctuations amplified by gravity. It analyzes how each model predicts distinct microwave background anisotropy patterns, with the COBE discovery providing initial support, though current data cannot yet distinguish between them.

ABSTRACT

Focus of these lectures is the challenge of explaining the origin of structure in the Universe. The interplay between quantum field theory and classical general relativity has given rise to several interesting cosmological models which contain mechanisms for generating density inhomogeneities. The three theories discussed here are the inflationary Universe, the cosmic string and the global texture models. The recent COBE discovery of anisotropies in the microwave background has provided some support for all three models. The present results do not allow a distinction between these models. Statistics which distinguish between the predictions of the three theories are discussed.

Motivation & Objective

• To examine the theoretical foundations of three leading models for the origin of cosmic structure: inflation, cosmic strings, and global texture.
• To assess the viability of these models in light of the recent COBE detection of cosmic microwave background anisotropies.
• To identify statistical observables that could distinguish between the predictions of the three models.
• To provide a pedagogical overview of quantum field theory and general relativity in cosmological contexts for researchers at the 7th Swieca Summer School.
• To lay the groundwork for future observational discrimination between competing structure formation mechanisms.

Proposed method

• Analyzes quantum field theory in curved spacetime to derive primordial density perturbations in the early universe.
• Applies linear perturbation theory to compute the evolution of initial inhomogeneities into large-scale structure.
• Uses the Sachs-Wolfe effect to relate primordial potential fluctuations to cosmic microwave background anisotropies.
• Compares angular power spectra of temperature fluctuations predicted by each model (inflation, cosmic strings, global texture).
• Evaluates the statistical properties of the predicted anisotropy patterns, focusing on multipole moments and correlation functions.
• Reviews the observational constraints from the COBE satellite, particularly the first detection of large-scale microwave background anisotropies.

Experimental results

Research questions

• RQ1 How do quantum fluctuations in the early universe lead to observable large-scale structure via inflation, cosmic strings, or global texture?
• RQ2 What are the distinct statistical signatures in the cosmic microwave background anisotropies predicted by each of the three models?
• RQ3 To what extent do the COBE observations support the predictions of inflation, cosmic strings, and global texture models?
• RQ4 Which statistical observables can most effectively discriminate between the three models based on microwave background data?
• RQ5 What are the theoretical and observational limitations in distinguishing between these competing structure formation mechanisms?

Key findings

• The COBE satellite's detection of large-scale microwave background anisotropies provides observational support for all three models—cosmic inflation, cosmic strings, and global texture.
• Each model predicts a unique angular power spectrum for microwave background anisotropies, particularly in the low-multipole regime.
• Inflation predicts a nearly scale-invariant spectrum of primordial fluctuations, consistent with COBE's observed normalization.
• Cosmic strings and global texture produce distinct non-Gaussian features and different power-law behaviors in the angular power spectrum compared to inflation.
• Despite the COBE results, current data do not allow a definitive distinction between the three models due to limited angular resolution and signal-to-noise.
• The paper identifies specific statistical tools—such as correlation functions and bispectra—that could differentiate the models with higher-precision data.