Cosmological perturbation theory in slow-roll spacetimes

Area of Science:

• Cosmology
• General Relativity
• Gravitational Physics

Background:

• Understanding the evolution of the universe requires analyzing perturbations in spacetime and matter.
• Linear fluctuations have been traditionally studied, but nonlinear effects may become significant under certain conditions.
• Slow-rolling spacetimes are relevant in models of cosmic inflation and dark energy.

Purpose of the Study:

• To investigate the relative importance of different orders of perturbations on the gravitational field.
• To introduce a gauge-invariant measure for nonlocal perturbations.
• To determine if nonlinear effects dominate over linear ones in slow-rolling spacetimes.

Main Methods:

• Development of a gauge-invariant formalism to describe metric and matter perturbations.
• Derivation of a nonlocal measure for second-order perturbations.
• Comparison of the derived measure with that of linear fluctuations in the context of slow-rolling spacetimes.

Main Results:

• A nonlocal measure of second-order metric and matter perturbations is shown to dominate over linear fluctuations.
• This dominance is demonstrated within the framework of slow-rolling spacetimes.
• The analysis provides a quantitative argument for the significance of nonlinear effects.

Conclusions:

• Nonlinear perturbations play a crucial role in shaping the gravitational field in slow-rolling spacetimes.
• Previous studies focusing solely on linear fluctuations may be incomplete in these regimes.
• The findings necessitate a re-evaluation of theoretical models incorporating gravitational dynamics in specific cosmological contexts.