$\delta N$ formalism on the past light-cone

Abstract

We apply the gradient expansion approximation to the light-cone gauge, obtaining a separate universe picture at non-linear order in perturbation theory within this framework. Thereafter, we use it to generalize the $\delta N$ formalism in terms of light-cone perturbations. As a consistency check, we demonstrate the conservation of the gauge invariant curvature perturbation on uniform density hypersurface $\zeta$ at the completely non-linear level. The approach studied provides a self-consistent framework to connect at non-linear level quantities from the primordial universe, such as $\zeta$, written in terms of the light-cone parameters, to late time observables.

33 pages, no figures. References and comments added. Accepted for publication in General Relativity and Gravitation

References in corpus (11)

• Generation of fluctuations during inflation: comparison of stochastic and field-theoretic approaches
• Stochastic growth of quantum fluctuations during slow-roll inflation
• Galaxy number counts to second order and their bispectrum
• Do stochastic inhomogeneities affect dark-energy precision measurements?
• Backreaction on the luminosity-redshift relation from gauge invariant light-cone averaging
• Stochastic inflationary dynamics beyond slow-roll and consequences for primordial black hole formation
• The luminosity distance-redshift relation up to second order in the Poisson gauge with anisotropic stress
• Non-Gaussianities due to Relativistic Corrections to the Observed Galaxy Bispectrum
• Generalized covariant prescriptions for averaging cosmological observables
• The skewness of the distance-redshift relation in $\Lambda$CDM
• Gauge invariance on the light-cone: curvature perturbations and radiative degrees of freedom

Cited by in corpus (1)

• A Light-Cone Approach to Higher-Order Cosmological Observables