Second-order cosmological perturbations produced by scalar-scalar coupling during inflation stage
arXiv:2307.08261 · doi:10.1007/s10714-024-03214-y
Abstract
We study the perturbations up to the 2nd-order for a power-law inflation driven by a scalar field in synchronous coordinates. We present the 1st-order solutions, and analytically solve the 2nd-order perturbed Einstein equation and scalar field equation, give the 2nd-order solutions for all the scalar, vector, and tensor metric perturbations, as well as the perturbed scalar field. During inflation, the 1st-order tensor perturbation is a wave and is decoupled from other perturbations, the scalar metric perturbation and the perturbed scalar field are coupled waves, propagating at the speed of light, differing from those in the dust and relativistic fluid models. The 1st-order vector perturbation is not wave and just decreases during inflation. The 2nd-order perturbed Einstein equation is similar in structure to the 1st-order one, but various products of the 1st-order perturbations occur as the effective source, among which the scalar-scalar coupling is considered in this paper. The solutions of all the 2nd-order perturbations consist of a homogeneous part similar to the 1st-order solutions, and an inhomogeneous part in a form of integrations of the effective source. The 2nd-order vector perturbation is also a wave since the effective source is composed of the 1st-order waves. We perform the residual gauge transformations between synchronous coordinates up to the 2nd-order, and identify the 1st-order and 2nd-order gauge modes.
arXiv comment54 pages, 2 figures
References in corpus (99)
- Planck 2018 results. X. Constraints on inflation
- Particle Physics Models of Inflation and the Cosmological Density Perturbation
- Cosmological Perturbation Theory in the Synchronous vs. Conformal Newtonian Gauge
- Cosmological Perturbation Theory in the Synchronous and Conformal Newtonian Gauges
- Non-Gaussianity from Inflation: Theory and Observations
- An All-Sky Analysis of Polarization in the Microwave Background
- Inflation Dynamics and Reheating
- Statistics of Cosmic Microwave Background Polarization
- Gravitational Wave Spectrum Induced by Primordial Scalar Perturbations
- Adiabatic and entropy perturbations from inflation
- The cosmological gravitational wave background from primordial density perturbations
- Second-Order Cosmological Perturbations from Inflation
- Cosmological Non-Linearities as an Effective Fluid
- Relativistic second-order perturbations of the Einstein-de Sitter Universe
- Perturbations of spacetime: gauge transformations and gauge invariance at second order and beyond
- CMB polarization from secondary vector and tensor modes
- General Relativistic Dynamics of Irrotational Dust: Cosmological Implications
- On Non-Gaussianity in the Curvaton Scenario
- Nonlinear perturbation theory with halo bias and redshift-space distortions via the Lagrangian picture
- Production and detection of relic gravitons in quintessential inflationary models
- Second-order Perturbations of the Friedmann World Model
- Cosmic Microwave Background Polarization
- Flowing with Time: a New Approach to Nonlinear Cosmological Perturbations
- Primordial Black Holes from Inflation and non-Gaussianity
- Perturbation Theory Reloaded: Analytical Calculation of Non-linearity in Baryonic Oscillations in the Real Space Matter Power Spectrum
- Resumming Cosmic Perturbations
- Evolution of second-order cosmological perturbations
- Primordial Black Holes from Sound Speed Resonance during Inflation
- Analytic approach to the polarization of the cosmic microwave background in flat and open universes
- Reheating After Quintessential Inflation and Gravitational Waves
- Higher-Order Gravitational Perturbations of the Cosmic Microwave Background
- Non-linear perturbations in multiple-field inflation
- Characterizing the Cosmological Gravitational Wave Background Anisotropies and non-Gaussianity
- Density Perturbations of Quantum Mechanical Origin and Anisotropy of the Microwave Background
- Second order perturbations of a Schwarzschild black hole
- Relic Gravitational Waves in the Accelerating Universe
- Gauge dependence of gravitational waves generated from scalar perturbations
- Large Angular Scale Polarization of the Cosmic Microwave Background and the Feasibility of its Detection
- Cosmological perturbation with two scalar fields in reheating after inflation
- Imprints of Relic Gravitational Waves in Cosmic Microwave Background Radiation
- Primordial Non-Gaussianity in the Cosmic Microwave Background
- Post-Newtonian Cosmological Dynamics in Lagrangian coordinates
- Analytic approach to the CMB polarizations generated by relic gravitational waves
- Gauge Invariant Variables in Two-Parameter Nonlinear Perturbations
- Non-linear inflationary perturbations
- Relic Gravitational Waves and Their Detection
- Gauge-invariant Formulation of the Second-order Cosmological Perturbations
- Stochastic backgrounds of relic gravitons: a theoretical appraisal
- Analytic spectrum of relic gravitational waves modified by neutrino free streaming and dark energy
- Third-order Perturbation Theory With Non-linear Pressure
- The Implications of the Microwave Background Anisotropies for Laser-Interferometer-Tested Gravitational Waves
- On the conservation of second-order cosmological perturbations in a scalar field dominated universe
- An exact analytic spectrum of relic gravitational waves in an accelerating universe
- CBR anisotropy from primordial gravitational waves in inflationary cosmologies
- A Relativistic Approch to Gravitational Instability in the Expanding Universe: Second Order Lagrangian Solutions
- Hamiltonian approach to 2nd order gauge invariant cosmological perturbations
- The Zel'dovich-type approximation for an inhomogeneous universe in general relativity: second-order solutions
- Sound speed resonance of the stochastic gravitational wave background
- The Zel'dovich Approximation and the Relativistic Hamilton-Jacobi Equation
- Vector modes generated by primordial density fluctuations
- Second-order perturbations of cosmological fluids: Relativistic effects of pressure, multi-component, curvature, and rotation
- Analytic Spectra of CMB Anisotropies and Polarization Generated by Relic Gravitational Waves with Modification due to Neutrino Free-Streaming
- Second order solutions of cosmological perturbation in the matter dominated era
- Approximate Analytic Spectra of Reionized CMB Anisotropies and Polarization generated by Relic Gravitational Waves
- Second-order perturbations of a zero-pressure cosmological medium: comoving vs. synchronous gauge
- Modifications by QCD transition and annihilation on analytic spectrum of relic gravitational waves in accelerating universe
- On second-order superhorizon perturbations in multifield inflationary models
- Perturbations of Matter Fields in the Second-order Gauge-invariant Cosmological Perturbation Theory
- Vacuum and Gravitons of Relic Gravitational Waves, and Regularization of Spectrum and Energy-Momentum Tensor
- Energy Momentum Pseudo-Tensor of Relic Gravitational Wave in Expanding Universe
- Second order perturbations of a zero-pressure cosmological medium: Proofs of the relativistic-Newtonian correspondence
- CMB Temperature Polarization Correlation and Primordial Gravitational Waves
- Relativistic-Newtonian correspondence of the zero-pressure but weakly nonlinear cosmology
- Second-order Cosmological Perturbations Engendered by Point-like Masses
- Adiabatic regularization of power spectrum and stress tensor of relic gravitational wave without low-frequency distortion
- Exact non-linear equations for cosmological perturbations
- Second-order cosmological perturbations. I. Produced by scalar-scalar coupling in synchronous gauge
- Second-order cosmological perturbations. IV. Produced by scalar-tensor and tensor-tensor couplings during the radiation dominated stage
- Second-order cosmological perturbations. II. Produced by scalar-tensor and tensor-tensor couplings
- Supersymmetry and Brane Cosmology
- Field Theory of the Correlation Function of Mass Density Fluctuations for Self-Gravitating Systems
- A Coarse-Grained Field Theory for Density Fluctuations and Correlation Functions of Galactic Objects
- A massless scalar field in Robertson-Walker spacetimes: Adiabatic regularization and Green's function
- Analytic Spectra of CMB Anisotropies and Polarization Generated by Scalar Perturbations in Synchronous Gauge
- Nonlinear Density Fluctuation Field Theory for Large Scale Structure
- Point-splitting regularization of the stress tensor of a coupling scalar field in de Sitter space
- Fully nonlinear and exact perturbations of the Friedmann world model: Non-flat background
- Cosmological nonlinear density and velocity power spectra including nonlinear vector and tensor modes
- Field Equation of Correlation Function of Mass Density Fluctuation for Self-Gravitating Systems
- Field Equation of Correlation Function of Mass Density Fluctuation for Self-Gravitating Systems
- Second-order cosmological perturbations. III. Produced by scalar-scalar coupling during radiation-dominated stage
- Maxwell field with gauge fixing term in de Sitter space: exact solution and stress tensor
- Estimation of spectrum and parameters of relic gravitational waves using space-borne interferometers
- Second order cosmological perturbations: new conserved quantities and the general solution at super-horizon scale
- The energy spectrum of gravitational waves in a loop quantum cosmological model
- Second-order effective energy-momentum tensor of gravitational scalar perturbations with perfect fluid
- The nonlinear field equation of the three-point correlation function of galaxies
- Analytical Equation of Three-point Correlation Function of Galaxies: to Third Order of Density Perturbation
- Second-order dust perturbations of the non-flat FLRW model with the positive cosmological constant