Related papers: Second-order cosmological perturbations. II. Produ…
We present a systematic study of the 2nd order scalar, vector and tensor metric perturbations in the Einstein-de Sitter Universe in synchronous coordinates. For the scalar-scalar coupling between 1st order perturbations, we decompose the…
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…
Gauge invariant treatments of the second order cosmological perturbation in a four dimensional homogeneous isotropic universe filled with the perfect fluid are completely formulated without any gauge fixing. We derive all components of the…
We continue to study the 2nd-order cosmological perturbations in synchronous coordinates in the framework of the general relativity (GR) during the radiation dominated (RD) stage, and to focus on the scalar-tensor and tensor-tensor…
We study the 2nd-order scalar, vector and tensor metric perturbations in Robertson-Walker (RW) spacetime in synchronous coordinates during the radiation dominated (RD) stage. The dominant radiation is modeled by a relativistic fluid…
Along the general framework of the gauge invariant perturbation theory developed in the papers [K. Nakamura, Prog. Theor. Phys. {\bf 110} (2003), 723; {\it ibid}, {\bf 113} (2005), 481.], we formulate the second order gauge invariant…
We consider the evolution of relativistic perturbations in the Einstein-de Sitter cosmological model, including second-order effects. The perturbations are considered in two different settings: the widely used synchronous gauge and the…
The second order perturbations in Friedmann-Robertson-Walker universe filled with a perfect fluid are completely formulated in the gauge invariant manner without any gauge fixing. All components of the Einstein equations are derived…
Gauge-invariant treatments of the second-order cosmological perturbation in a four dimensional homogeneous isotropic universe are formulated without any gauge fixing. We have derived the Einstein equations in the case of the single perfect…
Recently a new approach in constructing the conserved charges in cosmological Einstein's gravity was given. In this new formulation, instead of using the explicit form of the field equations a covariantly conserved rank four tensor was…
High-accuracy gravitational-wave modeling demands going beyond linear, first-order perturbation theory. Particularly motivated by the need for second-order perturbative models of extreme-mass-ratio inspirals and black hole ringdowns, we…
We consider in detail the problem of gauge dependence that exists in relativistic perturbation theory, going beyond the linear approximation and treating second and higher order perturbations. We first derive some mathematical results…
We derived the second-order perturbations of the Einstein equations and the Klein-Gordon equation for a generic situation in terms of gauge-invariant variables. The consistency of all the equations is confirmed. This confirmation implies…
Along the general framework of the gauge-invariant perturbation theory developed in the papers [K. Nakamura, Prog. Theor. Phys. {\bf 110} (2003), 723; {\it ibid}, {\bf 113} (2005), 481.], we re-derive the second-order Einstein equations on…
Based on the gauge invariant variables proposed in our previous paper [K. Nakamura, Prog. Theor. Phys. vol.110 (2003), 723.], some formulae of the perturbative curvatures of each order are derived. We follow the general framework of the…
We present a method for constructing gauge-invariant cosmological perturbations which are gauge-invariant up to second order. As an example we give the gauge-invariant definition of the second-order curvature perturbation on uniform density…
We use gauge-invariant cosmological perturbation theory to calculate the displacement field that sets the initial conditions for $N$-body simulations. Using first and second-order fully relativistic perturbation theory in the…
The study of long wavelength scalar perturbations, in particular the existence of conserved quantities when the perturbations are adiabatic, plays an important role in e.g. inflationary cosmology. In this paper we present some new conserved…
We consider instability of the Friedmann world model to the second-order in perturbations. We present the perturbed set of equations up to the second-order in the Friedmann background world model with general spatial curvature and the…
We derive the evolution equation for the second order curvature perturbation using standard techniques of cosmological perturbation theory. We do this for different definitions of the gauge invariant curvature perturbation, arising from…