Related papers: Conformal invariance of curvature perturbation
We explicitly show the fully non-linear equivalence of the $\delta$N and the covariant formalisms for the superhorizon curvature perturbations, which enables us to safely evaluate the non-Gaussian quantities of the curvature perturbation in…
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…
In this paper we study the evolution of cosmological perturbations through a nonsingular bouncing universe using covariant perturbation theory and examine the validity of linear perturbation theory. The bounce is modeled by a two component…
It is known that some cosmological perturbations are conformal invariant. This facilitates the studies of perturbations within some gravitational theories alternative to general relativity, for example the scalar-tensor theory, because it…
In this paper, we generalize the Weinberg's procedure to determine the comoving curvature perturbation $\cal R$ to non-attractor inflationary regimes. We show that both modes of $\cal R$ are related to a symmetry of the perturbative…
We claim that if by a choice of the couplings the theory can be made conformally invariant (vanishing of the beta functions) it is automatically finite and vice versa. This is demonstrated by explicit example in supersymmetric gauge theory.…
In recent years there has been a lot of interest in discussing frame dependences/independences of the cosmological perturbations under the conformal transformations. This problem has previously been investigated in terms of the covariant…
The method of a conformal transformation is applied to a general class of single field inflation models with non-minimal coupling to gravity and non-standard kinetic terms, in order to reduce the cosmological perturbative calculation to the…
We show how conformal invariance predicts the functional form of two-point correlators in one-dimensional periodic quantum systems. Numerical evidence for this functional form in a wide class of models --- including long-ranged ones --- is…
We present a conformally invariant generalized form of the free particle action by connecting the wave and particle aspects through gravity. Conformal invariance breaking is introduced by choosing a particular configurat$ of dynamical…
We discuss the issue of observables in general-relativistic perturbation theory, adopting the view that any observable in general relativity is represented by a scalar field on spacetime. In the context of perturbation theory, an observable…
Higher order conformal perturbation theory is studied for theories with and without boundaries. We identify systematically the universal quantities in the beta function equations, and we give explicit formulae for the universal coefficients…
We complete the formulation of a general framework for the analysis of high-order nonspherical perturbations of a four-dimensional spherical spacetime by including a gauge-invariant description of the perturbations. We present a general…
We show that under a general disformal transformation the linear comoving curvature perturbation is not identically invariant, but is invariant on superhorizon scales for any theory that is disformally related to Horndeski's theory. The…
Recently, the equivalence between the \delta N and covariant formalisms has been shown (Suyama et al. 2012), but they essentially assumed Einstein gravity in their proof. They showed that the evolution equation of the curvature covector in…
We construct discrete holomorphic observables in the Ising model at criticality and show that they have conformally covariant scaling limits (as mesh of the lattice tends to zero). In the sequel those observables are used to construct…
In second order perturbation theory different definitions are known of gauge invariant perturbations in single field inflationary models. Consequently the corresponding gauge invariant cubic actions do not have the same form. Here we show…
We present the results of a study of the gauge dependence of spacetime perturbations. In particular, we consider gauge invariance in general, we give a generating formula for gauge transformations to an arbitrary order n, and explicit…
Using the nonlinear $\delta N$ formalism, we consider a simple exactly soluble model of multi-component slow-roll inflation in which the nonlinear curvature perturbation can be evaluated analytically.
Gauge symmetries lead to first-class constraints. This assertion is of course true only for non trivial gauge symmetries, i.e., gauge symmetries that act non trivially on-shell on the dynamical variables. We illustrate this well-appreciated…