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 four-dimensional homogeneous isotropic background universe in gauge-invariant manner without ignoring any mode of perturbations. We consider the perturbations both in the universe dominated by the single perfect fluid and in that dominated by the single scalar field. We also confirmed the consistency of all equations of the second-order Einstein equation and the equations of motion for matter fields which are derived in the paper [K. Nakamura, arXiv:0804.3840 [gr-qc]]. This confirmation implies that the all derived equations of the second order are self-consistent and these equations are correct in this sense.
We present a formalism for analysis of linear Cauchy data on a Kottler metric. Our method removes redundancy due to gauge transformations and constraints. A set of four gauge-invariant, scalar functions on the Cauchy surface is produced and shown to contain full physical information from the initial data. The symplectic form of the theory and equations of motion are reformulated in terms of these invariants and some simple solutions are explored.
We discuss how the incorporation of a cosmological constant affects the perturbative quantization of (effective) Quantum General Relativity. To this end, we derive the gravitational Slavnov--Taylor identities and appropriate renormalization conditions for the cosmological constant. Additionally, we calculate the corresponding Feynman rules for any vertex valence and with general gauge parameter. Furthermore, we provide the BRST setup and generate the Faddeev--Popov ghost and the symmetric ghost via a gauge fixing fermion and a gauge fixing boson, respectively. Finally, we study the transversal…
The current status of the recent developments of the second-order gauge-invariant cosmological perturbation theory is reviewed. To show the essence of this perturbation theory, we concentrate only on the universe filled with a single scalar field. Through this review, we point out the problems which should be clarified for the further theoretical sophistication of this perturbation theory. This review is an extension of the review paper [K.~Nakamura, "Second-Order Gauge-Invariant Cosmological Perturbation Theory: Current Status", Advances in Astronomy, vol.2010 (2010), 576273.]. We also expect…
The issue of the gauge invariance of gravitational waves arises if they are produced in the early universe at second-order in perturbation theory. We address it by dividing the discussion about the gauge invariance in three parts: the production of gravitational waves, their propagation in the real universe, and their measurement.
In this short paper we determine the effects of structure on the cosmological consistency relation which is valid in a perfect Friedmann Universe. We show that within $Λ$CDM the consistency relation is violated by about 1.5% for redshifts $z\simeq 2$ and this violation raises up to 2% at $z\simeq 5$ and 3% at $z\simeq 10$ after which it settles at about 2.7% for $z>10$. This effect of cosmic structure on the distance redshift relation is also very sensitive to the determination of the dark energy equation of state via cosmic distances. It actually leads to an apparent unphysical behavior of $w…
The canonical structure of supergravity with a cosmological constant is analyzed in 2 + 1 dimensions using the Dirac constraint formalism. The first class constraints are used to find two Bosonic and one Fermionic gauge symmetries that satisfy a superalgebra. Provided the cosmological constant is negative, this novel algebra closes, without having to invoke the equations of motion or introducing auxiliary fields.
In this paper, we discuss the gravitational waves in the context of gauge theory gravity with a negative cosmological constant. The gauge theory gravity is a gravity theory under gauge formulation in the language of geometric algebra. In contrast to general relativity, the background spacetime in gauge theory gravity is flat, the gauge freedom comes from the fact that equations in terms of physical quantities should be kept in a covariant form under spacetime displacement and rotation. Similar to the electromagnetism, the gauge formulation enables us to interpret the gravitational force as a g…
Detailed analysis of the dependence of the one-loop counterterms on the gauge and parametrization in the Einstein gravity with the cosmological constant
We present a general formalism for the Hamiltonian description of perturbation theory around any spatially homogeneous spacetime. We employ and refine the Dirac method for constrained systems, which is very well-suited to cosmological perturbations. This approach includes a discussion of the gauge-invariant dynamics of perturbations as well as an analysis of gauge transformations, gauge-fixing, partial gauge-fixing and spacetime reconstruction. We will introduce the Kuchař parametrization of the kinematical phase space as a convenient tool for studying the gauge transformations. The key elemen…
We study the gauge invariant cosmological perturbations up to second order. We show that there are infinite families of gauge invariant variables at both of the first and second orders. The conversion formulae among different families are shown to be described by a finite number of bases that are gauge invariant. For the second order cosmological perturbations induced by the first order scalar perturbations, we explicitly represent the equations of motion of them in terms of the gauge invariant Newtonian, synchronous and hybrid variables, respectively.
Using the extended ADM-phase space formulation in the canonical framework we analyze the relationship between various gauge choices made in cosmological perturbation theory and the choice of geometrical clocks in the relational formalism. We show that various gauge invariant variables obtained in the conventional analysis of cosmological perturbation theory correspond to Dirac observables tied to a specific choice of geometrical clocks. As examples, we show that the Bardeen potentials and the Mukhanov-Sasaki variable emerge naturally in our analysis as observables when gauge fixing conditions …
