Tensor Mode Perturbations Research Articles

Extended minimal theories of massive gravity

In this work, we introduce a class of extended Minimal Theories of Massive Gravity (eMTMG), without requiring a priori that the theory should admit the same homogeneous and isotropic cosmological solutions as the de Rham-Gabadadze-Tolley massive gravity. The theory is constructed as to have only two degrees of freedom in the gravity sector. In order to perform this step we first introduce a precursor theory endowed with a general graviton mass term, to which, at the level of the Hamiltonian, we add two extra constraints as to remove the unwanted degrees of freedom, which otherwise would typically lead to ghosts and/or instabilities. On analyzing the number of independent constraints and the properties of tensor mode perturbations, we see that the gravitational waves are the only propagating gravitational degrees of freedom which do acquire a non-trivial mass, as expected. In order to understand how the effective gravitational force works for this theory we then investigate cosmological scalar perturbations in the presence of a pressureless fluid. We then restrict the whole class of models by imposing the following conditions at all times: 1) it is possible to define an effective gravitational constant, $G_{{\rm eff}}$; 2) the value $G_{\text{eff}}/G_{N}$ is always finite but not always equal to unity (as to allow some non-trivial modifications of gravity, besides the massive tensorial modes); and 3) the square of mass of the graviton is always positive. These constraints automatically make also the ISW-effect contributions finite at all times. Finally we focus on a simple subclass of such theories, and show they already can give a rich and interesting phenomenology.

Manifestly gauge-invariant cosmological perturbation theory from full loop quantum gravity

We apply the full theory of Loop Quantum Gravity (LQG) to cosmology and present a top-down derivation of gauge-invariant cosmological perturbation theory from quantum gravity. The derivation employs the reduced phase space formulation of LQG and the new discrete path integral formulation defined in arXiv:1910.03763. We demonstrate that in the semiclassical approximation and continuum limit, the result coincides with the existing formulation of gauge-invariant cosmological perturbation theory in e.g. arXiv:0711.0117. Time evolution of cosmological perturbations is computed numerically from the new cosmological perturbation theory of LQG, and various power spectrums are studied for scalar mode and tensor mode perturbations. Comparing these power spectrums with predictions from the classical theory demonstrate corrections in the ultra-long wavelength regime. These corrections are results from the lattice discretization in LQG. In addition, tensor mode perturbations at late time demonstrate the emergence of spin-2 gravitons as low energy excitations from LQG. The graviton has a modified dispersion relation and reduces to the standard graviton in the long wavelength limit.

Gravity waves in parity-violating Copernican universes

In recent work minimal theories allowing the variation of the cosmological constant by means of a balancing torsion, have been proposed. It was found that such theories contain parity violating homogeneous and isotropic solutions, due to a torsion structure called the Cartan spiral staircase. Their dynamics are controlled by Euler and Pontryagin quasi-topological terms in the action. Here we show that such theories predict a dramatically different picture for gravitational wave fluctuations in the parity violating branch. If the dynamics are ruled solely by the Euler-type term, then linear tensor mode perturbations are entirely undetermined, hinting at a new type of gauge invariance. The Pontryagin term not only permits for phenomenologically sounder background solutions (as found in previous literature), but for realistic propagation of gravitational wave modes. We discuss the observational constraints and predictions of these theories.

Running spectral index from large-field inflation with modulations revisited

We revisit large field inflation models with modulations in light of the recent discovery of the primordial B-mode polarization by the BICEP2 experiment, which, when combined with the Planck+WP+highL data, gives a strong hint for additional suppression of the CMB temperature fluctuations at small scales. Such a suppression can be explained by a running spectral index. In fact, it was pointed out by two of the present authors (TK and FT) that the existence of both tensor mode perturbations and a sizable running of the spectral index is a natural outcome of large inflation models with modulations such as axion monodromy inflation. We find that this holds also in the recently proposed multi-natural inflation, in which the inflaton potential consists of multiple sinusoidal functions and therefore the modulations are a built-in feature.

Gravitationally induced dark matter asymmetry and dark nucleon decay

The "gravitational baryogenesis" scenario is extended to generate both baryon and dark matter asymmetries, in the matter dominated era corresponding to post-inflationary reheating. A minimal extension requires a singlet fermion X for dark matter and a singlet scalar S. With two or more hidden sector fermions, the scenario can lead to nucleon decay into dark matter with a lifetime of order 10^{34-36} yr, which is relevant for current or future experiments. The correct multi-component relic density can be obtained if dark matter fermions couple to a sub-GeV vector boson that weakly interacts with the Standard Model through mixing. The typical inflationary scale in the scenario is of order 10^{16} GeV which suggests that tensor mode perturbations could potentially be within observational reach.

Gravitational waves in a spatially closed de Sitter spacetime

Perturbation of gravitational fields may be decomposed into scalar, vector and tensor components. In this paper we concern with the evolution of tensor mode perturbations in a spatially closed de Sitter background of Robertson–Walker form. It may be thought as gravitational waves in a classical description. The chosen background has the advantage of to be maximally extended and symmetric. Spatially flat models commonly emerge from inflationary scenarios are not completely extended. We first derive the general weak field equations. Then the form of the field equations in two special cases, planar and spherical waves, are obtained and their solutions are presented. The radiation field from an isolated source is calculated. We conclude with discussing the significance of the results and their implications.

Analytic formulae of the CMB bispectra generated from non-Gaussianity in the tensor and vector perturbations

We present a complete set of formulae for calculating the bispectra of CMB temperature and polarization anisotropies generated from non-Gaussianity in the vector and tensor mode perturbations. In the all-sky analysis it is found that the bispectrum formulae for the tensor and vector-mode non-Gaussianity formally take complicated forms compared to the scalar mode one because the photon transfer functions in the tensor and vector modes depend on the azimuthal angle between the direction of the wave number vector of the photon's perturbation and that of the line of sight. We demonstrate that flat-sky approximations remove this difficulty because this kind of azimuthal angle dependence apparently vanishes in the flat-sky limit. Through the flat-sky analysis, we also find that the vector or tensor bispectrum of $B$-mode polarization vanishes in the squeezed limit, unless the cosmological parity is violated at the nonlinear level.

Quasinormal modes for tensor and vector type perturbation of Gauss Bonnet black hole using third order WKB approach

We obtain the quasinormal modes for tensor perturbations of Gauss–Bonnet (GB) black holes in d = 5, 7, 8 dimensions and vector perturbations in d = 5, 6, 7 and 8 dimensions using third order WKB formalism. The tensor perturbation for black holes in d = 6 is not considered because of the fact that the black hole is unstable to tensor mode perturbations. In the case of uncharged GB black hole, for both tensor and vector perturbations, the real part of the QN frequency increases as the Gauss–Bonnet coupling (α′) increases. The imaginary part first decreases upto a certain value of α′ and then increases with α′ for both tensor and vector perturbations. For larger values of α′, the QN frequencies for vector perturbation differs slightly from the QN frequencies for tensorial one. It has also been shown that as α′ → 0, the quasinormal frequencies for tensor and vector perturbations of the Schwarzschild black hole can be obtained. We have also calculated the quasinormal spectrum of the charged GB black hole for tensor perturbations. Here we have found that the real oscillation frequency increases, while the imaginary part of the frequency falls with the increase of the charge. We also show that the quasinormal frequencies for scalar field perturbations and the tensor gravitational perturbations do not match as was claimed in the literature. The difference in the result increases if we increase the GB coupling.

Generality of singularity avoidance in superstring theory: Anisotropic case

In the one-loop string effective action, we study a generality of nonsingular cosmological solutions found in the isotropic and homogeneous case. We discuss Bianchi type-I and -IX spacetimes. We find that nonsingular solutions still exist in the Bianchi type-I model around nonsingular flat Friedmann solutions. On the other hand, we cannot find any nonsingular solutions in the Bianchi type-IX model. The nonexistence of a nonsingular Bianchi type-IX universe may be consistent with the analysis of Kawai, Sakagami, and Soda; i.e., the tensor-mode perturbations against a nonsingular flat Friedmann universe are unstable, because the Bianchi type-IX model is regarded as a closed Friedmann universe with a single gravitational wave. With the stability analysis of Kawai, Sakagami, and Soda, the nonsingular universe found in the isotropic case is unstable, and a singularity avoidance may not work in generic spacetimes.