Tensor Modes Research Articles

Detection of gravitational wave mixed polarization with single space-based detectors

General Relativity predicts only two tensor polarization modes for gravitational waves while at most six possible polarization modes are allowed in the general metric theory of gravity. The number of polarization modes is determined by the specific modified theory of gravity. Therefore, the determination of polarization modes can be used to test gravitational theory. We introduce a concrete data analysis pipeline for a space-based detector such as LISA to detect the polarization modes of gravitational waves. This method can be used for monochromatic gravitational waves emitted from any compact binary system with a known sky position and frequency to detect mixtures of tensor and extra polarization modes. We use the source $\mathrm{J}0806.3+1527$ with one year of simulation data as an example to show that this approach is capable of probing pure and mixed polarizations without knowing the exact polarization modes. We also find that the ability of detection of extra polarization depends on the gravitational-wave source location and the amplitude of nontensorial components.

Chirality of gravitational waves in Chern-Simons f(R) gravity cosmology

In this paper we shall consider an axionic Chern-Simons-corrected $f(R)$ gravity theoretical framework, and we shall study the chirality of the generated primordial gravitational waves. Particularly, we shall consider two main axion models, the canonical misalignment axion model and the kinetic axion model, both of which provide an interesting particle phenomenology, in the presence of ${R}^{2}$ terms in the inflationary Lagrangian. The axion does not affect significantly the background evolution during the inflationary era, which is solely controlled by ${R}^{2}$ gravity. However, due to the presence of the Chern-Simons term, the tensor perturbations are directly affected, and our aim is to reveal the extent of the effects of the Chern-Simons term on the gravitational wave modes, for both the axion models. We aim to produce analytical descriptions of the primordial tensor mode behavior, and thus we solve analytically the evolution equations of the tensor modes, for a nearly de Sitter primordial evolution controlled by the ${R}^{2}$ gravity. We focus the analytical study on superhorizon and subhorizon modes. For the misalignment model, we were able to produce analytic solutions for both the subhorizon and superhorizon modes, in which case we find the behavior of the circular polarization function. Our results indicate that the produced tensor spectrum is strongly chiral. For the kinetic axion model though, analytic solutions are obtained only for the superhorizon modes. In order to have a grasp of the behavior of the chirality of the tensor modes, we studied the chirality of the superhorizon modes, however, a more complete study is needed, which is impossible to do analytically though.

Covariate-Assisted Sparse Tensor Completion

We aim to provably complete a sparse and highly missing tensor in the presence of covariate information along tensor modes. Our motivation comes from online advertising where users’ click-through-rates (CTR) on ads over various devices form a CTR tensor that has about 96% missing entries and has many zeros on nonmissing entries, which makes the standalone tensor completion method unsatisfactory. Beside the CTR tensor, additional ad features or user characteristics are often available. In this article, we propose Covariate-assisted Sparse Tensor Completion (COSTCO) to incorporate covariate information for the recovery of the sparse tensor. The key idea is to jointly extract latent components from both the tensor and the covariate matrix to learn a synthetic representation. Theoretically, we derive the error bound for the recovered tensor components and explicitly quantify the improvements on both the reveal probability condition and the tensor recovery accuracy due to covariates. Finally, we apply COSTCO to an advertisement dataset consisting of a CTR tensor and ad covariate matrix, leading to 23% accuracy improvement over the baseline. An important by-product is that ad latent components from COSTCO reveal interesting ad clusters, which are useful for better ad targeting. Supplementary materials for this article are available online.

Theory-agnostic reconstruction of potential and couplings from quasinormal modes

In this work, we use a parametrized theory-agnostic approach that connects the observation of black hole quasi-normal modes with the underlying perturbation equations, with the goal of reconstructing the potential and the coupling functions appearing in the latter. The fundamental quasi-normal mode frequency and its first two overtones are modeled through a second order expansion in the deviations from general relativity, which are assumed to be small but otherwise generic. By using a principal component analysis, we demonstrate that percent-level measurements of the fundamental mode and its overtones can be used to constrain the effective potential of tensor perturbations and the coupling functions between tensor modes and ones of different helicity, without assuming an underlying theory. We also apply our theory-agnostic reconstruction framework to analyze simulated quasi-normal mode data produced within specific theories extending general relativity, such as Chern-Simons gravity.

GTT: Leveraging data characteristics for guiding the tensor train decomposition

The demand for searching, querying multimedia data such as image, video and audio is omnipresent, how to effectively access data for various applications is a critical task. Nevertheless, these data usually are encoded as multi-dimensional arrays, or tensor, and traditional data mining techniques might be limited due to the curse of dimensionality. Tensor decomposition is proposed to alleviate this issue. Commonly used tensor decomposition algorithms include CP-decomposition (which seeks a diagonal core) and Tucker-decomposition (which seeks a dense core). Naturally, Tucker maintains more information, but due to the denseness of the core, it also is subject to exponential memory growth with the number of tensor modes. Tensor train (TT) decomposition addresses this problem by seeking a sequence of three-mode cores: but unfortunately, currently, there are no guidelines to select the decomposition sequence. In this paper, we propose a GTT method for guiding the tensor train in selecting the decomposition sequence. GTT leverages the data characteristics (including number of modes, length of the individual modes, density, distribution of mutual information, and distribution of entropy) as well as the target decomposition rank to pick a decomposition order that will preserve information. Experiments with various data sets demonstrate that GTT effectively guides the TT-decomposition process towards decomposition sequences that better preserve accuracy.

Inflation with antisymmetric tensor field: new candidates

We study classes of inflation models driven by antisymmetric tensor field, with minimal and nonminimal couplings to gravity, that address the known issues of such models considered in the past. First, we show that with a different choice of the background structure of the antisymmetric tensor field, inflation is supported even for the minimal model with quadratic potential contrary to past results. We also include the nonminimal coupling to gravity and analyse perturbations to the antisymmetric tensor as well as the tensor modes of perturbed metric. The two models differ in terms of the behaviour of tensor modes, where the speed of the gravitational wave can be tuned to c in the latter model. The power spectrum and spectral index receive slight scale dependence. Finally, we consider a quartic potential motivated by the graceful exit to reheating phase, which requires a nonminimal coupling to support inflation. The two tensor modes of the perturbed metric are found to evolve differently in this model, and give rise to a highly scale-dependent power spectrum.

Sensitivity of third-generation interferometers to extra polarizations in the stochastic gravitational wave background

When modified theories of gravity are considered, at most six gravitational wave polarization modes are allowed and classified in tensor modes, the only ones predicted by General Relativity (GR), along with additional vector and scalar modes. Therefore, gravitational waves represent a powerful tool to test alternative theories of gravitation. In this paper, we forecast the sensitivity of third-generation ground-based interferometers, Einstein Telescope and Cosmic Explorer, to non-GR polarization modes focusing on the stochastic gravitational wave background. We consider the latest technical specifications of the two independent detectors and the full network in order to estimate both the optimal signal-to-noise ratio and the detectable energy density limits relative to all polarization modes in the stochastic background for several locations on Earth and orientations of the two observatories. By considering optimal detector configurations, we find that in 5 years of observation the detection limit for tensor and extra polarization modes could reach $h_0^2\Omega^{T,V,S}_{GW} \approx 10^{-12}-10^{-11}$, depending on the network configuration and the stochastic background (i.e., if only one among vector and scalar modes exists or both are present). This means that the network sensitivity to different polarization modes can be approximately improved by a factor $10^3$ with respect to second-generation interferometers. We finally discuss the possibility of breaking the scalar modes degeneracy by considering both detectors angular responses to sufficiently high gravitational wave frequencies.

Axion-gauge field dynamics with backreaction

Phenomenological success of inflation models with axion and SU(2) gauge fields relies crucially on control of backreaction from particle production. Most of the previous study only demanded the backreaction terms in equations of motion for axion and gauge fields be small on the basis of order-of-magnitude estimation. In this paper, we solve the equations of motion with backreaction for a wide range of parameters of the spectator axion-SU(2) model. First, we find a new slow-roll solution of the axion-SU(2) system in the absence of backreaction. Next, we obtain accurate conditions for stable slow-roll solutions in the presence of backreaction. Finally, we show that the amplitude of primordial gravitational waves sourced by the gauge fields can exceed that of quantum vacuum fluctuations in spacetime by a large factor, without backreaction spoiling slow-roll dynamics. Imposing additional constraints on the power spectra of scalar and tensor modes measured at CMB scales, we find that the sourced contribution can be more than ten times the vacuum one. Imposing further a constraint of scalar modes non-linearly sourced by tensor modes, the two contributions can still be comparable.

On the primordial correlation of gravitons with gauge fields

We calculate the primordial correlation of gravitons with an abelian gauge field non-minimally coupled through a dynamical dilaton field or a volume moduli during inflation in the early universe. In particular, we compute the cross-correlation of a tensor mode with two gauge field modes and the corresponding correlation functions for the associated magnetic and electric fields using the in-in formalism. Moreover, using semi-classical methods, we show that the three-point cross-correlation functions satisfy new consistency relations (soft theorems) in the squeezed limit. Our findings exhibit a complete agreement of the full in-in results with the new consistency relations. An interesting consequence of our scenario is the possibility of a novel correlation of the primordial tensor mode with the primordial curvature perturbation induced by higher order quantum gravity corrections. The anisotropic background created by long wavelength gauge field modes makes this correlation function non-vanishing. Finally, we discuss how these three-point correlation functions are imprinted on cosmological observables today and the applications to scenarios of inflationary magnetogenesis.

Primordial gravitational waves from excited states

We show that a scalar excited state with large occupation numbers during inflation leads to an enhancement of tensor modes and a characteristic pattern of order-one oscillations in the associated stochastic gravitational wave background (SGWB) sourced during inflation. An effective excited state, i.e. a departure from the Bunch-Davies vacuum, can emerge dynamically as the result of a transient non-adiabatic evolution, e.g. a sharp feature along the inflationary history. We provide an explicit example in a multifield context where the sharp feature triggering the excited state is identified with a strong turn in the inflationary trajectory. En passant, we derive a universal expression for the tensor power spectrum sourced at second order by an arbitrary number of scalar degrees of freedom during inflation, crucially taking into account the nontrivial structure of the Hilbert space in multifield setups. The SGWB sourced during inflation can overcome the standard scalar-induced SGWB sourced at horizon re-entry of the fluctuations after inflation, while being less constrained by perturbativity and backreaction bounds. In addition, one may entertain the possibility of detecting both since they peak at different frequencies exhibiting oscillations with distinct periods.

Abstract 9: Pervasive White Matter Microstructure Dysintegrity Related To High Blood Pressure Among Asymptomatic Population

Background: Blood pressure is the strongest contributor to clinically evident cerebrovascular disease. We investigated the role of blood pressure on white matter (WM) microstructure among asymptomatic individuals without clinically evident cerebrovascular disease. Methods: We conducted a nested study within the UK Biobank, restricting our analysis to participants without cerebrovascular disease or dementia and with available brain diffusion tensor imaging (DTI). We tested for association between systolic blood pressure (SBP) and six different DTI metrics: fractional anisotropy (FA), mean diffusivity (MD), tensor mode (MO), intra-cellular volume fraction (ICVF), isotropic or free water volume fraction (ISOVF), and orientation dispersion index (OD) across 48 WM tracts using multivariable linear regression adjusted for potential confounders. We used Bonferroni-corrected p-values (0.05/48) for statistical significance. Results: We analyzed 33,440 participants. Mean age was 63.0 (SD 7.7), and 17,688 (53%) were female. Higher SBP is independently associated with pervasive decrease in FA and ICVF and increase in MD (Figure), after adjustment for vascular risk-factors. SBP was also associated with lower neurite OD (a more specific metric of axonal damage) in bilateral posterior corona radiata, external capsule, medial lemniscus, and corticospinal tracs. FA and OD of external capsule and posterior corona radiata had the largest drop per 10 mmHg increase of SBP (steepest slope). Conclusions: Higher SBP is associated with pervasive WM microstructure dysintegrity in asymptomatic individuals without evident cerebrovascular disease. DTI metrics of the posterior corona radiata and external capsule are most reflective of variations in SBP and may provide a potential biomarker to assess subtle WM microstructural damage in hypertensive patients or monitor treatment response in clinical trials.

Stochastic approach to gravitational waves from inflation

We propose a coarse-graining procedure for describing the superhorizon dynamics of inflationary tensor modes. Our aim is to formulate a stochastic description for the statistics of spin-2 modes which seed the background of gravitational waves from inflation. Using basic principles of quantum mechanics, we determine a probability density for coarse-grained tensor fields, which satisfies a stochastic Fokker-Planck equation at superhorizon scales. The corresponding noise and drift are computable, and depend on the cosmological system under consideration. Our general formulas are applied to a variety of cosmological scenarios, also considering cases seldom considered in the context of stochastic inflation, and which are important for their observational consequences. We start obtaining the expected expressions for noise and drift in pure de Sitter and power-law inflation, also including a discussion of effects of non-attractor phases. We then apply our methods to describe scenarios with a transition from inflation to standard cosmological eras of radiation and matter domination. We show how the interference between modes flowing through the cosmological horizon, and modes spontaneously produced at superhorizon scales, can affect the stochastic evolution of coarse-grained tensor quantities. In appropriate limits, we find that the corresponding spectrum of tensor modes at horizon crossing matches with the results of quantum field theory calculations, but we also highlight where differences can arise.

Asymptotic analysis of Chern-Simons modified gravity and its memory effects

The gravitational memory effects of Chern-Simons modified gravity are considered in the asymptotically flat spacetime. If the Chern-Simons scalar does not directly couple with the ordinary matter fields, there are also displacement, spin and center-of-mass memory effects as in general relativity. This is because the term of the action that violates the parity invariance is linear in the scalar field but quadratic in the curvature tensor. This results in the parity violation occuring at the higher orders in the inverse luminosity radius. The scalar field does not induce any new memory effects that can be detected by interferometers or pulsar timing arrays. The asymptotic symmetry is group is also the extended Bondi-Metzner-Sachs group. The constraints on the memory effects excited by the tensor modes are obtained.

Polarization distortions of lensed gravitational waves

In general relativity (GR), gravitational waves (GWs) propagate the well-known plus and cross polarization modes which are the signature of a massless spin-2 field. However, diffraction of GWs caused by intervening objects along the line of sight can cause the apparent rise of additional polarizations due to GW-curvature interactions. In this paper, we continue the analysis by two of the authors of the present article, on lensing of gravitational waves beyond geometric optics. In particular, we calculate the lensing effect caused by a point-like lens, in the regime where its Schwarzschild radius $R_s$ is much smaller than the wavelength $\lambda$ of the signal, itself smaller than the impact parameter $b$. In this case, the curvature of spacetime induces distortions in the polarization of the wave such that effective scalar and vector polarizations may appear. We find that the amplitude of these apparent non-GR polarizations is suppressed by a factor $R_s\lambda/b^2$ with respect to the amplitude of the GR-like tensor modes. We estimate the probability to develop these extra polarization modes for a nearly monochromatic GW in the Pulsar Timing Arrays band traveling through a distribution of galaxies.

Feature Curves and Surfaces of 3D Asymmetric Tensor Fields.

3D asymmetric tensor fields have found many applications in science and engineering domains, such as fluid dynamics and solid mechanics. 3D asymmetric tensors can have complex eigenvalues, which makes their analysis and visualization more challenging than 3D symmetric tensors. Existing research in tensor field visualization focuses on 2D asymmetric tensor fields and 3D symmetric tensor fields. In this paper, we address the analysis and visualization of 3D asymmetric tensor fields. We introduce six topological surfaces and one topological curve, which lead to an eigenvalue space based on the tensor mode that we define. In addition, we identify several non-topological feature surfaces that are nonetheless physically important. Included in our analysis are the realizations that triple degenerate tensors are structurally stable and form curves, unlike the case for 3D symmetric tensors fields. Furthermore, there are two different ways of measuring the relative strengths of rotation and angular deformation in the tensor fields, unlike the case for 2D asymmetric tensor fields. We extract these feature surfaces using the A-patches algorithm. However, since three of our feature surfaces are quadratic, we develop a method to extract quadratic surfaces at any given accuracy. To facilitate the analysis of eigenvector fields, we visualize a hyperstreamline as a tree stem with the other two eigenvectors represented as thorns in the real domain or the dual-eigenvectors as leaves in the complex domain. To demonstrate the effectiveness of our analysis and visualization, we apply our approach to datasets from solid mechanics and fluid dynamics.

Low Rank Graph Regularization Embedding for 2D+3D Facial Expression Recognition

In this paper, a novel low rank graph regularization embedding for 3D facial expression recognition (LRGREFER) approach is proposed, in which the core tensor is utilized to characterize the low-rank attribute among the samples combined with the factor matrices with the graph regularization embedding. At first, a model based on a 4D tensor is constructed from the facial expression data. By Tucker decomposing the constructed 4D tensor, a resulting core tensor and factor matrices in different tensor modes are utilized to characterize the low-rankness among samples. Because of the loss of information during modelling the 4D tensor, the missing data from partly observed facial expression data are recovered by embedding the tensor completion. Finally, the proposed model is handled and solved by adopting the alternating direction method of multipliers (ADMM). Meanwhile, the classification prediction of facial expressions are implemented by Multi-class-SVM. Numerical experiments are conducted on BU-3DFE database. The experiment results have been verified that our proposed approach is more competitive.

Low Rank Tucker Decomposition for 2D+3D Facial Expression Recognition

In this paper, a novel low rank Tucker decomposition for 3D facial expression recognition (LRTDFER) approach is proposed, in which the core tensor is utilized to characterize the low-rank attribute among the samples combined with the factor matrices with the graph regularization embedding. At first, a model based on a 4D tensor is constructed from the facial expression data. By Tucker decomposing the constructed 4D tensor, a resulting core tensor and factor matrices in different tensor modes are utilized to characterize the low-rankness among samples. Because of the loss of information during modelling the 4D tensor, the missing data from partly observed facial expression data are recovered by embedding the tensor completion. Finally, the proposed model is handled and solved by adopting the alternating direction method of multipliers (ADMM). Meanwhile, the classification prediction of facial expressions are implemented by Multi-class-SVM. Numerical experiments are conducted on BU-3DFE database. The experiment results have been verified that our proposed approach is more competitive.

High-Order Coupled Fully Connected Tensor Network Decomposition for Hyperspectral Image Super-Resolution

Hyperspectral image super-resolution addresses the problem of fusing a low-resolution hyperspectral image (LR-HSI) and a high-resolution multispectral image (HR-MSI) to produce a high-resolution hyperspectral image (HR-HSI). Tensor analysis has been proven to be an efficient method for hyperspectral image processing. However, the existing tensor-based methods of hyperspectral image super-resolution like the tensor train and tensor ring decomposition only establish an operation between adjacent two factors and are highly sensitive to the permutation of tensor modes, leading to an inadequate and inflexible representation. In this paper, we propose a novel method for hyperspectral image super-resolution by utilizing the specific properties of high-order tensors in fully-connected tensor network decomposition. The proposed method first tensorizes the target HR-HSI into a high-order tensor that has multiscale spatial structures. Then, a coupled fully-connected tensor network decomposition model is proposed to fuse the corresponding high-order tensors of LR-HSI and HR-MSI. Moreover, a weighted-graph regularization is imposed on the spectral core tensors to preserve spectral information. In the proposed model, the superiorities of the fully-connected tensor network decomposition lie in the outstanding capability for characterizing adequately the intrinsic correlations between any two modes of tensors and the essential invariance for transposition. Experimental results on three data sets show the effectiveness of the proposed approach as compared to other hyperspectral image super-resolution methods.

Beating the Lyth Bound by Parametric Resonance during Inflation.

We propose a novel mechanism for enhancing primordial gravitational waves without significantly affecting the curvature perturbations produced during inflation. This is achieved due to nonlinear sourcing of resonantly amplified scalar field fluctuations. Our result is an explicit scale-dependent counterexample of the famous Lyth bound, which opens up a promising perspective of producing detectable inflationary tensor modes with low-scale inflation and a sub-Planckian field excursion. We explicitly demonstrate the testability of our mechanism with upcoming cosmic microwave background B-mode observations.

Minimal theory of massive gravity and constraints on the gravitonmass

The Minimal theory of Massive Gravity (MTMG) is endowed non-linearlywith only two tensor modes in the gravity sector which acquire a non-zeromass. On a homogeneous and isotropic background the theory is knownto possess two branches: the self-accelerating branch with a phenomenologyin cosmology which, except for the mass of the tensor modes, exactlymatches the one of ΛCDM; and the normal branch which insteadshows deviation from General Relativity in terms of both backgroundand linear perturbations dynamics. For the latter branch we studyusing several early and late times data sets the constraints on today'svalue of the graviton mass μ0, finding that (μ0/H 0)2 = 0.119-0.098 +0.12at 68% CL, which in turn gives an upper bound at 95% CL as μ0 < 8.4 × 10-34 eV. This corresponds to the strongest bound on the mass of the gravitonfor the normal branch of MTMG.