arXiv subjects

Xian Gao

Publications and source records attributed to Xian Gao.

At least 55 records · Page 3Linked to original sources

arXiv2022

Polarized gravitational waves in the parity violating scalar-nonmetricity theory

There has been increasing interest in investigating the possible parity violating features in the gravity theory and on the cosmological scales. In this work, we consider a class of scalar-nonmetricity theory, of which the Lagrangian is polynomial built of the nonmetricity tensor and a scalar field. The nonmetricity tensor is coupled with the scalar field through its first order derivative. Besides the monomials that are quadratic order in the nonmetricity tensor, we also construct monomials that are cubic order in the nonmetricity tensor in both the parity preserving and violating cases. These monomials act as the non-canonical (i.e., non-quadratic) kinetic terms for the spacetime metric, and will change the behavior in the propagation of the gravitational waves. We find that the gravitational waves are generally polarized, which present both the amplitude and velocity birefringence features due to the parity violation of the theory. Due to the term proportional to $1/k$ in the phase velocities, one of the two polarization modes suffers from the gradient instability on large scales.

gr-qc↗

arXiv2022

Circularly polarized scalar induced gravitational waves from the Chern-Simons modified gravity

We investigate the scalar induced gravitational waves (SIGWs) in the Chern-Simons (CS) modified gravity during the radiation dominated era. The SIGWs are circularly polarized, which provide us a tool to test the possible parity violation in the early universe. We derive the semianalytic expressions to evaluate the fractional energy density of the SIGWs, $Ω_{\mathrm{GW}}$, which receives contributions from the general relativity (GR) and the correction due to the parity-violating term, respectively. We find that the degree of the circular polarization of the SIGWs can be as large as of order unity, although the contribution to $Ω_{\mathrm{GW}}$ from the CS term is at most of the same order as that from the GR.

gr-qc↗

arXiv2022

Cosmological perturbations in the spatially covariant gravity with a dynamical lapse function

We investigate the scalar perturbations in a class of spatially covariant gravity theory with a dynamical lapse function. Generally, there are two scalar degrees of freedom due to the presence of the velocity of the lapse function. We treat the scalar perturbations as analogues of those in a two-field inflationary mode, in which one is light mode and the other is the heavy mode. This is justified by the fact that the scalar mode due to the dynamical lapse function becomes infinitely heavy in the limit when the lapse function reduces to be an auxiliary variable. The standard approaches of multiple filed perturbations can be applied to deal with our model. By integrating out the heavy mode and derive the effective theory for the single light field, we find the solution to the single mode in the form of plane waves. Then we calculate the corrections to the power spectrum of the light mode from the heavy mode, by making use of the standard perturbative method of field theory. At last, when the two fields are not weakly coupled, we find a power law mode for the coupled system in large scales.

gr-qc↗

arXiv2021

Covariant 3+1 correspondence of the spatially covariant gravity and the degeneracy conditions

A necessary condition for a generally covariant scalar-tensor theory to be ghostfree is that it contains no extra degrees of freedom in the unitary gauge, in which the Lagrangian corresponds to the spatially covariant gravity. Comparing with analysing the scalar-tensor theory directly, it is simpler to map the spatially covariant gravity to the generally covariant scalar-tensor theory using the gauge recovering procedures. In order to ensure the resulting scalar-tensor theory to be ghostfree absolutely, i.e., no matter if the unitary gauge is accessible, a further covariant degeneracy/constraint analysis is required. We develop a method of covariant 3+1 correspondence, which map the spatially covariant gravity to the scalar-tensor theory in 3+1 decomposed form without fixing any coordinates. Then the degeneracy conditions to remove the extra degrees of freedom can be found easily. As an illustration of this approach, we show how the Horndeski theory is recovered from the spatially covariant gravity. This approach can be used to find more general ghostfree scalar-tensor theory.

gr-qc↗

arXiv2021

Spatially covariant gravity with two degrees of freedom: perturbative analysis

We revisit the problem of building the Lagrangian of a large class of metric theories that respect spatial covariance, which propagate at most two degrees of freedom and in particular no scalar mode. The Lagrangians are polynomials built of the spatially covariant geometric quantities. By expanding the Lagrangian around a cosmological background and focusing on the scalar modes only, we find the conditions for the coefficients of the monomials in order to eliminate the scalar mode at the linear order in perturbations. We find the conditions up to $d=4$ with $d$ the total number of derivatives in the monomials and determine the explicit Lagrangians for the cases of $d=2$, $d=3$ as well as the combination of $d=2$ and $d=3$. We also expand the Lagrangian of $d=2$ to the cubic order in perturbations, and find additional conditions for the coefficients such that the scalar mode is eliminated up to the cubic order. This perturbative analysis can be performed order by order, and one expects to determine the final Lagrangian at some finite order such that the scalar mode is fully eliminated. Our analysis provides an alternative and complimentary approach to building spatially covariant gravity with only tensorial degrees of freedom. The resulting theories can be used as alternatives to the general relativity to describe the tensorial gravitational waves in a cosmological setting.

gr-qc↗

arXiv2020

Minimally modified gravity with an auxiliary constraint: a Hamiltonian construction

Working directly with a general Hamiltonian for the spacetime metric with the $3+1$ decomposition and keeping only the spatial covariance, we investigate the possibility of reducing the number of degrees of freedom by introducing an auxiliary constraint. The auxiliary constraint is considered as part of the definition of the theory. Through a general Hamiltonian analysis, we find the conditions for the Hamiltonian as well as for the auxiliary constraint, under which the theory propagates two tensorial degrees of freedom only. The class of theories satisfying these conditions can be viewed as a new construction for the type-II minimally modified gravity theories, which propagate the same degrees of freedom of but are not equivalent to general relativity in the vacuum. We also illustrate our formalism by a concrete example, and derive the dispersion relation for the gravitational waves, which can be constrained by observations.

gr-qc↗

arXiv2020

Higher derivative scalar-tensor theory from the spatially covariant gravity: a linear algebraic analysis

We investigate the ghostfree scalar-tensor theory with a timelike scalar field, with derivatives of the scalar field up to the third order and with the Riemann tensor up to the quadratic order. We build two types of linear spaces. One is the set of linearly independent generally covariant scalar-tensor monomials, the other is the set of linearly independent spatially covariant gravity monomials. We argue that these two types of linear space are isomorphic to each other in the sense of gauge fixing/recovering procedures. We then identify the subspaces in the spatially covariant gravity, which are spanned by linearly independent monomials built of the extrinsic and intrinsic curvature, the lapse function as well as their spatial derivatives, up to the fourth order in the total number of derivatives. The vectors in these subspaces, i.e., spatially covariant polynomials, automatically propagate at most three degrees of freedom. As a result, their images under the gauge recovering mappings are automatically the subspaces of scalar-tensor theory that propagate up to three degrees of freedom as long as the scalar field is timelike. The mappings from the spaces of spatially covariant gravity to the spaces of scalar-tensor theory are encoded in the projection matrices, of which we also derived the expressions explicitly. Our formalism and results can be useful in deriving the generally covariant higher derivative scalar-tensor theory without ghost(s).

gr-qc↗

arXiv2020

Higher derivative scalar-tensor theory and spatially covariant gravity: the correspondence

We investigate the correspondence between generally covariant higher derivative scalar-tensor theory and spatially covariant gravity theory. The building blocks are the scalar field and spacetime curvature tensor together with their generally covariant derivatives for the former, and the spatially covariant geometric quantities together with their spatially covariant derivatives for the later. In the case of a single scalar degree of freedom, they are transformed to each other by gauge fixing and recovering procedures, of which we give the explicit expressions. We make a systematic classification of all the scalar monomials in the spatially covariant gravity according to the total number of derivatives up to $d=4$, and their correspondence to the scalar-tensor monomials. We discusse the possibility of using spatially covariant monomials to generate ghostfree higher derivative scalar-tensor theories. We also derive the covariant 3+1 decomposition without fixing any specific coordinate, which will be useful when performing a covariant Hamiltonian analysis.

gr-qc↗

arXiv2020

Structural phase transitions and photoluminescence mechanism in a layer of 3D hybrid perovskite nanocrystals

Although the structural phase transitions in single-crystal hybrid methyl-ammonium (MA) lead halide perovskites (MAPbX3, X = Cl, Br, I) are common phenomena, they have never been observed in the corresponding nanocrystals. Here we demonstrate that two-photon-excited photoluminescence (PL) spectroscopy is capable of monitoring the structural phase transitions in MAPbX3 nanocrystals because nonlinear susceptibilities govern the light absorption rates. We provide experimental evidence that the orthorhombic-to-tetragonal structural phase transition in a single layer of 20-nm-sized 3D MAPbBr3 nanocrystals is spread out within the 70 - 140 K range. This structural phase instability range arises because, unlike in single-crystal MAPbX3, free rotations of MA ions in the corresponding nanocrystals are no longer restricted by a long-range MA dipole order. The resulting configurational entropy loss can be even enhanced by the interfacial electric field arising due to charge separation at the MAPbBr3/ZnO heterointerface, extending the orthorhombic-to-tetragonal structural phase instability range from 70 to 230 K. We conclude that the weak sensitivity of conventional one-photon-excited PL spectroscopy to the structural phase transitions in 3D MAPbX3 nanocrystals results from the structural phase instability providing negligible distortions of PbX6 octahedra. In contrast, the intensity of two-photon-excited PL and electric-field-induced one-photon-excited PL still remains sensitive enough to weak structural distortions due to the higher rank tensor nature of nonlinear susceptibilities involved. We also show that room-temperature PL originates from the radiative recombination of the optical-phonon vibrationally excited polaronic quasiparticles with energies might exceed the ground-state Frohlich polaron and Rashba energies due to optical-phonon bottleneck.

physics.app-ph↗

arXiv2020

Higher derivative scalar-tensor monomials and their classification

We make a full classification of scalar monomials built of the Riemann curvature tensor up to the quadratic order and of the covariant derivatives of the scalar field up to the third order. From the point of view of the effective field theory, the third or even higher order covariant derivatives of the scalar field are of the same order as the higher curvature terms, and thus should be taken into account. Moreover, higher curvature terms and higher order derivatives of the scalar field are complementary to each other, of which novel ghost-free combinations may exist. We make a systematic classification of all the possible monomials, according to the numbers of Riemann tensor and higher derivatives of the scalar field in each monomial. Complete basis of monomials at each order are derived, of which linear combinations may yield novel ghost-free Lagrangians. We also develop a diagrammatic representation of the monomials, which may help to simplify the analysis.

gr-qc↗

arXiv2019

Learning and Optimization with Bayesian Hybrid Models

Bayesian hybrid models fuse physics-based insights with machine learning constructs to correct for systematic bias. In this paper, we compare Bayesian hybrid models against physics-based glass-box and Gaussian process black-box surrogate models. We consider ballistic firing as an illustrative case study for a Bayesian decision-making workflow. First, Bayesian calibration is performed to estimate model parameters. We then use the posterior distribution from Bayesian analysis to compute optimal firing conditions to hit a target via a single-stage stochastic program. The case study demonstrates the ability of Bayesian hybrid models to overcome systematic bias from missing physics with less data than the pure machine learning approach. Ultimately, we argue Bayesian hybrid models are an emerging paradigm for data-informed decision-making under parametric and epistemic uncertainty.

math.OC↗

arXiv2019

Spatially covariant gravity theories with two tensorial degrees of freedom: the formalism

Within the general framework of spatially covariant theories of gravity, we study the conditions for having only the two tensorial degrees of freedom. Generally, there are three degrees of freedom propagating in the theory, of which two are tensorial and one is of the scalar type. Through a detailed Hamiltonian analysis, we find two necessary and sufficient conditions to evade the scalar type degree of freedom. The first condition implies that the lapse-extrinsic curvature sector must be degenerate. The second condition ensures that the dimension of the phase space at each spacetime point is even, so that the scalar type degree of freedom is eliminated completely. We also compare our results with the previous studies, and apply our formalism to a simple example, in which the Lagrangian is quadratic in the extrinsic curvature.

gr-qc↗

arXiv2019

Primordial perturbations and non-Gaussianities in Hořava-Lifshitz gravity

We investigate primordial perturbations and non-gaussianities in the Hořava-Lifshitz theory of gravitation. In the UV limit, the scalar perturbation in the Hořava theory is naturally scale-invariant, ignoring the details of the expansion of the Universe. One may thus relax the exponential inflation and the slow-roll conditions for the inflaton field. As a result, it is possible that the primordial non-gaussianities, which are ``slow-roll suppressed'' in the standard scenarios, become large. We calculate the non-gaussianities from the bispectrum of the perturbation and find that the equilateral-type non-gaussianity is of the order of unity, while the local-type non-gaussianity remains small, as in the usual single-field slow-roll inflation model in general relativity. Our result is a new constraint on the the Hořava-Lifshitz gravity.

hep-th↗

arXiv2019

Propagation of the gravitational waves in a cosmological background

We investigate the propagation of the gravitational waves in a cosmological background. Based on the framework of spatially covariant gravity, we derive the general quadratic action for the gravitational waves. The spatial derivatives of the extrinsic curvature and the parity-violating terms are systematically introduced. Special attention is paid to the propagation speed of the gravitational waves. We find that it is possible to make the two polarization modes propagate in the same speed, which may differ from that of the light, in the presence of parity-violating terms in the action. In particular, we identify a large class of spatially covariant gravity theories with parity violation, in which both the polarization modes propagate in the speed of light. Our results imply that there are more possibilities in the framework of spatially covariant gravity in light of the propagation speed of the gravitational waves.

gr-qc↗

arXiv2019

Spatially covariant gravity with velocity of the lapse function: the Hamiltonian analysis

We investigate a large class of gravity theories that respect spatial covariance, and involve kinetic terms for both the spatial metric and the lapse function. Generally such kind of theories propagate four degrees of freedom, one of which is an unwanted scalar mode. Through a detailed Hamiltonian analysis, we find that the condition requiring the kinetic terms to be degenerate is not sufficient to evade the unwanted scalar mode in general. This is because the primary constraint due to the degeneracy condition does not necessarily induce a secondary constraint, if the mixing terms between temporal and spatial derivatives are present. In this case, the second condition that we dub as the consistency condition must be imposed in order to ensure the existence of the secondary constraint and thus to remove the unwanted mode. We also show how our formalism works through an explicit example, in which the degeneracy condition is not sufficient and thus the consistency condition must be imposed.

gr-qc↗

arXiv2019

Spatially covariant gravity: Perturbative analysis and field transformations

We make a perturbative analysis of the number of degrees of freedom in a large class of metric theories respecting spatial symmetries, of which the Lagrangian includes kinetic terms of both the spatial metric and the lapse function. We show that, as long as the kinetic terms are degenerate, the theory propagates a single scalar mode at the linear order in perturbations around a Friedmann-Robertson-Walker background. Nevertheless, an unwanted mode will reappear pathologically, either at nonlinear orders around the Friedmann-Robertson-Walker background, or at linear order around an inhomogeneous background. In both cases, it turns out that a consistency condition has to be imposed in order to remove the unwanted mode. This perturbative approach provides an alternative and also complementary point of view of the conditions derived in a Hamiltonian analysis. We also discuss the relation under field redefinitions, between theories with and without the time derivative of the lapse function.

gr-qc↗

arXiv2019

Higher derivative scalar-tensor theory through a non-dynamical scalar field

We propose a new class of higher derivative scalar-tensor theories without the Ostrogradsky's ghost instabilities. The construction of our theory is originally motivated by a scalar field with spacelike gradient, which enables us to fix a gauge in which the scalar field appears to be non-dynamical. We dub such a gauge as the spatial gauge. Though the scalar field loses its dynamics, the spatial gauge fixing breaks the time diffeomorphism invariance and thus excites a scalar mode in the gravity sector. We generalize this idea and construct a general class of scalar-tensor theories through a non-dynamical scalar field, which preserves only spatial covariance. We perform a Hamiltonian analysis and confirm that there are at most three (two tensors and one scalar) dynamical degrees of freedom, which ensures the absence of a degree of freedom due to higher derivatives. Our construction opens a new branch of scalar-tensor theories with higher derivatives.

hep-th↗

arXiv2018

Primordial gravitational waves and perturbations during an inhomogeneous inflation

We investigate the inhomogeneous inflation, in which the space exponentially expands with inhomogeneities, and its cosmological perturbations. The inhomogeneous inflation is realized by introducing scalar fields with spacelike gradients that break the spatial symmetry. We find that the space can expand uniformly in different direction with the same rate. By using the perturbative method, we calculate the corrections to the power spectra of gravitational waves and curvature perturbation up to the linear order in the background inhomogeneities. Since the background is inhomogeneous, perturbations modes with different wave numbers get correlated. We show that generally the power spectra of perturbations depend on the ratio and the angle of wave numbers of the two correlated modes. In particular, the two circular polarization modes of the gravitational waves gain different powers when the background inhomogeneity is of vector or tensor type.

astro-ph.CO↗