Ke Wang, Qing-Guo Huang
We investigate how the production of gravitational waves (GWs) is affected by the GW velocity $(c_T)$ during preheating after inflation. For instance, we simulate the production of GWs after $λϕ^4$ chaotic inflation, and find that GW spectrum is enhanced for $c_T<1$, but distorted (suppressed at low frequency, but enhanced at high frequency) for $c_T>1$.
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We study the production of primordial black holes (PBHs) during the preheating stage that follows a chaotic inflationary phase. The scalar fields present in the process are evolved numerically using a modified version of the HLATTICE code. From the output of the numerical simulation, we compute the probability distribution of curvature fluctuations, paying particular attention to sub-horizon scales. We find that in some specific models these modes grow to large amplitudes developing highly non-Gaussian probability distributions. We then calculate PBH abundances using the standard Press-Schecht…
The nonlinear dynamics of preheating after early-Universe inflation is often studied with lattice simulations. In this work I present a new lattice code HLATTICE. It differs from previous public available codes in the following three aspects: (i) A much higher accuracy is achieved with a modified sixth-order symplectic integrator; (ii) scalar, vector, and tensor metric perturbations in synchronous gauge and their feedback to the dynamics of scalar fields are all included; (iii) the code uses a projector that completely removes the scalar and vector components defined by the discrete spatial de…
Fermion creation during preheating in the presence of multiple scalar fields exhibits a range of interesting behaviour relevant to estimating post-inflation gravitino abundances. We present non-perturbative analysis of this phenomenon over a 6-dimensional parameter space in an expanding background paying particular attention to the interplay between instant and direct fermion preheating. In the broad resonance regime we find that instant fermion production is sensitive to suppression of the long wavelength scalar field modes during inflation. Further, the standard scenario of resonant fermioni…
Transient Acceleration after Non-minimal M-flation Preheating
本文在非最小M-flation预加热中用LATTICEEASY格点模拟表明，粒子产生导致的势修正可诱发瞬态加速，并使预加热引力波振幅降低近一个数量级。
The Preheating Stage on The Starobinsky Inflation after ACT
基于ACT最新数据重新研究Starobinsky暴胀模型，发现需增加e-fold数并降低再加热温度，通过引入旁观场实现有效预加热，并给出可行参数集。
In this paper we explored in detail a phenomenological model of modified single field natural inflation in light of recent cosmological experiments, BICEP2. Our main goal is to construct an inflationary model which not only predicts the important cosmological quantities such as $(n_s, r)$ compatible with experimental observation, but also is consistent with the low energy effective theory framework. Therefore, all the fundamental scale apart from $M_p$ and quantities of our interest should be within the sub-Planckian region. In order to achieve our goal we modify the usual single field natural…
The $R^2$-Higgs inflation: $R^3$ contribution and preheating after ACT and SPT data
$R^2$-Higgs 抖动模型通过引入 $R^3$ 项和预热机制，解释了高谱指数 $n_s$ 的观测结果。
Studies of dark energy at advanced gravitational-wave (GW) interferometers normally focus on the dark energy equation of state $w_{\rm DE}(z)$. However, modified gravity theories that predict a non-trivial dark energy equation of state generically also predict deviations from general relativity in the propagation of GWs across cosmological distances, even in theories where the speed of gravity is equal to $c$. We find that, in generic modified gravity models, the effect of modified GW propagation dominates over that of $w_{\rm DE}(z)$, making modified GW propagation a crucial observable for da…
The mirage of luminal modified gravitational-wave propagation
本文利用共形不变性与有效场论证明，光速修正引力的引力波传播与 GR 相同，但 JW 度规最小耦合会改变 GW 与 EM 光度距离关系，并推广至非光速及速度随时间变化理论。
Low-energy alternatives to General Relativity (GR) generically modify the phase of gravitational waves (GWs) during their propagation. As detector sensitivities increase, it becomes key to understand how these modifications affect the GW higher modes and to disentangle possible degeneracies with astrophysical phenomena. We apply a general formalism -- the WKB approach -- for solving analytically wave propagation in the spatial domain with a modified dispersion relation (MDR). We compare this WKB approach to applying a stationary phase approximation (SPA) in the temporal domain with time delays…
We study the propagation of the scalar modes around a Friedmann-Lemaitre-Robertson-Walker universe for general modifications of gravity in the presence of a real scalar field. In general, there will be two propagating scalar perturbation fields, which will have in total four degrees of freedom. Two of these degrees will have a superluminal propagation--with k-dependent speed of propagation--whereas the other two will travel with the speed of light. Therefore, the scalar degrees of freedom do not modify the general feature of modified gravity models: the appearance of modes whose frequency depe…
It has been recently shown that quadruply lensed gravitational-wave (GW) events due to coalescing binaries can be localized to one or just a few galaxies, even in the absence of an electromagnetic counterpart. We discuss how this can be used to extract information on modified GW propagation, which is a crucial signature of modifications of gravity at cosmological scales. We show that, using quadruply lensed systems, it is possible to constrain the parameter $Ξ_0$ that characterizes modified GW propagation, without the need of imposing a prior on $H_0$. A LIGO/Virgo/Kagra network at target sens…
Modified gravitational wave propagation is a smoking gun of modifications of gravity at cosmological scales, and can be the most promising observable for testing such theories. The observation of gravitational waves (GW) in recent years has allowed us to start probing this effect, and here we briefly review two promising ways of testing it. We will show that, already with the current network of detectors, it is possible to reach an interesting accuracy in the estimation of the $Ξ_0$ parameter (that characterizes modified gravitational wave propagation, with $Ξ_{0, {\rm GR}} = 1$) and with next…
Recent work has shown that modified gravitational wave (GW) propagation can be a powerful probe of dark energy and modified gravity, specific to GW observations. We use the technique of Gaussian processes, that allows the reconstruction of a function from the data without assuming any parametrization, to measurements of the GW luminosity distance from simulated joint GW-GRB detections, combined with measurements of the electromagnetic luminosity distance by simulated DES data. For the GW events we consider both a second-generation LIGO/Virgo/Kagra (HVLKI) network, and a third-generation detect…
Analytical Study of Deflection Angle and Time Delay in Kerr Spacetime with Modified Propagation
研究克尔时空中引力透镜效应，通过采用变形色散关系解析推导偏转角和时间延迟，建立框架量化与标准光子传播的偏差，表明相关可观测量可用于探测强场环境中引力的紫外修正。
In modified gravity the propagation of gravitational waves (GWs) is in general different from that in general relativity. As a result, the luminosity distance for GWs can differ from that for electromagnetic signals, and is affected both by the dark energy equation of state $w_{\rm DE}(z)$ and by a function $δ(z)$ describing modified propagation. We show that the effect of modified propagation in general dominates over the effect of the dark energy equation of state, making it easier to distinguish a modified gravity model from $Λ$CDM. We illustrate this using a nonlocal modification of gravit…
Modified gravitational wave (GW) propagation is a generic phenomenon in modified gravity. It affects the reconstruction of the redshift of coalescing binaries from the luminosity distance measured by GW detectors, and therefore the reconstruction of the actual masses of the component compact stars from the observed (`detector-frame') masses. We show that, thanks to the narrowness of the mass distribution of binary neutron stars, this effect can provide a clear signature of modified gravity, particularly for the redshifts explored by third generation GW detectors such as Einstein Telescope and …
Dynamical Dark Energy or Modified Gravity? Signatures in Gravitational Wave Propagation
本文利用DESI BAO DR2和DESyr5超新星数据，通过模型无关方法重建暗能量密度，研究f(Q)修正引力中的有效引力耦合和引力波阻尼参数，发现不同数据集在阻尼参数上预测显著差异，为区分暗能量与修正引力提供依据。
Strong lensing of gravitational waves with modified propagation
本研究探讨了传播修正对强透镜引力波波形的影响，发现局部修正可改变像位置和放大因子，并导致波形与广义相对论模板匹配度下降，为探测修正传播提供了观测目标。
We consider the evolution of cosmological gravitational waves in scalar-tensor theory and $F(R)$ gravity theory as typical models of the modified gravity. Although the propagation speed is not changed from the speed of light, the propagation phase changes when we compare the propagation in these modified gravity theories with the propagation in the $Λ$CDM model. The phase change might be detected in future observations.
Non-thermal particle production in Einstein-Cartan gravity with modified Holst term and non-minimal couplings
本文研究了带修正Holst项与非极小耦合的Einstein-Cartan引力中的非热费米子产生，通过辅助场法将其转化为赝标量-张量理论，揭示了暴胀后真空失稳导致的粒子产生机制及其质量与螺旋度依赖性。
Modifications of General Relativity leave their imprint both on the cosmic expansion history through a non-trivial dark energy equation of state, and on the evolution of cosmological perturbations in the scalar and in the tensor sectors. In particular, the modification in the tensor sector gives rise to a notion of gravitational-wave (GW) luminosity distance, different from the standard electromagnetic luminosity distance, that can be studied with standard sirens at GW detectors such as LISA or third-generation ground based experiments. We discuss the predictions for modified GW propagation fr…
We consider Modified Gravity models involving inverse powers of fourth-order curvature invariants. Using these models' equivalence to the theory of a scalar field coupled to a linear combination of the invariants, we investigate the properties of the propagating modes. Even in the case for which the fourth derivative terms in the field equations vanish, we find that the second derivative terms can give rise to ghosts, instabilities, and superluminal propagation speeds. We establish the conditions which the theories must satisfy in order to avoid these problems in Friedmann backgrounds, and sho…
Wave-optics gravitational wave lensing in modified gravity
本文在修正引力框架下研究波动光学区域的引力波透镜效应，提出曲率耦合传播方程，揭示低频极限下放大因子不再趋近于1的新现象，并通过扭曲波解释和散射振幅语言描述这一效应。
Effective speed approach for modified scalar field propagation
本文提出有效速度方法研究标量场传播，推导出有效度规和应力能张量，验证了能量条件的满足。
We investigate the propagation of scalar waves induced by matter sources in the context of scalar-tensor theories of gravity which include screening mechanisms for the scalar degree of freedom. The usual approach when studying these theories in the non-linear regime of cosmological perturbations is based on the assumption that scalar waves travel at the speed of light. Within General Relativity such approximation is good and leads to no loss of accuracy in the estimation of observables. We find, however, that mass terms and non-linearities in the equations of motion lead to propagation and dis…
We perform a linear stability analysis of dynamical Chern-Simons modified gravity in the geometric optics approximation and find that it is linearly stable on the backgrounds considered. Our analysis also reveals that gravitational waves in the modified theory travel at the speed of light in Minkowski spacetime. However, on a Schwarzschild background the characteristic speed of propagation along a given direction splits into two modes, one subluminal and one superluminal. The width of the splitting depends on the azimuthal components of the propagation vector, is linearly proportional to the m…
The linearized Einstein field equations provide a low-energy wave equation for the propagation of gravitational fields which may originate from a high energy source. Motivated by loop quantum gravity, we propose the polymer quantization scheme to derive the effective propagation of such waves on a classical Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime. To overcome the challenge of polymer quantizing a time-dependent Hamiltonian, we rewrite such a Hamiltonian in a time-independent manner in the extended phase space, polymerize it, and then transform it back to the usual phase space. In …
We present a detailed study of the methodology for correlating `dark sirens' (compact binaries coalescences without electromagnetic counterpart) with galaxy catalogs. We propose several improvements on the current state of the art, and we apply them to the GWTC-2 catalog of LIGO/Virgo gravitational wave (GW) detections, and the GLADE galaxy catalog, performing a detailed study of several sources of systematic errors that, with the expected increase in statistics, will eventually become the dominant limitation. We provide a measurement of $H_0$ from dark sirens alone, finding as the best result…
Probing modified gravitational-wave propagation with extreme mass-ratio inspirals
本研究首次利用LISA模拟探测的极端质量比旋近系统作为暗哨声，结合贝叶斯方法约束广义相对论的参数化偏离，发现其在修正引力波传播约束上优于第二代地面探测器，最乐观情形下可比肩第三代探测器。
Modified gravitational wave propagations in linearized gravity with Lorentz and diffeomorphism violations and their gravitational wave constraints
本文在SME线性化引力框架下研究洛伦兹与微分同胚破坏对引力波传播的修正，计算双星并合波形的退相效应，并利用BILBY对GWTC-3事件进行贝叶斯推断，给出各破坏系数的90%置信区间约束。
Accelerating the standard siren method: Improved constraints on modified gravitational-wave propagation with future data
本文提出 CHIMERA 2.0 计算框架，利用 GPU 加速算法高效分析数千个引力波事件，联合推断宇宙学、修改引力波传播及种群超参数，显著提升了对未来 LIGO-Virgo-KAGRA O5 运行数据的限制能力。
We study the cosmological propagation of gravitational waves (GWs) beyond general relativity (GR) across homogeneous and isotropic backgrounds. We consider scenarios in which GWs interact with an additional tensor field and use a parametrized phenomenological approach that generically describes their coupled equations of motion. We analyze four distinct classes of derivative and non-derivative interactions: mass, friction, velocity, and chiral. We apply the WKB formalism to account for the cosmological evolution and obtain analytical solutions to these equations. We corroborate these results b…
Modified propagation of gravitational waves from the early radiation era
本研究在修正引力理论中，通过WKB估计和数值模拟，分析了引力波摩擦与张量速度过剩对早期辐射时代至今引力波谱的影响，发现摩擦项可修正低频谱斜率，并基于PTA观测对组合效应给出约束。
Several numerical relativity groups are using a modified ADM formulation for their simulations, which was developed by Nakamura et al (and widely cited as Baumgarte-Shapiro-Shibata-Nakamura system). This so-called BSSN formulation is shown to be more stable than the standard ADM formulation in many cases, and there have been many attempts to explain why this re-formulation has such an advantage. We try to explain the background mechanism of the BSSN equations by using eigenvalue analysis of constraint propagation equations. This analysis has been applied and has succeeded in explaining other s…
Multiple-scale analysis of modified gravitational-wave propagation
本文通过多尺度分析研究修改引力波传播，揭示了多自旋-2场相互作用对引力波振幅和相位的非平凡修改，为测试新引力理论提供新方法。
We consider thermal effects in the propagation of gravitational waves on a cosmological background. In particular, we consider scalar field cosmologies and study gravitational modes near cosmological singularities. We point out that the contribution of thermal radiation can heavily affect the dynamics of gravitational waves giving enhancement or dissipation effects both at quantum and classical level.These effects are considered both in General Relativity and in modified theories like $F(R)$ gravity which can be easily reduced to scalar-tensor cosmology. The possible detection and disentanglem…
Constraints on parity and Lorentz violations in gravity from GWTC-3 through a parametrization of modified gravitational wave propagations
本研究利用GWTC-3的致密双星并合数据，通过参数化修正广义相对论下的引力波传播波形，检验引力的宇称与洛伦兹对称性，未发现破缺信号，给出了多项相关严格约束及首个洛伦兹破缺阻尼效应约束。
Forecasting Constraints on Cosmology and Modified Gravitational-wave Propagation by Combining Strongly Lensed Gravitational Waves and Galaxy Surveys
本文首次利用双像强引力透镜引力波事件进行时间延迟宇宙学分析，结合未来星系巡天，预测对哈勃常数、暗能量参数及修正引力波传播的约束精度。
The effective field theory of dark energy and modified gravity is supposed to well describe, at low energies, the behaviour of the gravity modifications due to one extra scalar degree of freedom. The usual curvature perturbation is very useful when studying the conditions for the avoidance of ghost instabilities as well as the positivity of the squared speeds of propagation for both the scalar and tensor modes, or the Stückelberg field performs perfectly when investigating the evolution of linear perturbations. We show that the viable parameters space identified by requiring no-ghost instabili…
A joint hierarchical Bayesian analysis of the binary black hole (BBH) mass function, merger rate evolution and cosmological parameters can be used to extract information on both the cosmological and population parameters. We extend this technique to include the effect of modified gravitational wave (GW) propagation. We discuss the constraints on the parameter $Ξ_0$ that describes this phenomenon (with $Ξ_0=1$ in General Relativity, GR) using the data from the GWTC-3 catalog. We find the constraints $Ξ_0 = 1.2^{+0.7}_{-0.7}$ with a flat prior on $Ξ_0$, and $Ξ_0 = 1.0^{+0.4}_{-0.8}$ with a prior…
Constraining the modified friction in gravitational wave propagation with precessing black hole binaries
本文研究了利用地面引力波探测器观测进动双黑洞来约束引力波传播中的修改摩擦效应，发现进动效应能显著提高光度距离测量精度，使约束结果比现有分析改善约2个数量级。
The cosmological primordial power spectrum is known to be one of the most promising observable to probe quantum gravity effects. In this article, we investigate how the tensor power spectrum is modified by Loop Quantum Gravity corrections. The two most important quantum terms, holonomy and inverse volume, are explicitly taken into account in a unified framework. The equation of propagation of gravitational waves is derived and solved for one set of parameters.
We review the new theory of modified supergravity, dubbed F(\cal R) supergravity, and some of its recent applications to inflation and reheating in the early universe cosmology. The F(\cal R) supergravity is the N=1 locally supersymmetric extension of the f(R) gravity in four space-time dimensions. A manifestly supersymmetric formulation of the F(\cal R) supergravity exist in terms of N=1 superfields, by using the (old) minimal Poincar'e supergravity in curved superspace. We find the conditions for stability, the absence of ghosts and tachyons. Three models of the F(\cal R) supergravity are st…
How well can modified gravitational wave propagation be constrained with strong lensing?
本文提出利用强引力透镜产生的多重引力波信号与电磁观测结合，通过比较光度距离来约束引力替代理论中的修改引力波传播效应，发现该方法可较GW170817的约束改善约5至100倍。
Gravitational-wave sources can serve as standard sirens to probe cosmology by measuring their luminosity distance and redshift. Such standard sirens are also useful to probe theories beyond general relativity with a modified gravitational-wave propagation. Many of previous studies on the latter assume multi-messenger observations so that the luminosity distance can be measured with gravitational waves while the redshift is obtained by identifying sources' host galaxies from electromagnetic counterparts. Given that gravitational-wave events of binary neutron star coalescences with associated el…
This paper attempts to clarify the deep consequences of Barrow fractal black hole spacetime configurations caused by quantum gravity on neutrino pair annihilation and accretion disk dynamics. We systematically derive the analytical expression for the innermost stable circular orbit (ISCO) radius ($r_{\text{ISCO}}\propto M^{2/(2+Δ)}$) by building a Barrow-modified static spherically symmetric metric ($r\rightarrow r^{1+Δ/2}$), and we find that increasing $Δ$ significantly shifts the ISCO inward. We numerically solve the radiation flux, effective temperature, and differential luminosity distribu…
We analyze the features of the Minkowskian limit of a particular non-analytical f(R) model, whose Taylor expansion in the weak field limit does not hold, as far as gravitational waves (GWs) are concerned. We solve the corresponding Einstein equations and we find an explicit expression of the modified GWs as the sum of two terms, i.e. the standard one and a modified part. As a result, GWs in this model are not transverse, and their polarization is different from that of General Relativity. The velocity of the GW modified part depends crucially on the parameters characterizing the model, and it …
Cosmology and modified GW propagation from the BNS mass function at third-generation detector networks
本文基于BNS质量函数，利用Einstein Telescope和Cosmic Explorer探测器网络，研究Hubble常数H₀和修改引力波传播参数Xi₀的约束，发现网络配置对精度有显著影响。
We present a general description of the propagation properties of quantum gravity modified electrodynamics characterized by constitutive relations up to second order in the correction parameter. The effective description corresponds to an electrodynamics in a dispersive and absorptive non-local medium, where the Green functions and the refraction indices can be explicitly calculated. The reality of the electromagnetic field together with the requirement of causal propagation in a given referrence frame leads to restrictions in the form of such refraction indices. In particular, absorption must…
Modeling Uncertainties in Modified Gravity Predictions for the Stochastic Gravitational-Wave Background
研究修正引力对未解析双黑洞合并产生的随机引力波背景的影响，用特定模型纳入天体物理不确定性，通过对不同探测器的注入-恢复分析，表明频率相关的ppE修正可被第三代探测器约束。
We explore the impact of modified gravity on B-modes, identifying two main separate effects: lensing and propagation of tensor modes. The location of the inflationary peak of the BB spectrum depends on the speed of gravitational waves; the amplitude of the lensing contribution depends on the anisotropic stress. We single out these effects using the quasi-static regime and considering models for which the background and the growth of matter perturbations are standard. Using available data we obtain that the gravitational wave speed is compatible with the speed of light and constrained to within…
The observation of GW170817 binary neutron star (BNS) merger event has imposed strong bounds on the speed of gravitational waves (GWs) locally, inferring that the speed of GWs propagation is equal to the speed of light. Current GW detectors in operation will not be able to observe BNS merger to long cosmological distance, where possible cosmological corrections on the cosmic expansion history are expected to play an important role, specially for investigating possible deviations from general relativity. Future GW detectors designer projects will be able to detect many coalescences of BNS at hi…
Propagation effects of Lorentz violation in gravitational waves
本文研究了洛伦兹和微分同胚违反算子对引力波传播的影响，分析了维度四和五系数对张量引力辐射的修正，推导了修正波算子的 retarded Green 函数，并通过双星系统展示了洛伦兹违反如何改变观测到的应变。
The family of metrics corresponding to the plane-fronted gravitational waves with parallel propagation, commonly referred to as the family of pp-wave metrics, is studied in the context of various modified gravitational models in a self-contained and coherent manner by using a variant of the null coframe formulation of Newman and Penrose and the exterior algebra of differential forms on pseudo-Riemannian manifolds.
Gravitational wave polarizations with different propagation speeds
提出一种与模型无关的方法，直接从度规微扰计算以不同速度传播的引力波偏振，扩展参数化后爱因斯坦形式体系，并讨论传播速度差异对广义相对论零流测试的影响。
We study the gravitational waves in modified Gauss-Bonnet gravity. Applying the metric perturbation around a cosmological background, we obtain explicit expressions for the wave equations. It is shown that the speed of the traceless mode is equal to the speed of light. An additional massive scalar mode appears in the propagation of the gravitational waves. To find phenomena beyond the general relativity the scalar mode mass is calculated as a function of the background curvature in some typical models.
The propagation of nonrelativistic excitations in material media with topological defects can be modeled in terms of an external torsion field modifying the Schroedinger equation. Through a perturbative approach, we find a solution for the wave function which gives corrections in the interference patterns of the order of 0.1 Angstrom, for a possible experimental setup at atomic scales. Finally, we demonstrate how this geometric, but effective, approach can indeed accommodate a probabilistic interpretation of the wave function although the perturbative theory is nonunitary.
Using the Bondi-Sachs formalism, the problem of a gravitational wave source surrounded by a spherical dust shell is considered. Using linearized perturbation theory, the geometry is found in the regions: in the shell, exterior to the shell, and interior to the shell. It is found that the dust shell causes the gravitational wave to be modified both in magnitude and phase, but without any energy being transferred to or from the dust.
Gravitational Waves on Charged Black Hole Backgrounds in Modified Gravity
本文在修改引力的有效场论框架下计算Reissner-Nördstrom黑洞背景上引力波的径向与角向传播速度，得到新的极端质量-电荷关系，并利用因果性论证对EFT参数提出新的约束。
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