Halo model is a physically intuitive method for modelling the non-linear power spectrum, especially for the alternatives to the standard $Λ$CDM models. In this paper, we exam the Sheth-Tormen barrier formula adopted in the previous \texttt{CHAM} method \citep{2018MNRAS.476L..65H}. As an example, we model the ellipsoidal collapse of top-hat dark matter haloes in $f(R)$ gravity. A good agreement between Sheth-Tormen formula and our result is achieved. The relative difference in the ellipsoidal collapse barrier is less than or equal to $1.6\%$. Furthermore, we verify that, for F4 and F5 cases of Hu-Sawicki $f(R)$ gravity, the screening mechanism do not play a crucial role in the non-linear power spectrum modelling up to $k\sim1[h/{\rm Mpc}]$. We compare two versions of modified gravity modelling, namely with/without screening. We find that by treating the effective Newton constant as constant number ($G_{\rm eff}=4/3G_N$) is acceptable. The scale dependence of the gravitational coupling is sub-relevant. The resulting spectra in F4 and F5, are in $0.1\%$ agreement with the previous \texttt{CHAM} results. The published code is accelerated significantly. Finally, we compare our halo model prediction with N-body simulation. We find that the general spectrum profile agree, qualitatively. However, via the halo model approach, there exists a systematic under-estimation of the matter power spectrum in the co-moving wavenumber range between $0.3 h/{\rm Mpc}$ and $3 h/{\rm Mpc}$. These scales are overlapping with the transition scales from two halo term dominated regimes to those of one halo term dominated.
Astrophysical Tests of Modified Gravity: A Screening Map of the Nearby Universe
Hui，Nicolis and Stubbs（2009）和Jain and VanderPlas（2011）最近强调了修正引力理论在邻近宇宙中的天体物理检验。这种测试的一个关键要素是筛选机制，从而在大质量晕或像银河系这样的高密度环境中恢复广义相对论。在引力的变色龙理论中，包括所有的f（R）模型，场矮星系可能是未屏蔽的，因此感受到额外的力，而不是屏蔽星系。研究筛选和未筛选星系之间差异的第一步是创建3D筛选地图。我们使用N体模拟来测试和校准简单的近似，以确定在星系目录中的屏蔽水平。由于观测不准确，筛选图中的系统误差的来源进行了建模，并估计其污染。然后，我们应用我们的方法来创建一个地图，以200 Mpc的斯隆数字巡天足迹使用数据从斯隆调查和其他来源。在两篇配套论文中，这张地图将被用于使用距离指示器和矮星系盘进行新的引力测试。我们还公开了我们的筛选地图。
We present a formalism to study screening mechanisms in modified theories of gravity via perturbative methods in different cosmological scenarios. We consider Einstein frame posed theories that are recast as Jordan frame theories, where a known formalism is employed, though the resulting non-linearities of the Klein-Gordon equation acquire an explicit coupling between matter and the scalar field, which is not present in Jordan frame theories. The obtained growth functions are then separated in screening and non-screened contributions to facilitate its analysis. This allows us to compare severa…
We describe the effects of the cosmological background on the K-mouflage screening properties of an astrophysical structure. We show that the K-mouflage screening of the spatial gradients of the scalar field, i.e. the screening of the fifth force, happens inside a dynamically generated screening radius. This radius is smaller than the location where the quasistatic approximation, i.e. where the spatial gradients exceed the time derivative, holds. Even though this quasistatic radius is much smaller than the size of the matter overdensity, spatial gradients remain well described by the quasistat…
The Vainshtein mechanism, present in many models of gravity, is very effective at screening dark matter halos such that the fifth force is negligible and general relativity is recovered within their Vainshtein radii. Vainshtein screening is independent of halo mass and environment, in contrast to e.g. chameleon screening, making it difficult to test. However, our previous studies have found that the dark matter particles in filaments, walls, and voids are not screened by the Vainshtein mechanism. We therefore investigate whether cosmic voids, identified as local density minima using a watershe…
The Brans-Dicke theory of gravity is one of the oldest ideas to extend general relativity by introducing a non-minimal coupling between the scalar field and gravity. The Solar System tests put tight constraints on the theory. In order to evade these constraints, various screening mechanisms have been proposed. These screening mechanisms allow the scalar field to couple to matter as strongly as gravity in low density environments while suppressing it in the Solar System. The Vainshtein mechanism, which is found in various modified gravity models such as massive gravity, braneworld models and sc…
We study nonlinear effects of perturbations around a cosmological background in projected massive gravity, which admits self-accelerating solutions in an open FLRW universe. Using the zero-curvature scaling limit, we derive nonlinear equations containing all the relevant terms on subhorizon scales. We find that the solution for a scalar graviton vanishes completely for all scales, which agrees with the linear perturbation analysis in the previous study. In addition, the effects on the gravitational potential due to the next order perturbation are strongly suppressed within the horizon. Therefo…
Future large-scale structure surveys will measure three-point statistics with high statistical significance. This will offer significant improvements on our understanding of gravity, provided we can model these statistics accurately. We assess the performance of several schemes for theoretical modelling of the matter bispectrum, including halo-model based approaches and fitting formulae. We compare the model predictions against N-body simulations, considering scales up to $k_{\rm max} = 4 h/{\rm Mpc}$, well into non-linear regime of structure formation. Focusing on the equilateral configuratio…
Environmental screening of dark matter haloes in $f(R)$ gravity
在某些修正的引力理论中，太阳系对偏离广义相对论的限制是通过所谓的屏蔽机制来满足的，这使得理论能够在物质密度高或引力势深的区域恢复到广义相对论。就变色龙理论而言，屏蔽有两个贡献--自我屏蔽，这是由于物体本身的质量造成的，以及环境屏蔽，这是由周围物质引起的--这两个贡献通常是纠缠在一起的，第二个贡献对于质量较小的物体来说更重要。对环境对屏蔽的影响的定量理解可以证明在使用本星系群和矮星系等系统对这些理论进行观测测试时至关重要，因为环境可以以各种方式推断。我们使用Shi et al.（2015）的高分辨率{ \sc liminality}模拟来测试不同环境定义的保真度。我们发现，尽管在实践中定义环境的不同方法并不完全一致，但它们可以提供有用的指导，并交叉检查暗物质晕的屏蔽程度。此外，在暗物质晕中的次晕的筛选主要是由环境决定的，次晕质量起着次要的作用，这意味着在次晕没有得到很好解决的情况下，低分辨率的模拟仍然可以用于理解次晕内重力的变化。
We propose a new framework for testing gravity using cluster observations, which aims to provide an unbiased constraint on modified gravity models from Sunyaev Zel'dovich (SZ) and X-ray cluster counts and the cluster gas fraction, among other possible observables. Focusing on a popular $ f(R) $ model of gravity, we propose a novel procedure to recalibrate mass scaling relations from $ Λ$CDM to $ f(R) $ gravity for SZ and X-ray cluster observables. We find that the complicated modified gravity effects can be simply modelled as a dependence on a combination of the background scalar field and red…
Impact on the power spectrum of Screening in Modified Gravity Scenarios
我们使用半解析的方法研究了$f(R)$、$f(R)$和$f(R)$类型的屏蔽修正重力对结构形成的影响，从准线性到非线性。对于这样的模型，其中新的标量场的范围通常是在Mpc的范围内，并在宇宙学的背景下，非线性技术需要了解的偏差相比，$Λ$ -CDM模板的物质密度对比度的功率谱。这是目前普遍使用广泛的N体模拟解决。在这里，我们提出了新的结果相结合的精确微扰理论在一个循环水平（和部分remation的微扰系列）与晕模型。前者允许一个扩展的线性微扰分析$k\lesssim 0.15{\rm h Mpc}^{-1}$在微扰水平，而后者导致一个合理的，高达百分之几，协议与数值模拟$k\lesssim 3{\rm h Mpc}^{-1}$的大曲率$f(R)$模型，和$k\lesssim 1{\rm h Mpc}^{-1}$的介子和介子，在$z=0$。我们还讨论了如何不同的行为的微扰膨胀和球形崩溃的$f(R)$，pathon，和pathon模型。
Screened modified gravity (SMG) and Brans-Dicke (BD) gravity are typical examples of scalar-tensor theories with and without screening mechanisms, which can suppress the scalar field in dense regions. In this paper, we investigate the tests of time-varying gravitational constant $G$, gravitational dipole radiation, and Nordtvedt effect in BD and SMG theories, respectively. We place new constraints on these theories by combining Cassini experiment, lunar laser ranging (LLR) measurements, and pulsar observations from PSRs J1738$+$0333 and J0348$+$0432. We find that screening mechanism has import…
We use high-precision combined strong/weak lensing and kinematics measurements of the total mass profiles of the observed galaxy clusters MACS~J1206.2-0847 and Abell~S1063, to constrain the relativistic sector of the general DHOST dark energy theories, which exhibit a partial breaking of the so called Vainsthein screening mechanism, on the linear level of scalar fluctuations around a cosmological background. In particular, by using the \textsc{MG-MAMMPOSSt} framework developed in Pizzuti et al. 2021, for the kinematics analysis of member galaxies in clusters along with lensing mass profile rec…
We introduce the LOCal Universe Screening Test Suite (LOCUSTS) project, an effort to create 'screening maps' in the nearby Universe to identify regions in our neighbourhood which are screened, i.e., regions where deviations from General Relativity (GR) are suppressed, in various modified gravity (MG) models. In these models, deviations from the GR force law are often stronger for smaller astrophysical objects, making them ideal test beds of gravity in the local Universe. However, the actual behaviour of the modified gravity force also depends on the environment of the objects, and to make accu…
In this paper we study long range modifications of gravity in the consistent framework of bigravity, which introduces a second massive spin-2 field and allows to continuously interpolate between the regime of General Relativity (mediated by a massless spin-2 field) and massive gravity (mediated by a massive spin-2 field). In particular we derive for the first time the equations for light deflection in this framework and study the effect on the lensing potential of galaxy clusters. By comparison of kinematic and lensing mass reconstructions, stringent bounds can be set on the parameter space of…
Modified gravity theories with an effective Newton constant that varies over cosmological timescales generally predict a different gravitational wave luminosity distance than General Relativity. While this holds for a uniform variation, we show that if locally screened at the source and at the observer as required to pass stringent astrophysical tests of gravity, the General Relativistic distance is restored. In the absence of such a screening, the same effect must modify electromagnetic luminosity distances inferred from supernovae Type Ia, to the extent that the effects can cancel in the com…
We investigate the efficiency of screening mechanisms in the hybrid metric-Palatini gravity. The value of the field is computed around spherical bodies embedded in a background of constant density. We find a thin shell condition for the field depending on the background field value. In order to quantify how the thin shell effect is relevant, we analyze how it behaves in the neighborhood of different astrophysical objects (planets, moons or stars). We find that the condition is very well satisfied except only for some peculiar objects. Furthermore we establish bounds on the model using data fro…
We study cosmic voids in the normal-branch Dvali-Gabadadze-Porrati (nDGP) braneworld models, which are representative of a class of modified gravity theories where deviations from General Relativity are usually hidden by the Vainshtein screening in high-density environments. This screening is less efficient away from these environments, which makes voids ideally suited for testing this class of models. We use N-body simulations of $Λ$-cold dark matter ($Λ$CDM) and nGDP universes, where dark matter haloes are populated with mock galaxies that mimic the clustering and number densities of the BOS…
Gravitational theories differing from General Relativity may explain the accelerated expansion of the Universe without a cosmological constant. However, to pass local gravitational tests, a "screening mechanism" is needed to suppress, on small scales, the fifth force driving the cosmological acceleration. We consider the simplest of these theories, i.e. a scalar-tensor theory with first-order derivative self-interactions, and study isolated (static and spherically symmetric) non-relativistic and relativistic stars. We produce screened solutions and use them as initial data for non-linear numer…
We investigate the impact of modified-gravity models on the Lyman-$α$ power spectrum. Building a simple analytical modeling, based on a truncated Zeldovich approximation, we estimate the intergalactic medium power spectrum and the Lyman-$α$ flux decrement power spectrum along the line of sight. We recover the results of numerical simulations for $f(R)$-gravity models and present new results for K-mouflage scenarios. We find that the shape of the distortion due to the modified gravity depends on the model, through the scale-dependence or not of their growth rate. This is more clearly seen in th…
We study a new model of Energy-Momentum Squared Gravity (EMSG), called Energy-Momentum Log Gravity (EMLG), constructed by the addition of the term $f(T_{μν}T^{μν})=α\ln(λ\,T_{μν}T^{μν})$, envisaged as a correction, to the Einstein-Hilbert action with cosmological constant $Λ$. The choice of this modification is made as a specific way of including new terms in the right-hand side of the Einstein field equations, resulting in constant effective inertial mass density and, importantly, leading to an explicit exact solution of the matter energy density in terms of redshift. We look for viable cosmo…
Long range scalar fields with a coupling to matter appear to violate known bounds on gravitation in the solar system and the laboratory. This is evaded thanks to screening mechanisms. In this short review, we shall present the various screening mechanisms from an effective field theory point of view. We then investigate how they can and will be tested in the laboratory and on astrophysical and cosmological scales.
Current constraints on gravity are relatively weak on galactic and intergalactic scales. Screened modified gravity models can exhibit complex behaviour there without violating stringent tests of gravity within our Solar System. They might hence provide viable extensions of the theory of gravity. Here, we use galaxy kinematics to constrain screened modified gravity models. We focus on chameleon $f(R)$ gravity and predict its impact on galaxy rotation curves and radial acceleration relations. This is achieved by post-processing state-of-the-art galaxy formation simulations from the \textsc{aurig…
The symmetron model is a scalar-tensor theory of gravity with a screening mechanism that suppresses the effect of the symmetron field at high densities characteristic of the solar system and laboratory scales but allows it to act with gravitational strength at low density on the cosmological scale. We elucidate the screening mechanism by showing that in the quasi-static Newtonian limit there are precise analogies between symmetron gravity and electrostatics for both strong and weak screening. For strong screening we find that large dense bodies behave in a manner analogous to perfect conductor…
We introduce $\texttt{Hi-COLA}$, a code designed to run fast, approximate $\textit{N}$-body simulations of non-linear structure formation in reduced Horndeski gravity. Given an input Lagrangian, $\texttt{Hi-COLA}$ dynamically constructs the appropriate field equations and consistently solves for the cosmological background, linear growth, and screened fifth force of that theory. Hence $\texttt{Hi-COLA}$ is a general, adaptable, and useful tool that allows the mildly non-linear regime of many Horndeski theories to be investigated for the first time, at low computational cost. In this work, we f…
在广义相对论以及修正引力的f（R）和Wavelon模型的背景下，我们使用了一个球形模型和一个扩展的漂移集形式主义（extended excursion set formalism with driving diffusive barriers）来预测宇宙空洞的丰度。我们检测球形空洞从一套N体模拟这些引力理论和比较测得的空洞丰度理论预测。我们发现，我们的模型正确地描述了丰富的暗物质和星系空洞，提供了一个更好的拟合比以前的建议，在文献中的基础上静态障碍。我们使用模拟丰度结果来拟合丰度模型自由参数作为修改后的重力参数的函数，并表明暗物质空隙的计数可以提供有趣的约束修改后的重力。对于星系空洞，更密切相关的光学观测，我们发现，约束修改重力从空洞丰度单独可能是更具挑战性的。在目前和即将进行的星系调查的背景下，空洞和晕统计数据，包括其丰度，配置文件和相关性的组合，应有效地区分显示不同的筛选机制的修改后的重力模型。
We study a model of quintessential inflation constructed in $R^2$ modified gravity with a non-minimally coupled scalar field, in the Palatini formalism. Our non-minimal inflaton field is characterised by a simple exponential potential. We find that successful quintessential inflation can be achieved with no fine-tuning on the model parameters. Predictions on the characteristics of dark energy will be tested by observations in the near future, while contrast with existing observations provides insights on the modified gravity background, such as the value of the non-minimal coupling and its run…
We construct a generalization of the standard $Λ$CDM model, wherein we simultaneously replace the spatially flat Robertson-Walker metric with its simplest anisotropic generalization (LRS Bianchi I metric), and couple the cold dark matter to the gravity in accordance with the energy-momentum squared gravity (EMSG) of the form $f(T_{μν}T^{μν})\propto T_{μν}T^{μν}$. These two modifications -- namely, two new stiff fluid-like terms of different nature -- can mutually cancel out, i.e., the shear scalar can be screened completely, and reproduce mathematically exactly the same Friedmann equation of t…
