Modified Gravity Models Research Articles

Fully relativistic predictions in Horndeski gravity from standard Newtonian N-body simulations

The N-body gauge allows the introduction of relativistic effects in Newtonian cosmological simulations. Here we extend this framework to general Horndeski gravity theories, and investigate the relativistic effects that the scalar field introduces in the matter power spectrum at intermediate and large scales. In particular, we show that the kineticity function at these scales enhances the amplitude of the signal of contributions coming from the extra degree of freedom. Using the Quasi-Static Approximation (QSA), we separate modified gravity effects into two parts: one that only affects small-scale physics, and one that is due to relativistic effects. This allows our formalism to be readily implemented in modified gravity N-body codes in a straightforward manner, e.g., relativistic effects can be included as an additional linear density field in simulations. We identify the emergence of gravity acoustic oscillations (GAOs) in the matter power spectrum at large scales, k ∼ 10-3–10-2 Mpc-1. GAO features have a purely relativistic origin, coming from the dynamical nature of the scalar field. GAOs may be enhanced to detectable levels by the rapid evolution of the dark energy sound horizon in certain modified gravity models and can be seen as a new test of gravity at scales probed by future galaxy and intensity-mapping surveys.

Fast generation of mock galaxy catalogues in modified gravity models with COLA

We investigate the viability of producing galaxy mock catalogues with COmoving Lagrangian Acceleration (COLA) simulations in Modified Gravity (MG) models employing the Halo Occupation Distribution (HOD) formalism. In this work, we focus on two theories of MG: f(R) gravity with the chameleon mechanism, and a braneworld model (nDGP) that incorporates the Vainshtein mechanism. We use a suite of full N-body simulations in MG as a benchmark to test the accuracy of COLA simulations. At the level of Dark Matter (DM), we show that COLA accurately reproduces the matter power spectrum up to k ∼ 1 h Mpc-1, while it is less accurate in reproducing the velocity field. To produce halo catalogues, we find that the rockstar halo-finder does not perform well with COLA simulations. On the other hand, using a simple Friends-of-Friends (FoF) finder and an empirical mass conversion from FoF to spherical over-density masses, we are able to produce halo catalogues in COLA that are in good agreement with those in N-body simulations. To consider the effects of the MG fifth force on the halo profile, we derive simple fitting formulae for the concentration-mass and the velocity dispersion-mass relations that we calibrate using rockstar halo catalogues in N-body simulations. We then use these results to extend the HOD formalism to modified gravity simulations in COLA. We use an HOD model with five parameters that we tune to obtain galaxy catalogues in redshift space. We find that despite the great freedom of the HOD model, MG leaves characteristic imprints in the redshift space power spectrum multipoles and these features are well captured by the COLA galaxy catalogues.

The Economic Network Resilience of the Guanzhong Plain City Cluster, China: A network analysis from the evolutionary perspective

AbstractThis article applies the network analysis to evaluate the resilience of economic network in Guanzhong Plain City Cluster (GPCC) and examine the impact of network structural properties on economic resilience, thus providing an innovative research perspective and a theoretical framework for evaluating the economic resilience of the city cluster. A modified gravity model is introduced to construct the economic network. Three structural properties of the network, hierarchy, assortativity, and cohesion, are used to evaluate the resilience of the GPCC from 2008 to 2018 and illustrate the characteristics of the resilience. The results show that the economic network of the GPCC is strongly hierarchical with a growing trend, a declining disassortativity, and a weak cohesion. Although the network has formed a core‐peripheral structure, its hierarchy and disassortativity would result in low resilience and high vulnerability, at the risk of external shocks to the GPCC. The impact of the network structure on economic resilience is analyzed by using a regression model, which verifies the validity of applying the network theory to resilience analysis. The results suggest that improving the interactions and economic connections between core and peripheral cities will strengthen the resilience of the GPCC.

MOG cosmology without dark matter and the cosmological constant

ABSTRACT In this work, we investigate the MOdified Gravity (MOG) theory for dynamics of the Universe and compare the results with the Lambda cold dark matter (ΛCDM) cosmology. We study the background cosmological properties of the MOG model and structure formation at the linear perturbation level. We compare the two models with the currently available cosmological data by using statistical Bayesian analyses. After obtaining updated constraints on the free parameters, we use some methods of model selection to assist in choosing the more consistent model such as the reduced chi-squared ($\chi ^2_{\rm red}$) and a number of the basic information criteria such as the Akaike Information Criterion (AIC), the Bayes factor or Bayesian Information Criterion (BIC), and Deviance Information Criterion (DIC). MOG model appears to be consistent with the ΛCDM model by the results of $\chi ^2_{\rm red}$ and DIC for an overall statistical analysis using the background data and the linear growth of structure formation.

Two-dimensional black holes in the limiting curvature theory of gravity

In this paper we discuss modified gravity models in which growth of the curvature is dynamically restricted. To illustrate interesting features of such models we consider a modification of two-dimensional dilaton gravity theory which satisfies the limiting curvature condition. We show that such a model describes two-dimensional black holes which contain the de Sitter-like core instead of the singularity of the original non-modified theory. In the second part of the paper we study Vaidya type solutions of the model of the limiting curvature theory of gravity and used them to analyse properties of black holes which are created by the collapse of null fluid. We also apply these solutions to study interesting features of a black hole evaporation.

Estimating the route-level passenger demand profile from bus dwell times

This paper explores the feasibility of estimating the demand profile of a bus route consisting of boarding flows, alighting flows, passenger loads, and origin–destination (OD) flows using dwell times as the main data source. Dwell times can be obtained from Automatic Vehicle Location (AVL) data, or door opening and closing records. This data is often more obtainable than the direct demand information based on passenger counts or fare collection information. A flexible Bayesian framework allowing for various dwell time models is employed to infer the passenger demand profile conditional on the observed bus dwell times. We model passenger flows by stop-specific arrival rates and a conditional alighting probability matrix. A modified gravity model is used to further explain the alighting probability matrix and to reduce the number of unknown parameters. Hamiltonian Monte Carlo sampling is implemented to draw the posterior distribution for the parameters of interest. The methodology is validated by three lines of a bus system where alighting times are the main activity time. For these lines dwell time as well as passenger count data are available. The case study shows that accurate estimates of alighting flows and passenger loads can be derived by the proposed framework with dwell times only but that room remains for improving the accuracy of boarding flows and OD flows. Additional boarding counts of a few bus runs, which can be easily integrated into the observation block of the estimation framework, raise the estimation accuracy of boarding and OD flows to an acceptable level. We therefore conclude that the proposed methodology can help “data-poor” bus operators to overcome demand estimation problems for transit planning and operation.

Modified gravity: A unified approach

Starting from the original Einstein action, sometimes called the Gamma squared action, we propose a new setup to formulate modified theories of gravity. This can yield a theory with second order field equations similar to those found in other popular modified gravity models. Using a more general setting the theory gives fourth order equations. This model is based on the metric alone and does not require more general geometries. It is possible to show that our new theory and the recently proposed $f(Q)$ gravity models are equivalent at the level of the action and at the level of the field equations, provided that appropriate boundary terms are taken into account. Our theory can also match up with $f(R)$ gravity which is an expected result. Perhaps more surprisingly, we can also show that this equivalence extends to $f(T)$ gravity at the level of the action and its field equations, provided that appropriate boundary terms are taken in account. While these three theories are conceptually different and are based on different geometrical settings, we can establish the necessary conditions under which their field equations are indistinguishable. The final part requires matter to couple minimally to gravity. Through this work we emphasise the importance played by boundary terms which are at the heart of our approach.

Investigating cosmological GAN emulators using latent space interpolation

ABSTRACT Generative adversarial networks (GANs) have been recently applied as a novel emulation technique for large-scale structure simulations. Recent results show that GANs can be used as a fast and efficient emulator for producing novel weak lensing convergence maps as well as cosmic web data in 2D and 3D. However, like any algorithm, the GAN approach comes with a set of limitations, such as an unstable training procedure, inherent randomness of the produced outputs, and difficulties when training the algorithm on multiple data sets. In this work, we employ a number of techniques commonly used in the machine learning literature to address the mentioned limitations. Specifically, we train a GAN to produce weak lensing convergence maps and dark matter overdensity field data for multiple redshifts, cosmological parameters, and modified gravity models. In addition, we train a GAN using the newest Illustris data to emulate dark matter, gas, and internal energy distribution data simultaneously. Finally, we apply the technique of latent space interpolation as a tool for understanding the feature space of the GAN algorithm. We show that the latent space interpolation procedure allows the generation of outputs with intermediate cosmological parameters that were not included in the training data. Our results indicate a 1–20 per cent difference between the power spectra of the GAN-produced and the test data samples depending on the data set used and whether Gaussian smoothing was applied. Similarly, the Minkowski functional analysis indicates a good agreement between the emulated and the real images for most of the studied data sets.

Mg-mamposst: a code to test modifications of gravity with internal kinematics and lensing analyses of galaxy clusters

ABSTRACT We present an upgraded version of mg-mamposst, an extension of the mamposst (Modelling Anisotropy and Mass Profile of Spherical Observed Systems) algorithm that performs Bayesian fits of models of mass and velocity anisotropy profiles to the distribution of tracers in projected phase space, to handle modified gravity models and constrain their parameters. The new version implements two distinct types of gravity modifications, namely general chameleon and Vainshtein screening, and is further equipped with a Monte Carlo Markov chain module for an efficient parameter space exploration. The programme is complemented by the clustergen code, capable of producing mock galaxy clusters under the assumption of spherical symmetry, dynamical equilibrium, and Gaussian local velocity distribution functions as in mamposst. We demonstrate the potential of the method by analysing a set of synthetic, isolated spherically symmetric dark matter haloes, focusing on the statistical degeneracies between model parameters. Assuming the availability of additional lensing-like information, we forecast the constraints on the modified gravity parameters for the two models presented, as expected from joint lensing + internal kinematics analyses, in view of upcoming galaxy cluster surveys. In Vainshtein screening, we forecast the weak lensing effect through the estimation of the full convergence-shear profile. For chameleon screening, we constrain the allowed region in the space of the two free parameters of the model, further focusing on the $\displaystyle f(\mathcal {R})$ subclass to obtain realistic bounds on the background field $\displaystyle |f_{\mathcal {R}0}|$. Our analysis demonstrates the complementarity of internal kinematics and lensing probes for constraining modified gravity theories, and how the bounds on Vainshtein-screened theories improve through the combination of the two probes.

Rescaled Einstein-Hilbert gravity from f(R) gravity: Inflation, dark energy, and the swampland criteria

We consider a class of exponential models of $f(R)$ gravity, in the presence of a canonical scalar field, for which at early times the effective Lagrangian of the theory becomes that of a rescaled canonical scalar field with the Einstein-Hilbert term becoming $\sim \alpha R$, with $\alpha$ a dimensionless constant. This rescaled Einstein-Hilbert scalar field theory at early times alters the inflationary phenomenology of well-known scalar field models of inflation, but more importantly, in the context of this rescaled theory, the Swampland criteria are easily satisfied, assuming that the scalar field is slowly rolling. We consider two models of inflation to exemplify our study, a fibre inflation model and a model that belongs to the general class of supergravity $\alpha$-attractor models. The inflationary phenomenology of the models is demonstrated to be viable, and for the same set of values of the free parameters of each model which ensure their inflationary viability, all the known Swampland criteria are satisfied too, and we need to note that we assumed that the first Swampland criterion is marginally satisfied by the scalar field, so $\phi\sim M_p$ during the inflationary era. Finally, we examine the late-time phenomenology of the fibre inflation potential in the presence of the full $f(R)$ gravity, and we demonstrate that the resulting model produces a viable dark energy era, which resembles the $\Lambda$-Cold-Dark-Mater model. Thus in the modified gravity model we present, the Universe is described by a rescaled Einstein-Hilbert gravity at early times, hence in some sense the modified gravity effect is minimal primordially, and the scalar field controls mainly the dynamics with a rescaled Ricci scalar gravity. However $f(R)$ gravity dominates at late-times, where it controls the dynamics, synergistically with the scalar field.

Proca-stinated cosmology. Part II. Matter, halo, and lensing statistics in the vector Galileon

The generalised Proca (GP) theory is a modified gravity model in which the acceleration of the cosmic expansion rate can be explained by self interactions of a cosmological vector field. In this paper we study a particular sub-class of the GP theory, with up to cubic order Lagrangian, known as the cubic vector Galileon (cvG) model. This model is similar to the cubic scalar Galileon (csG) in many aspects, including a fifth force and the Vainshtein screening mechanism, but with the additional flexibility that the strength of the fifth force depends on an extra parameter — interpolating between zero and the full strength of the csG model — while the background expansion history is independent of this parameter. It offers an interesting alternative to ΛCDM in explaining the cosmic acceleration, as well as a solution to the tension between early- and late-time measurements of the Hubble constant H 0. To identify the best ways to test this model, in this paper we conduct a comprehensive study of the phenomenology of this model in the nonlinear regime of large-scale structure formation, using a suite of N-body simulations run with the modified gravity code ECOSMOG. By inspecting thirteen statistics of the dark matter field, dark matter haloes and weak lensing maps, we find that the fifth force in this model can have particularly significant effects on the large-scale velocity field and lensing potential at late times, which suggest that redshift-space distortions and weak lensing can place strong constraints on it.

Cosmological gravity on all scales. Part II. Model independent modified gravity N-body simulations

Model-independent constraints on modified gravity models hitherto exist mainly on linear scales [1]. A recently developed formalism presented a consistent parameterisation that is valid on all scales [2]. Using this approach, we perform model-independent modified gravity N-body simulations on all cosmological scales with a time-dependent μ. We present convergence tests of our simulations, and we examine how well existing fitting functions reproduce the non-linear matter power spectrum of the simulations. We find that although there is a significant variation in the accuracy of all of the fitting functions over the parameter space of our simulations, the ReACT [3] framework delivers the most consistent performance for the matter power spectrum. We comment on how this might be improved to the level required for future surveys such as Euclid and the Vera Rubin Telescope (LSST). We also show how to compute weak-lensing observables consistently from the simulated matter power spectra in our approach, and show that ReACT also performs best when fitting the weak-lensing observables. This paves the way for a full model-independent test of modified gravity using all of the data from such upcoming surveys.

Tourism Economic Network Structural Characteristics of National Parks in the Central Region of China

The social network analysis has been actively applied in various tourist destinations, with a few studies on the tourism economic network structure of national parks. Taking the national parks in the Central Region of China as research objects, this study applies the modified gravity model to measure the strength of tourism economic connection. The social network analysis method (SNA) is used to analyze the network structure of tourism economic connection among national parks from the perspectives of overall network density, network centrality, and cohesive subgroups. The results show that the intensity of the tourism relationships among national parks in Central China is unbalanced in spatial distribution. The structure of tourism economic network presents a multi-core model. Lushan Mountain, Shaoshan, Wudang Mountain, and other national parks play a necessary role in the transmission of regional tourism economic elements. There are cohesive subgroups of connections among national parks, which are closely related to administrative divisions and regional cultural background. The subgroups of interior scenes in the same province are more closely related, and the degree of tourism integration still needs to be improved. The study advances the understanding of tourism economic network relationships among tourist attractions in a destination.

Cosmic voids in modified gravity models with massive neutrinos

ABSTRACT Cosmic voids are progressively emerging as a new viable cosmological probe. Their abundance and density profiles are sensitive to modifications of gravity, as well as to dark energy and neutrinos. The main goal of this work is to investigate the possibility of exploiting cosmic void statistics to disentangle the degeneracies resulting from a proper combination of f(R) modified gravity and neutrino mass. We use N-body simulations to analyse the density profiles and size function of voids traced by both dark matter particles and haloes. We find clear evidence of the enhancement of gravity in f(R) cosmologies in the void density profiles at z = 1. However, these effects can be almost completely overridden by the presence of massive neutrinos because of their thermal free streaming. Despite the limited volume of the analysed simulations does not allow us to achieve a statistically relevant abundance of voids larger than 40 Mpc h−1, we find that the void size function at high redshifts and for large voids is potentially an effective probe to disentangle these degenerate cosmological models, which is key in the prospective of the upcoming wide-field redshift surveys.

Is there any measurable redshift dependence on the SN Ia absolute magnitude?

We test the cosmological implications of a varying absolute magnitude of Type Ia supernovae using the Pantheon compilation, by reconstructing different phenomenological approaches that could justify a varying absolute magnitude, but also approaches based on cosmic voids, modified gravity models and a binning scheme. In all the cases considered in this work, we find good agreement with the expected values of the standard ΛCDM model and no evidence of new physics.

Nonlinear cosmological structure with ultralight bosons via modified gravity

Ultra-light bosons as dark matter has become a model of major interest in Cosmology, due to the possible imprint of a distinct signature in the cosmic structure both at the linear and non-linear scales. In this work we show that the equations of motion for density perturbations for this kind of models can be written in terms of a modified gravitational potential. Taking advantage of this parallelism, we use the MG-PICOLA code originally developed for modified gravity models to evolve the density field of axion models with and without self-interaction. Our results indicate that the quantum potential adds extra suppression of power at the non-linear level, and it is even capable of smoothing any bumpy features initially present in the mass power spectrum.

Analysis on the Housing Price Relationship Network of Large and Medium-Sized Cities in China Based on Gravity Model

The relationship among cities is getting closer, so are housing prices. Based on the sale price of stocking houses in thirty-five large and medium-sized cities in China from 2010 to 2021, this study established the modified gravity model and used the method of social network analysis to explore the spatial linkage of urban housing prices. The results show that: (1) from the overall network structure, the integration degree of housing price network in China is still at a low stage, and the influence of housing price is polarized; (2) from the individual network structure, Beijing, Shanghai, Shenzhen, Nanjing, Hangzhou, and Hefei have a higher degree of centrality. Chengdu, Xining, Kunming, Urumqi, and Lanzhou stay in an isolation position every year; (3) from the results of cohesive subgroup analysis, different cities play different roles in the block each year and have different influences on other cities. (4) Emergencies, such as outbreaks of COVID-19, also have an impact on the housing price network. Structural divergence among urban housing prices has become more pronounced, and the diversity of house price network has been somewhat reduced. Based on the above findings, this paper puts forward some recommendations for the healthy development of housing market from the perspective of housing price network.

Testing F(R) Gravity with the Simulated Data of Gravitational Waves from the Einstein Telescope

Abstract In this paper we analyze the implications of gravitational waves (GWs) as standard sirens on the modified gravity models by using the third-generation GW detector, i.e., the Einstein Telescope. Two viable models in f(R) theories within the Palatini formalism are considered in our analysis ( and ), with the combination of simulated GW data and the latest electromagnetic (EM) observational data (including the recently released Pantheon type Ia supernovae sample, the cosmic chronometer data, and baryon acoustic oscillation distance measurements). Our analysis reveals that the standard siren GWs, which provide an independent and complementary alternative to current experiments, could effectively eliminate the degeneracies among parameters in the two modified gravity models. In addition, we thoroughly investigate the nature of geometrical dark energy in the modified gravity theories with the assistance of Om(z) and statefinder diagnostic analysis. The present analysis makes it clear-cut that the simplest cosmological constant model is still the most preferred by the current data. However, the combination of future naturally improved GW data and the most recent EM observations will reveal the consistency or acknowledge the tension between the ΛCDM model and modified gravity theories.

Baryonic Tully–Fisher Test of Grumiller’s Modified Gravity Model

We test the Grumiller's quantum motivated modified gravity model, which at large distances modifies the Newtonian potential and describes the galactic rotation curves of disk galaxies in terms of a Rindler acceleration term without the need of any dark matter, against the baryonic Tully-Fisher feature that relates the total baryonic mass of a galaxy with flat rotation velocity of the galaxy. We estimate the Rindler acceleration parameter from observed baryonic mass versus rotation velocity data of a sample of sixty galaxies. Grumiller's model is found to describe the observed data reasonably well.

Generalized unimodular gravity as a new form of k -essence

We consider modifications of general relativity characterized by a special noncovariant constraint on metric coefficients, which effectively generates a perfect-fluid type of matter stress tensor in Einstein equations. Such class of modified gravity models includes recently suggested generalized unimodular gravity (GUMG), its simplest version---unimodular gravity---and self-gravitating media theories. We make these gravity models covariant by introducing four Stueckelberg fields and show that in the case of generalized unimodular gravity three out of these fields dynamically decouple. This means that the covariant form of generalized unimodular gravity is dynamically equivalent a special form of $k$-essence theory with translationally noninvariant kinetic term in the Lagrangian which can be reconstructed from the parameters of GUMG theory. We provide the examples, where such reconstruction can be done explicitly, and briefly discuss theories beyond GUMG, related to self-gravitating media models. Also we compare GUMG $k$ inflation with cuscuton models of dynamically inert $k$-essence field and discuss motivation for GUMG coming from effective field theory.