We study the growth of matter density perturbations delta_m for a number of viable f(R) gravity models that satisfy both cosmological and local gravity constraints, where the Lagrangian density f is a function of the Ricci scalar R. If the parameter m=Rf_{,RR}/f_{,R} today is larger than the order of 10^{-6}, linear perturbations relevant to the matter power spectrum evolve with a growth rate s=d (ln delta_m)/d (ln a) (a is the scale factor) that is larger than in the LCDM model. We find the window in the free parameter space of our models for which spatial dispersion of the growth index gamma_0= gamma(z=0) (z is the redshift) appears in the range of values 0.40< gamma_0<0.55, as well as the region in parameter space for which there is essentially no dispersion and gamma_0 converges to values around 0.40<gamma_0<0.43. These latter values are much lower than in the LCDM model. We show that these unusual dispersed or converged spectra are present in most of the viable f(R) models with m(z=0) larger than the order of 10^{-6}. These properties will be essential in the quest for f(R) modified gravity models using future high-precision observations and they confirm the possibility to distinguish clearly most of these models from the LCDM model.
A probability of distinguishing between $Λ$CDM model and modified gravity is studied by using the future observations for the growth rate of cosmic structure (Euclid redshift survey). Adopting extended DGP model, Kinetic Gravity Braiding model, and Galileon model as modified gravity, we compare predicted cosmic growth rate by models to the mock observational data. The growth rate $fσ_8$ in the original DGP model is suppressed compared with the $Λ$CDM case, for the same value of the current density parameter of matter $Ω_{m,0}$, because of the suppression of effective gravitational constant. In…
We calculate the spectrum of the relic gravitational wave due to the trans-Planckian effect in which the standard linear dispersion relations may be modified. Of the modified dispersion relations suggested in literatures which have investigated the trans-Planckian effect, we especially use the Corley-Jacobson dispersion relations. The Corley-Jacobson type modified dispersion relations can be obtained from Hořava-Lifshitz gravity which is non-relativistic and UV complete. Although it is not clear how the transitions from Hořava-Lifshitz gravity in the UV regime to Einstein gravity in the IR lim…
We discuss the prospects for bounding and perhaps even measuring quantum gravity effects on the dispersion of light using the highest energy photons produced in gamma ray bursts measured by the Fermi telescope. These prospects are brigher than might have been expected as in the first 10 months of operation Fermi has reported so far eight events with photons over 100 MeV seen by its Large Area Telescope (LAT). We review features of these events which may bear on Planck scale phenomenology and we discuss the possible implications for the alternative scenarios for in-vacua dispersion coming from …
We compare observational data of growth rate with the prediction by Galileon theory. For the same value of the energy density parameter $Ω_{m,0}$, the growth rate in Galileon models is enhanced compared with the $Λ$CDM case, due to the enhancement of Newton's constant. The smaller $Ω_{m,0}$ is, the more suppressed growth rate is. Hence the best fit value of $Ω_{m,0}$ in the Galileon model is 0.16 from only the growth rate data, which is considerably smaller than such value obtained from observations of supernovae Ia, the cosmic microwave background and baryon acoustic oscillations. This result…
We provide for the first time the growth index of linear matter fluctuations of the power law $f(T) \propto (-T)^{b}$ gravity model. We find that the asymptotic form of this particular $f(T)$ model is $γ\approx \frac{6}{11-6b}$ which obviously extends that of the $Λ$CDM model, $γ_Λ\approx 6/11$. Finally, we generalize the growth index analysis of $f(T)$ gravity in the case where $γ$ is allowed to vary with redshift.
We perform cosmological perturbation theory in Hassan-Rosen bimetric gravity for general homogeneous and isotropic backgrounds. In the de Sitter approximation, we obtain decoupled sets of massless and massive scalar gravitational fluctuations. Matter perturbations then evolve like in Einstein gravity. We perturb the future de Sitter regime by the ratio of matter to dark energy, producing quasi-de Sitter space. In this more general setting the massive and massless fluctuations mix. We argue that in the quasi-de Sitter regime, the growth of structure in bimetric gravity differs from that of Eins…
We propose a scale dependent analytic approximation to the exact linear growth of density perturbations in Scalar-Tensor (ST) cosmologies. In particular, we show that on large subhorizon scales, in the Newtonian gauge, the usual scale independent subhorizon growth equation does not describe the growth of perturbations accurately, as a result of scale-dependent relativistic corrections to the Poisson equation. A comparison with exact linear numerical analysis indicates that our approximation is a significant improvement over the standard subhorizon scale independent result on large subhorizon s…
We place tight constraints on the growth index $γ$ by using the recent growth history results of 2dFGRS, SDSS-LRG, VIMOS-VLT deep Survey (VVDS) and {\em WiggleZ} datasets. In particular, we investigate several parametrizations of the growth index $γ(z)$, by comparing their cosmological evolution using observational growth rate data at different redshifts. Utilizing a standard likelihood analysis we find that the use of the combined growth data provided by the 2dFGRS, SDSS-LRG, VVDS and {\em WiggleZ} galaxy surveys, puts the most stringent constraints on the value of the growth index. As an exa…
We consider the linear growth of matter perturbations on low redshifts in modified gravity Dark Energy (DE) models where G_eff(z,k) is explicitly scale-dependent. Dispersion in the growth today will only appear for scales of the order the critical scale ~ λ_{c,0}, the range of the fifth-force today. We generalize the constraint equation satisfied by the parameters γ_0(k) and γ'_0(k) \equiv \frac{dγ(z,k)}{dz}(z=0) to models with G_{eff,0}(k) \ne G. Measurement of γ_0(k) and γ'_0(k) on several scales can provide information about λ_{c,0}. In the absence of dispersion when λ_{c,0} is large compar…
It is possible to dualize theories based on deformed dispersion relations and Einstein gravity so as to map them into theories with trivial dispersion relations and rainbow gravity. This often leads to "dual inflation" without the usual breaking of the strong energy condition. We identify the dispersion relations in the original frame which map into "intermediate" inflationary models. These turn out to be particularly simple: power-laws modulated by powers of a logarithm. The fluctuations predicted by these scenarios are near, but not exactly scale-invariant, with a red running spectral index.…
We test Einstein gravity using cosmological observations of both expansion and structure growth, including the latest data from supernovae (Union2.1), CMB (WMAP7), weak lensing (CFHTLS) and peculiar velocity of galaxies (WiggleZ). We fit modified gravity parameters of the generalized Poisson equations simultaneously with the effective equation of state for the background evolution, exploring the covariances and model dependence. The results show that general relativity is a good fit to the combined data. Using a Pad{é} approximant form for the gravity deviations accurately captures the time an…
Recent observations of ultra-dwarf galaxy NGC1052-DF2 started an interesting discussion between dark matter hypothesis and modified gravity theories. Reported low velocity dispersion (< 10.5 km/s at 90% confidence level) derived from the kinematic data of 10 globular clusters in the galaxy points towards an extraordinarily low dynamical mass ($\sim$ $3.4 \times 10^{8} M_{\odot}$) which is of the same order of the luminous mass ($\sim$ $2.0 \times 10^{8} M_{\odot}$) in the galaxy. This has been interpreted as the first evidence of a galaxy `without Dark Matter'. It has been argued that dark mat…
Various approaches to quantum gravity such as string theory, loop quantum gravity and Horava-Lifshitz gravity predict modifications of the energy-momentum dispersion relation. Magueijo and Smolin incorporated the modified dispersion relation (MDR) with the general theory of relativity to yield a theory of gravity's rainbow. In this paper, we investigate the Schwarzschild metric in the context of gravity's rainbow. We investigate rainbow functions from three known modified dispersion relations that were introduced by Amelino-Camelia, et el. in [arXiv:hep-th/9605211, arXiv:0806.0339v2, arXiv:ast…
We studied the cosmological constraints on the Galileon gravity obtained from observational data of the growth rate of matter density perturbations, the supernovae Ia (SN Ia), the cosmic microwave background (CMB), and baryon acoustic oscillations (BAO). For the same value of the energy density parameter of matter $Ω_{m,0}$, the growth rate $f$ in Galileon models is enhanced, relative to the $Λ$CDM case, because of an increase in Newton's constant. The smaller $Ω_{m,0}$ is, the more growth rate is suppressed. Therefore, the best fit value of $Ω_{m,0}$ in the Galileon model, based only the grow…
We study background dynamics and the growth of matter perturbations in the extended quasidilaton setup of massive gravity. For the analysis of perturbations, we first choose a scalar field matter component and obtain the conditions under which all scalar perturbations are stable. We work in unitary gauge for the matter field, which allows us to directly map to known results in the limit of general relativity. By performing a parameter search, we find that the perturbations are unstable in general, while a particular choice of potential, where the scalar field effectively behaves like pressurel…
We derive the evolution equation of growth factor for the matter over-dense perturbation in $f(T)$ gravity. For instance, we investigate its behavior in power law model at small redshift and compare it to the prediction of $Λ$CDM and dark energy with the same equation of state in the framework of Einstein general relativity. We find that the perturbation in $f(T)$ gravity grows slower than that in Einstein general relativity if $\p f/\p T>0$ due to the effectively weakened gravity.
In the present paper, we investigate the linear growth of matter fluctuations based on a concrete model of the projected massive gravity, which is free of the Boulware-Deser ghost and preserves the global Lorentz symmetry. We found that at subhorizon scales, the modification to the linear growth is strongly suppressed even without nonlinear screening of an additional force. In addition, we obtain observational constraints from distance and redshift space distortion measurements and find that there is a parameter region that is consistent both observationally and theoretically.
The present work is related to anisotropic cosmological evolution in metric $f(R)$ theory of gravity. The initial part of the paper develops the general cosmological dynamics of homogeneous anisotropic Bianchi-I spacetime in $f(R)$ cosmology. The anisotropic spacetime is pervaded by a barotropic fluid which has isotropic pressure. The paper predicts nonlinear growth of anisotropy in such spacetimes. In the later part of the paper we display the predictive power of the nonlinear differential equation responsible for the cosmological anisotropy growth in various relevant cases. We present the ex…
We introduce a cosmological model in the framework of Generalised Massive Gravity. This theory is an extension of non-linear massive gravity with a broken translation symmetry in the Stückelberg space. In a recent work, we showed the existence of cosmological solutions stable against linear perturbations. In the present paper, we build up on the previous result and study the evolution of the background solutions and the linear perturbations. At the background level, we find that the mass terms act like a fluid with time dependent equation of state $w < -1$ at late times. At linear order, we de…
Using redshift space distortion data, we perform model-independent reconstructions of the growth history of matter inhomogeneity in the expanding Universe using two methods: crossing statistics and Gaussian processes. We then reconstruct the corresponding history of the Universe background expansion and fit it to type Ia supernovae data, putting constraints on $(Ω_\mathrm{m,0},σ_{8,0})$. The results obtained are consistent with the concordance flat-$Λ$CDM model and General Relativity as the gravity theory given the current quality of the inhomogeneity growth data.
We present Keck LRIS spectroscopy for a sample of 103 massive galaxies with redshifts 0.9 < z < 1.6. Of these, 56 are quiescent with high signal-to-noise absorption line spectra, enabling us to determine robust stellar velocity dispersions for the largest sample yet available beyond a redshift of 1. Together with effective radii measured from deep Hubble Space Telescope images, we calculate dynamical masses and address key questions relating to the puzzling size growth of quiescent galaxies over 0 < z < 2. We examine the relationship between stellar and dynamical masses at high redshift, findi…
We present a general parallelized and easy-to-use code to perform numerical simulations of structure formation using the COLA (COmoving Lagrangian Acceleration) method for cosmological models that exhibit scale-dependent growth at the level of first and second order Lagrangian perturbation theory. For modified gravity theories we also include screening using a fast approximate method that covers all the main examples of screening mechanisms in the literature. We test the code by comparing it to full simulations of two popular modified gravity models, namely $f(R)$ gravity and nDGP, and find go…
We re-analyze the nonlocal gravity model of Deser and Woodard which was proposed to account for the current phase of cosmic acceleration. We show that the growth of perturbations predicted by this nonlocal gravity model when its background evolution is fixed by some particular non-$Λ$CDM models can be substantially lower than when its background is fixed by $Λ$CDM. This can be seen when we consider the background expansion by a dark energy model with a slightly less negative equation of state with respect to cosmological constant. Our results hints towards a fact that the choice of the backgro…
The Sloan Digital Sky Survey (SDSS) provides data on several hundred thousand galaxies. Precise location of these galaxies in the sky, along with information about their luminosities and line-of-sight (Doppler) velocities allows one to construct a three-dimensional map of their location and estimate their line-of-sight velocity dispersion. This information, in principle, allows one to test dynamical gravity models, specifically models of satellite galaxy velocity dispersions near massive hosts. A key difficulty is the separation of true satellites from interlopers. We sidestep this problem by …
Adding to our previous method for dealing with gravitational modifications at redshift $z\gtrsim3$ through a single parameter, we investigate treatment of lower redshift modifications to linear growth observables. We establish subpercent accurate fits to the redshift space distortion observable $fσ_8(a)$ using two parameters binned in redshift, testing the results for modifications with time dependence that rises, falls, is nonmonotonic, is multipeaked, and corresponds to $f(R)$ and braneworld gravity. The residuals are then propagated to cosmological parameter biases for DESI observations, an…
This study is devoted to the implications of scale-dependent gravity in Cosmology. Redshift-space distortion data indicate that there is a tension between $Λ$CDM and available observations as far as the value of the rms density fluctuation, $σ_8$, is concerned. It has been pointed out that this tension may be alleviated in alternative theories in which gravity is weaker at red-shift $z \sim 1$. We study the evolution of density perturbations for non-relativistic matter on top of a spatially flat FLRW Universe, and we compute the combination $A=f σ_8$ in the framework of scale-dependent gravity…
In this work, I present for the first time the analysis concerning the growth of matter fluctuations in the framework of $f(R,T)$ modified gravity where I presume $f(R,T) = R + λT$, where $R$ denote the Ricci scalar, $T$ the trace of the energy-momentum tensor and $λ$ a constant. I first solve the Friedman equations assuming a dust universe ($ω=0$) for the Hubble parameter $H(z)$ and then employ it in the equation of matter density fluctuations $δ(z)$ to solve for $δ(z)$ and the growth rate $f(z)$. Next, I proceed to show the behavior of $f(z)$ and $δ(z)$ with redshift for some values of $λ$ w…
Cosmic growth of large scale structure probes the entire history of cosmic expansion and gravitational coupling. To get a clear picture of the effects of modification of gravity we consider a deviation in the coupling strength (effective Newton's constant) at different redshifts, with different durations and amplitudes. We derive, analytically and numerically, the impact on the growth rate and growth amplitude. Galaxy redshift surveys can measure a product of these through redshift space distortions and we connect the modified gravity to the observable in a way that may provide a useful parame…
Future 21 cm intensity mapping surveys such as SKA can provide precise information on the spatial distribution of the neutral hydrogen (HI) in the post-reionization epoch. This information will allow to test the standard LCDM paradigm and with that the nature of gravity. In this work, we employ the SHYBONE simulations, which model galaxy formation in f(R) modified gravity using the IllustrisTNG model, to study the effects of modified gravity on HI abundance and power spectra. We find that the enhanced growth low-mass dark matter halos experience in f(R) gravity at high redshifts alters the HI …
In this work, we use a combined approach of Hubble parameter data together with redshift-space-distortion $(fσ_8)$ data, which together are used to reconstruct the teleparallel gravity (TG) Lagrangian via Gaussian processes (GP). The adopted Hubble data mainly comes from cosmic chronometers, while for the Type Ia supernovae data we use the latest jointly calibrated Pantheon compilation. Moreover, we consider two main GP covariance functions, namely the squared-exponential and Cauchy kernels in order to show consistency (to within 1$σ$ uncertainties). The core results of this work are the numer…
Constraining Scale-Dependent Growth in $f(R)$ Gravity with Future 21 cm Surveys
Indian Institute of Technology Mandi（印度理工学院曼迪分校）；University of Cape Town（开普敦大学）；North-West University（西北大学）；South African Astronomical Observatory（南非天文台）；Duy Tan University（Duy 坦大学）
By relaxing the conventional assumption of a purely gravitational interaction between dark energy and dark matter, substantial alterations to the growth of cosmological structure can occur. In this work we focus on the homogeneous transfer of energy from a decaying form of dark energy. We present simple analytic solutions to the modified growth rates of matter fluctuations in these models, and demonstrate that neglecting physics within the dark sector may induce a significant bias in the inferred growth rate, potentially offering a false signature of modified gravity.
The scatter in the apparent magnitude of type Ia supernovae induced by stochastic gravitational lensing is highly dependent on the nonlinear growth of cosmological structure. In this paper, we show that such a dependence can potentially be employed to gain significant information about the mass clustering at small scales. While the mass clustering ultimately hinges on cosmology, here we demonstrate that, upon obtaining more precise observational measurements through future cosmological surveys, the lensing dispersion can very effectively be used to gain information on the poorly understood ast…
An important piece of evidence for dark matter is the need to explain the growth of structure from the time of horizon entry and radiation-matter equality to the formation of stars and galaxies. This cannot be explained by using general relativity without dark matter. So far, dark matter particles have not been detected in laboratory measurements or at the LHC. We demonstrate that enhanced structure growth can happen in a modified gravity theory (MOG). The vector field and particle introduced in the theory to explain galaxy and cluster dynamics plays an important role in generating the require…
The growth rate of the large-scale structure of the universe has been advocated as the observable par excellence for testing gravity on cosmological scales. By considering linear-order deviations from General Relativity, we show that corrections to the growth rate, f, can be expressed as an integral over a `source' term, weighted by a theory-independent `response kernel'. This leads to an efficient and accurate `plug-and-play' expression for generating growth rates in alternative gravity theories, bypassing lengthy theory-specific computations. We use this approach to explicitly show that f is…
We present a simple fitting formula for the scale-dependent growth rate of Hu-Sawicki model in $f(R)$ modified gravity. We compare the accuracy of the fitting function against numerical results and report achieving a sub-percent maximum error for all different studied cases. The validity of the fitting function is tested against a wide range of scales, $10^{-4} \le k \le 5 \ [\mathrm{Mpc}^{-1}]$ , for various redshift values in the range of $z \in [0.0,\ 3.0]$ and different $|f_R^0|$ values. This formula is useful in producing predictions for cosmological probes that are sensitive to growth ra…
We present numerical calculation of the evolution of a background space-time metric and sub-horizon matter density perturbations in viable $f(R)$ gravity models of present dark energy and cosmic acceleration. We found that viable models generically exhibit recent crossing of the phantom boundary $w_{DE}=-1$. Moreover, as a consequence of the anomalous growth of density perturbations during the end of the matter-dominated stage, their growth index evolves non-monotonically with time and may even become negative.
Measurements of the growth index $γ(z)$ provide a clue as to whether Einstein's field equations encompass gravity also on large cosmic scales, those where the expansion of the universe accelerates. We show that the information encoded in this function can be satisfactorily parameterized using a small set of coefficients $γ_i$ in such a way that the true scaling of the growth index is recovered to better than $1\%$ in most dark energy and dark gravity models. We find that the likelihood of current data is maximal for $γ_0=0.74\pm 0.44$ and $γ_1=0.01\pm0.46$, a measurement compatible with the $Λ…
In 'modified' gravity the observed acceleration of the universe is explained by changing the gravitational force law or the number of degrees of freedom in the gravitational sector. Both possibilities can be tested by measurements of cosmological structure formation. In this paper we elaborate the details of such tests using the Galileon model as a case study. We pay attention to the possibility that each new degree of freedom may have stochastically independent initial conditions, generating different types of potential well in the early universe and breaking complete correlation between dens…
The growth index $γ_L$ was proposed to investigate the possible deviation from the standard $Λ$CDM model and Einstein's gravity theory in a dynamical perspective. Recently, thanks to the measurement of the cosmic growth rate via the redshift-space distortion, one can understand the evolution of density contrast through $fσ_8(z)$, where $f(z)=d\ln δ/d \ln a$ is the growth rate of matter and $σ_8(z)$ is the rms amplitude of the density contrast $δ$ at the comoving $8h^{-1}$ Mpc scale. In this paper, we use the redshift space distortion data points to study the growth index on the bases of Einste…
In this work we study the simultaneous effect of primordial non-Gaussianity and the modification of the gravity in $f(R)$ framework on large scale structure observations. We show that non-Gaussianity and modified gravity introduce a scale dependent bias and growth rate functions. The deviation from $Λ$CDM in the case of primordial non-Gaussian models is in large scales, while the growth rate deviates from $Λ$CDM in small scales for modified gravity theories. We show that the redshift space distortion can be used to distinguish positive and negative $f_{NL}$ in standard background, while in $f(…
We use growth of structure data to constrain the effective field theory of dark energy. Considering as case study Horndeski theories with the speed of gravitational waves equal to that of light, we show how constraints on the free parameters and the large-scale structure phenomenological functions can be improved by two ingredients: firstly by complementing the set of redshift-space distortions data with the three recent measurements of the growth rate $f$ and the amplitude of matter fluctuations $σ_8$ from the VIPERS and SDSS collaborations; secondly by applying a local Solar System bound on …
Redshift space distortions caused by galaxy peculiar velocities provide a window onto the growth rate of large scale structure and a method for testing general relativity. We investigate through a comparison of N-body simulations to various extensions of perturbation theory beyond the linear regime, the robustness of cosmological parameter extraction, including the gravitational growth index, γ. We find that the Kaiser formula and some perturbation theory approaches bias the growth rate by 1-sigma or more relative to the fiducial at scales as large as k > 0.07 h/Mpc. This bias propagates to es…
We perform a validation of estimates of the growth rate of structure, described by the parameter combination $fσ_8$, in modified gravity cosmologies. We consider an analysis pipeline based on the redshift-space distortion modelling of the clustering wedges statistic of the galaxy correlation function and apply it to mock catalogues of $Λ{\rm CDM}$ and the normal branch of DGP cosmologies. We employ a halo occupation distribution approach to construct our mocks, which we ensure resemble the CMASS sample from BOSS in terms of the total galaxy number density and large scale amplitude of the power…
Parameterized frameworks for modified gravity are potentially useful tools for model-independent tests of General Relativity on cosmological scales. The toy model of an Einstein-de Sitter (EdS) universe provides a safe testbed in which to improve our understanding of their behaviour. We implement a mathematically consistent parameterization at the level of the field equations, and use this to calculate the evolution of perturbations in an EdS scenario. Our parameterization explicitly allows for new scalar degrees of freedom, and we compare this to theories in which the only degrees of freedom …
The low-redshift velocity field is a unique probe of the growth of cosmic structure and gravity. We propose to use distances from gravitational wave (GW) detections, in conjunction with the redshifts of their host galaxies from wide field spectroscopic surveys (e.g. DESI, 4MOST, TAIPAN), to measure peculiar motions within the local Universe. Such measurement has the potential to constrain the growth rate $fσ_8$ and test gravity through determination of the gravitational growth index $γ$, complementing constraints from other peculiar velocity measurements. We find that binary neutron star merge…
Searches for modified gravity in the large-scale structure try to detect the enhanced amplitude of density fluctuations caused by the fifth force present in many of these theories. Neutrinos, on the other hand, suppress structure growth below their free-streaming length. Both effects take place on comparable scales, and uncertainty in the neutrino mass leads to a degeneracy with modified gravity parameters for probes that are measuring the amplitude of the matter power spectrum. We explore the possibility to break the degeneracy between modified gravity and neutrino effects in the growth of st…
The dispersion relation of graviton is a fundamental issue for fundamental physics about gravity. In this paper we investigate how the modified dispersion relation of graviton affects the cosmic microwave background (CMB) power spectra, in particular the B-mode polarization. Our results will be useful to test the dispersion relation of graviton at the energy scale around $10^{-29}$ eV.
A class of well-behaved modified gravity models with long enough matter domination epoch and a late-time accelerated expansion is confronted with SNIa, CMB, SDSS, BAO and H(z) galaxy ages data, as well as current measurements of the linear growth of structure. We show that the combination of geometrical probes and growth data exploited here allows to rule out f(R) gravity models, in particular, the logarithmic of curvature model. We also apply solar system tests to the models in agreement with the cosmological data. We find that the exponential of the inverse of the curvature model satisfies a…
