Viable modifications of gravity on cosmological scales predominantly rely on screening mechanisms to recover Einstein's Theory of General Relativity in the Solar System, where it has been well tested. A parametrisation of the effects of such modifications in the spherical collapse model is presented here for the use of modelling the modified nonlinear cosmological structure. The formalism allows an embedding of the different screening mechanisms operating in scalar-tensor theories through large values of the gravitational potential or its first or second derivatives as well as of linear suppression effects or more general transitions between modified and Einstein gravity limits. Each screening or suppression mechanism is parametrised by a time, mass, and environment dependent screening scale, an effective modified gravitational coupling in the fully unscreened limit that can be matched to linear theory, the exponent of a power-law radial profile of the screened coupling, determined by derivatives, symmetries, and potentials in the scalar field equation, and an interpolation rate between the screened and unscreened limits. Along with generalised perturbative methods, the parametrisation may be used to formulate a nonlinear extension to the linear parametrised post-Friedmannian framework to enable generalised tests of gravity with the wealth of observations from the nonlinear cosmological regime.
We use a kinematic parametrisation of the luminosity distance to measure the angular distribution on the sky of time derivatives of the scale factor, in particular the Hubble parameter H_0, the deceleration parameter q_0, and the jerk parameter j_0. We apply a recently published method to complement probing the inhomogeneity of the large-scale structure by means of the inhomogeneity in the cosmic expansion. This parametrisation is independent of the cosmological equation of state, which renders it adequate to test interpretations of the cosmic acceleration alternative to the cosmological const…
Next generation surveys will observe the large-scale structure of the Universe with unprecedented accuracy. This will enable us to test the relationships between matter over-densities, the curvature perturbation and the Newtonian potential. Any large-distance modification of gravity or exotic nature of dark energy modifies these relationships as compared to those predicted in the standard smooth dark energy model based on General Relativity. In linear theory of structure growth such modifications are often parameterised by virtue of two functions of space and time that enter the relation of th…
We present new cosmological parameter constraints for general Horndeski scalar-tensor theories, using CMB, redshift space distortion, matter power spectrum and BAO measurements from the Planck, SDSS/BOSS and 6dF surveys. We focus on theories with cosmological gravitational waves propagating at the speed of light, $c_{\rm GW} = c$, implementing and discussing several previously unaccounted for aspects in the constraint derivation for such theories, that qualitatively affect the resulting constraints. In order to ensure our conclusions are robust, we compare results for three different parametri…
The growing wealth of cosmological observations places increasingly more stringent constraints on dark energy and alternative gravity models. Particularly successful in efficiently probing the vast model space has been the effective field theory of dark energy and modified gravity, providing a unified framework for generalised cosmological predictions. However, the optimal parametrisation of the free time-dependent functions inherent to the formalism is still unresolved. It should respect a multitude of requirements, ranging from simplicity, generality, and representativity of known theories t…
Model-independent parametrisations of modified gravity have attracted a lot of attention over the past few years; numerous combinations of experiments and observables have been suggested to constrain these parameterisations, and future surveys look very promising. Galaxy Clusters have been mentioned, but not looked at as extensively in the literature as some other probes. Here we look at adding Galaxy Clusters into the mix of observables and examine whether they could improve the constraints on the modified gravity parameters. In particular, we forecast the constraints from combining the Planc…
The spectrograph ESPRESSO recently obtained a limit on the variation of the fine-structure constant, $α$, through measurements along the line of sight of a bright quasar with a precision of $1.36$ ppm at $1σ$ level. This imposes new constraints on cosmological models with a varying $α$. We assume such a model where the electromagnetic sector is coupled to a scalar field dark energy responsible for the current acceleration of the Universe. We parametrise the variation of $α$ with two extra parameters, one defining the cosmological evolution of the quintessence component and the other fixing the…
Model-independent parametrisations of modified gravity have attracted a lot of attention over the past few years and numerous combinations of experiments and observables have been suggested to constrain the parameters used in these models. Galaxy clusters have been mentioned, but not looked at as extensively in the literature as some other probes. Here we look at adding galaxy clusters into the mix of observables and examine how they could improve the constraints on the modified gravity parameters. In particular, we forecast the constraints from combining Planck satellite Cosmic Microwave Back…
We embed linear and nonlinear parametrisations of beyond standard cosmological physics in the halo model reaction framework, providing a model-independent prescription for the nonlinear matter power spectrum. As an application, we focus on Horndeski theories, using the Effective Field Theory of Dark Energy (EFTofDE) to parameterise linear and quasi-nonlinear perturbations. In the nonlinear regime we investigate both a nonlinear parameterised-post Friedmannian (nPPF) approach as well as a physically motivated and approximate phenomenological model based on the error function (Erf). We compare t…
We consider the possibility of generalizing the Newtonian law of gravity and the transition to a general relativistic model for weak fields with the inclusion of a repulsive term identified as a cosmological constant. The analysis includes that of the test particle's motion in a modified gravitational field of the Hilbert metric and then the problem of the reverse transition from the post-Galilean case to the construction of a modified exact point mass metric which includes the $Λ$-term.
Cosmological solutions derived by Nariai and Tomita (1971) and by Starobinsky (1980) are compared, and it is shown that the former derived de Sitter expansion in the R^2 modified gravity (without cosmological constant) at the earliest stage, and nine years later the latter derived the well-known inflationary solution. Next the property of their simplified models is described using the method of conformal transformations, and how the inflation arises and the singularity is avoided is shown. Finally the initial and final states of the inflation are discussed.
We present a general approach for modelling the small-scale suppression in the linear matter power spectrum induced by the presence of non-cold dark matter. We show that the new parametrisation accurately describes a large variety of non-thermal scenarios, removing the need to individually test each of them. We discuss the first astrophysical constraints on its free parameters and we outline the next steps for pursuing a full statistical data analysis.
New corrections to General Relativity are considered in the context of modified $f(R)$ gravity, that satisfy cosmological and local gravity constraints. The proposed models behave asymptotically as $R-2Λ$ at large curvature and show the vanishing of the cosmological constant at the flat spacetime limit. The chameleon mechanism and thin shell restrictions for local systems were analyzed, and bounds on the models were found. The steepness of the deviation parameter $m$ at late times leads to measurable signal of scalar-tensor regime in matter perturbations, that allows to detect departures form …
The Generalized Uncertainty Principle (GUP) has emerged in numerous attempts to a theory of quantum gravity and predicts the existence of a minimum length in Nature. In this work, we consider two cosmological models arising from Friedmann equations modified by the GUP (in its linear and quadratic formulations) and compare them with observational data. Our aim is to derive constraints on the GUP parameter and discuss the viability and physical implications of such models. We find for the parameter in the quadratic formulation the constraint $α^{2}_{Q}<10^{59}$ (tighter than most of those obtain…
Deviations from the standard $Λ$CDM model motivate an interpretation of early universe cosmology using the Scalar-Tensor-Vector-Gravity (STVG) theory. A constraint analysis carried out by Valentino, Melchiorri and Silk, revealed deviations from the growth of structure predicted by General Relativity, and a lensing anomaly in the angular CMB power spectrum data. The modified gravity (MOG) theory resolves the lensing deviation from the standard model and provides an explanation of the CMB and structure growth data.
Modified Gravity (MOG) has been used successfully to explain the rotation curves of galaxies, the motion of galaxy clusters, the Bullet Cluster, and cosmological observations without the use of dark matter or Einstein's cosmological constant. We review the main theoretical ideas and applications of the theory to astrophysical and cosmological data.
Recently we have derived a set of mapping relations that enables the reconstruction of the family of Horndeski scalar-tensor theories which reproduce the background dynamics and linear perturbations of a given set of effective field theory of dark energy coefficients. In this paper we present a number of applications of this reconstruction. We examine the form of the underlying theories behind different phenomenological parameterizations of modified gravity and dark energy used in the literature, as well as examine theories that exhibit weak gravity, linear shielding, and minimal self-accelera…
This thesis investigates a toy model for inflation in a class of modified theories of gravity in the metric formalism. Instead of the standard procedure -- assuming a non-linear Lagrangian $f(R)$ in the Jordan frame -- we start from a simple ϕ^2 potential in the Einstein frame and investigate the corresponding $f(R)$ in the former picture. Such approach yields plenty of new pieces of information, namely a self-terminating inflationary solution with a linear Lagrangian, a robust criterion for stability of such theories, a dynamical effective potential for the Ricci scalar $R$, the addition of a…
The one-loop effective action for non-minimal scalar modified gravity on de Sitter background with a constant scalar field is found. The corresponding induced cosmological constant is evaluated. It is shown that quantum effects in non-minimal modified gravity may induce an early-time de Sitter universe even in the situation when such solution does not occur on the classical level. Classical reconstruction of the theory is presented in such a way that the resulting theory has a cosmological solution unifying early-time inflation with late-time acceleration.
The cosmological phenomenology of gravity is typically studied in two limits: relativistic perturbation theory (on large scales) and Newtonian gravity (required for smaller, non-linear, scales). Traditional approaches to model-independent modified gravity are based on perturbation theory, so do not apply on non-linear scales. Future surveys such as Euclid will produce significant data on both linear and non-linear scales, so a new approach is required to constrain model-independent modified gravity by simultaneously using all of the data from these surveys. We use the higher order equations fr…
This article deals with the study of Bianchi type-I universe in the context of f(R,T) gravity. Einstein's field equations in f(R,T) gravity has been solved in presence of cosmological constant ? and quadratic equation of state. Here we have discussed two classes of f(R,T) gravity i.e. f(R,T) = R + 2f(T) and f(R,T) = f_1(R) + f_2(T). A set of models has been taken into consideration based on the plausible relation. Also we have studied the some physical and kinematical properties of the models.
A general nonperturvative loop quantization procedure for metric modified gravity is reviewed. As an example, this procedure is applied to scalar-tensor theories of gravity. The quantum kinematical framework of these theories is rigorously constructed. Both the Hamiltonian and master constraint operators are well defined and proposed to represent quantum dynamics of scalar-tensor theories. As an application to models, we set up the basic structure of loop quantum Brans-Dicke cosmology. The effective dynamical equations of loop quantum Brans-Dicke cosmology are also obtained, which lay a founda…
We consider some cosmological aspects of nonlocal modified gravity with $Λ$ term, where nonlocality is of the type $R \mathcal{F}(\Box) R$. Using ansatz of the form $\Box R = r R +s,$ we find a few a(t) nonsingular bounce cosmological solutions for all three values of spatial curvature parameter k. We also discuss this modified gravity model from F(R) theory point of view.
Screened modified gravity (SMG) is a kind of scalar-tensor theories with screening mechanisms, which can generate screening effect to suppress the fifth force in high density environments and pass the solar system tests. Meanwhile, the potential of scalar field in the theories can drive the acceleration of the late universe. In this paper, we calculate the parameterized post-Newtonian (PPN) parameters $γ$ and $β$, the effective gravitational constant $G_{\rm eff}$ and the effective cosmological constant $Λ$ for SMG with a general potential $V$ and coupling function $A$. The dependence of these…
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 pote…
We investigate the cosmological and the local tests of the f(R) theory of modified gravity via the observations of (1) the cosmic expansion and (2) the cosmic structures and via (3) the solar-system experiments. To fit the possible cosmic expansion histories under consideration, for each of them we reconstruct f(R), known as "designer f(R)". We then test the designer f(R) via the cosmic-structure constraints on the metric perturbation ratio Psi/Phi and the effective gravitational coupling G_eff and via the solar-system constraints on the Brans-Dicke theory with the chameleon mechanism. We find…
Model-independent constraints on modified gravity models hitherto exist mainly on linear scales. A recently developed formalism presented a consistent parameterisation that is valid on all scales. 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 f…
Versions of parameterized pseudo-Newtonian gravity theories specially designed for cosmology have been introduced in recent cosmology literature. The modifications demand a zero-pressure fluid in the context of versions of modified Poisson-like equation with two different gravitational potentials. We consider such modifications in the context of relativistic gravity theories where the action is a general algebraic function of the scalar curvature, the scalar field, and the kinetic term of the field. In general it is not possible to isolate the zero-pressure fluid component simultaneously deman…
We present $\texttt{MG-evolution}$, an $N$-body code simulating the cosmological structure formation for parametrised modifications of gravity. It is built from the combination of parametrised linear theory with a parametrisation of the deeply nonlinear cosmological regime extrapolated from modified spherical collapse computations that cover the range of known screening mechanisms. We test $\texttt {MG-evolution}$, which runs at the speed of conventional $Λ$CDM simulations, against a suit of existing exact model-specific codes, encompassing linearised and chameleon $f(R)$ gravity as well as th…
We explore the cosmological implications of five modified gravity (MG) models by using the recent cosmological observational data, including the recently released SNLS3 type Ia supernovae sample, the cosmic microwave background anisotropy data from the Wilkinson Microwave Anisotropy Probe 7-yr observations, the baryon acoustic oscillation results from the Sloan Digital Sky Survey data release 7, and the latest Hubble constant measurement utilizing the Wide Field Camera 3 on the Hubble Space Telescope. The MG models considered include the Dvali-Gabadadze-Porrati(DGP) model, two $f(R)$ models, a…
Model-independent parametrisations for examining departures from General Relativity have been increasingly studied over the past few years. Various observables have been used to constrain the parameters and forecasts for future surveys have been carried out. In one such forecast, galaxy cluster counts were used to constrain the parameters. Here, we carry out a limited set of $N$-body simulations, with a modified Poisson equation, to examine the accuracy of existing mass functions for modified gravity cosmologies. As well as altering the gravitational calculation, we include the effect of a scr…
As an alternative to the LCDM concordance model, Scalar-Tensor-Vector Modified Gravity (MOG) theory reproduces key cosmological observations without postulating the presence of an exotic dark matter component. MOG is a field theory based on an action principle, with a variable gravitational constant and a repulsive vector field with variable range. MOG yields a phenomenological acceleration law that includes strong tensorial gravity partially canceled by a repulsive massive vector force. This acceleration law can be used to model the CMB acoustic spectrum and the matter power spectrum yielding…
In this paper we introduce a new public Einstein-Boltzmann solver, \texttt{MGCLASS II}, built as a modification to the publicly available \texttt{CLASS} code, that allows to obtain cosmological observables for Modified Gravity theories. It implements several commonly used parameterizations of deviations from General Relativity, computing their impact on the growth of structure as well as on the background evolution of the Universe, together with a subset of available alternative theories, still not completely ruled out by observations. \texttt{MGCLASS II} is built in such a way to be compatibl…
Cosmological perturbations are considered in $f(T)$ and in scalar-torsion $f(φ)T$ teleparallel models of gravity. Full sets of linear perturbation equations are accurately derived and analysed at the relevant limits. Interesting features of generalisations to other teleparallel models, spatially curved backgrounds, and rotated tetrads are pointed out.
The clustering ratio $η$, a large-scale structure observable originally designed to constrain the shape of the power spectrum of matter density fluctuations, is shown to provide a sensitive probe of the nature of gravity in the cosmological regime. We apply this analysis to $F(R)$ theories of gravity using the luminous red galaxy (LRG) sample extracted from the spectroscopic Sloan Digital Sky Survey (SDSS) data release 7 and 10 catalogues. We find that General Relativity (GR), complemented with a Friedmann-Robertson-Walker (FRW) cosmological model with parameters fixed by the Planck satellite,…
Our modified gravity theory (MOG) is a gravitational theory without exotic dark matter, based on an action principle. MOG has been used successfully to model astrophysical phenomena such as galaxy rotation curves, galaxy cluster masses, and lensing. MOG may also be able to account for cosmological observations. We assume that the MOG point source solution can be used to describe extended distributions of matter via an appropriately modified Poisson equation. We use this result to model perturbation growth in MOG and find that it agrees well with the observed matter power spectrum at present. A…
Since the discovery of the accelerated expansion of the present Universe, significant theoretical developments have been made in the area of modified gravity. In the meantime, cosmological observations have been providing more high-quality data, allowing us to explore gravity on cosmological scales. To bridge the recent theoretical developments and observations, we present an overview of a variety of modified theories of gravity and the cosmological observables in the cosmic microwave background and large-scale structure, supplemented with a summary of predictions for cosmological observables …
We revisit Ricci dark energy in Chern-Simons modified gravity. As far as the cosmological evolution, this is nothing but the Ricci dark energy with a minimally coupled scalar without potential which means that the role of Chern-Simons term is suppressed. Using the equation of state parameter, this model is similar to the modified Chaplygin gas model only when two are around the de Sitter universe deriving by the cosmological constant in the future. However, two past evolutions are different.
The cosmological reconstruction scheme for modified $F(R)$ gravity is developed in terms of e-folding (or, redshift). It is demonstrated how any FRW cosmology may emerge from specific $F(R)$ theory. The specific examples of well-known cosmological evolution are reconstructed, including $Λ$CDM cosmology, deceleration with transition to phantom superacceleration era which may develop singularity or be transient. The application of this scheme to viable $F(R)$ gravities unifying inflation with dark energy era is proposed. The additional reconstruction of such models leads to non-leading gravitati…
In this paper we investigate cosmological dynamics on the normal branch of a DGP-inspired scenario within a phase space approach where induced gravity is modified in the spirit of $f(R)$-theories. We apply the dynamical system analysis to achieve the stable solutions of the scenario in the normal DGP branch. Firstly, we consider a general form of the modified induced gravity and we show that there is a standard de Sitter point in phase space of the model. Then we prove that this point is stable attractor only for those $f(R)$ functions that account for late-time cosmic speed-up.
During hundred years of General Relativity (GR), many significant gravitational phenomena have been predicted and discovered. General Relativity is still the best theory of gravity. Nevertheless, some (quantum) theoretical and (astrophysical and cosmological) phenomenological difficulties of modern gravity have been motivation to search more general theory of gravity than GR. As a result, many modifications of GR have been considered. One of promising recent investigations is Nonlocal Modified Gravity. In this article we present a brief review of some nonlocal gravity models with their cosmolo…
We study cosmological constraints on the various accelerating models of the universe using the time evolution of the cosmological redshift of distant sources. The important characteristic of this test is that it directly probes the expansion history of the universe. In this work we analyze the various models of the universe which can explain the late time acceleration, within the framework of General Theory of Relativity (GR) (XCDM, scalar field potentials) and beyond GR (f(R) gravity model).
The quasi-static solutions of the matter density perturbation in various dark energy models and modified gravity models have been investigated in numerous papers. However, the oscillating solutions in those models have not been investigated enough so far. In this paper, the oscillating solutions, which have a possibility to unveil the difference between the models of the late-time accelerated expansion of the Universe, are also mentioned by using appropriate approximations.
Very recently, Verlinde considered a theory in which space is emergent through a holographic scenario, and proposed that gravity can be explained as an entropic force caused by changes in the information associated with the positions of material bodies. Then, motivated by the Debye model in thermodynamics which is very successful in very low temperatures, Gao modified the entropic force scenario. The modified entropic force (MEF) model is in fact a modified gravity model, and the universe can be accelerated without dark energy. In the present work, we consider the cosmological constraints on t…
We present a new massively parallel code for N-body and cosmological hydrodynamical simulations of modified gravity models. The code employs a multigrid-accelerated Newton-Gauss-Seidel relaxation solver on an adaptive mesh to efficiently solve for perturbations in the scalar degree of freedom of the modified gravity model. As this new algorithm is implemented as a module for the P-Gadget3 code, it can at the same time follow the baryonic physics included in P-Gadget3, such as hydrodynamics, radiative cooling and star formation. We demonstrate that the code works reliably by applying it to simp…
Along this review, we focus on the study of several properties of modified gravity theories, in particular on black-hole solutions and its comparison with those solutions in General Relativity, and on Friedmann-Lemaitre-Robertson-Walker metrics. The thermodynamical properties of fourth order gravity theories are also a subject of this investigation with special attention on local and global stability of paradigmatic f(R) models. In addition, we revise some attempts to extend the Cardy-Verlinde formula, including modified gravity, where a relation between entropy bounds is obtained. Moreover, a…
We perform observational tests of modified gravity on cosmological scales following model-dependent and model-independent approaches using the latest astronomical observations, including measurements of the local Hubble constant, cosmic microwave background, the baryonic acoustic oscillations and redshift space distortions derived from galaxy surveys including the SDSS BOSS and eBOSS, as well as the weak lensing observations performed by the CFHTLenS team. Using all data combined, we find a deviation from the prediction of general relativity in both the effective Newton's constant, $μ(a,k)$, a…
We consider modified gravity cosmological models that can be transformed into two-field chiral cosmological models by the conformal metric transformation. For the $R^2$ gravity model with an additional scalar field and the corresponding two-field model with the cosmological constant and nonstandard kinetic part of the action, the general solutions have been obtained in the spatially flat FLRW metric. We analyze the correspondence of the cosmic time solutions obtained and different possible evolutions of the Hubble parameters in the Einstein and Jordan frames.
Recently Horava proposed a renormalizable gravity theory in four dimensions which reduces to Einstein gravity with a non-vanishing cosmological constant in IR but with improved UV behaviors. Here, I study an IR modification which breaks "softly" the detailed balance condition in Horava model and allows the asymptotically flat limit as well. I obtain the black hole and cosmological solutions for "arbitrary" cosmological constant that represent the analogs of the standard Schwartzschild-(A)dS solutions which can be asymptotically (A)dS as well as flat and I discuss some thermodynamical propertie…
This thesis introduces a set of methods for testing models of modified gravity using galaxy clusters. In particular, a technique for constraining models with a chameleon screening is introduced. In addition, the outlined technique is expanded to test a wider class of models, such as the theory of emergent gravity. Finally, the first part of the thesis is concluded by adapting the mentioned tests for model independent constraints. The obtained results indicate that galaxy clusters can be used to obtain some of the most powerful constraints on cosmological scales. The second part of the thesis i…
Cosmological equations were recently derived by Padmanabhan from the expansion of cosmic space due to the difference between the degrees of freedom on the surface and in the bulk in a region of space. In this study, a modified Rényi entropy is applied to Padmanabhan's `holographic equipartition law', by regarding the Bekenstein--Hawking entropy as a nonextensive Tsallis entropy and using a logarithmic formula of the original Rényi entropy. Consequently, the acceleration equation including an extra driving term (such as a time-varying cosmological term) can be derived in a homogeneous, isotropi…
We revisit gauge invariant cosmological perturbations in UV-modified, z = 3 Horava gravity with one scalar matter field, which has been proposed as a renormalizable gravity theory without the ghost problem in four dimensions. We confirm that there is no extra graviton modes and general relativity is recovered in IR, which achieves the consistency of the model. From the UV-modification terms which break the detailed balance condition in UV, we obtain scale-invariant power spectrums for non-inflationary backgrounds, like the power-law expansions, without knowing the details of early expansion hi…
We have found for the general class of Modified Gravity Models f(R,G) a new instability which can arise in vacuum for the scalar modes of the cosmological perturbations if the background is not de Sitter. In particular, the short-wavelength modes, if stable, in general have a group velocity which depends linearly in k, the wave number. Therefore these modes will be in general superluminal. We have also discussed the condition for which in general these scalar modes will be ghost-like. There is a subclass of these models, defined out of properties of the function f(R,G) and to which the f(R) an…
It has been shown recently that the normal branch of a DGP braneworld scenario self-accelerates if the induced gravity on the brane is modified in the spirit of $f(R)$ modified gravity. Within this viewpoint, we investigate cosmological viability of the Hu-Sawicki type modified induced gravity. Firstly, we present a dynamical system analysis of a general $f(R)$-DGP model. We show that in the phase space of the model, there exist three standard critical points; one of which is a de Sitter point corresponding to accelerating phase of the universe expansion. The stability of this point depends on…
In this article we continue to test cosmological models centred on Modified Newtonian Dynamics (MOND) with light sterile neutrinos, which could in principle be a way to solve the fine-tuning problems of the standard model on galaxy scales while preserving successful predictions on larger scales. Due to previous failures of the simple MOND cosmological model, here we test a speculative model where the modified gravitational field is produced only by the baryons and the sterile neutrinos produce a purely Newtonian field (hence Modified Baryonic Dynamics). We use two component cosmological simula…
