We present the data-driven reconstruction of gravitational theories and Dark Energy models on cosmological scales. We showcase the power of present cosmological probes at constraining these models and quantify the knowledge of their properties that can be acquired through state of the art data. This reconstruction exploits the power of the Effective Field Theory approach to Dark Energy and Modified Gravity phenomenology, which compresses the freedom in defining such models into a finite set of functions that can be reconstructed across cosmic times using cosmological data. We consider several model classes described within this framework and thoroughly discuss their phenomenology and data implications. We find that some models can alleviate the present discrepancy in the determination of the Hubble constant as inferred from the cosmic microwave background and as directly measured. This results in a statistically significant preference for the reconstructed theories over the standard cosmological model.
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…
Recent cosmological observations are in good agreement with the scalar spectral index $n_s$ with $n_s-1\simeq -2/N$, where $N$ is the number of e-foldings. In the previous work, the reconstruction of the inflaton potential for a given $n_s$ was studied, and it was found that for $n_s-1=-2/N$, the potential takes the form of either $α$-attractor model or chaotic inflation model with $ϕ^2$ to the leading order in the slow-roll approximation. Here we consider the reconstruction of $f(R)$ gravity model for a given $n_s$ both in the Einstein frame and in the Jordan frame. We find that for $n_s-1=-2…
We present an Effective Field Theory based reconstruction of quintessence models of dark energy directly from cosmological data. We show that current cosmological data possess enough constraining power to test several quintessence model properties for redshifts $z\in [0,1.5]$ with no assumptions about the behavior of the scalar field potential. We use measurements of the cosmic microwave background, supernovae distances, and the clustering and lensing of galaxies to constrain the evolution of the dark energy equation of state, Swampland Conjectures, the shape of the scalar field reconstructed …
We consider cosmological scenarios based on $f(R,T)$ theories of gravity ($R$ is the Ricci scalar and $T$ is the trace of the energy-momentum tensor) and numerically reconstruct the function $f(R,T)$ which is able to reproduce the same expansion history generated, in the standard General Relativity theory, by dark matter and holographic dark energy. We consider two special $f(R,T)$ models: in the first instance, we investigate the modification $R + 2f(T)$, i.e. the usual Einstein-Hilbert term plus a $f(T)$ correction. In the second instance, we consider a $f(R)+λT$ theory, i.e. a $T$ correctio…
We propose a new reconstruction method for scalar--tensor gravity based on the use of conformal transformations. The new method allows the derivation of a set of interesting exact cosmological solutions in brans Dicke gravity as well as other extensions of General Relativity.
A variant of the accelerating cosmology reconstruction program is developed for $f(R)$ gravity and for a modified Yang-Mills/Maxwell theory. Reconstruction schemes in terms of e-foldings and by using an auxiliary scalar field are developed and carefully compared, for the case of $f(R)$ gravity. An example of a model with a transient phantom behavior without real matter is explicitly discussed in both schemes. Further, the two reconstruction schemes are applied to the more physically interesting case of a Yang-Mills/Maxwell theory, again with explicit examples. Detailed comparison of the two sc…
Motivated by a recent work of us [1], we reconstruct the different f(T)-gravity models corresponding to a set of dark energy scenarios containing the polytropic, the standard Chaplygin, the generalized Chaplygin and the modified Chaplygin gas models. We also derive the equation of state parameter of the selected f(T)-gravity models and obtain the necessary conditions for crossing the phantom-divide line.
It is investigated the reconstruction during the slow-roll inflation in the most general class of scalar-torsion theories whose Lagrangian density is an arbitrary function $f(T,ϕ)$ of the torsion scalar $T$ of teleparallel gravity and the inflaton $ϕ$. For the class of theories with Lagrangian density $f(T,ϕ)=-M_{pl}^{2} T/2 - G(T) F(ϕ) - V(ϕ)$, with $G(T)\sim T^{s+1}$ and the power $s$ as constant, we consider a reconstruction scheme for determining both the non-minimal coupling function $F(ϕ)$ and the scalar potential $V(ϕ)$ through the parametrization (or attractor) of the scalar spectral i…
Using the Navarro-Frenk-White (NFW) dark matter density profile we reconstruct an effective field theory model for gravity at large distances from a central object by demanding that the vacuum solution has the same gravitational properties as the NFW density profile has in the context of General Relativity (GR). The dimensionally reduced reconstructed action for gravity leads to a vacuum metric that includes a modified Rindler acceleration term in addition to the Schwarzschild and cosmological constant terms. The new term is free from infrared curvature singularities and leads to a much better…
Here we briefly discuss the Einstein-Aether gravity theory by modification of Einstein-Hilbert action. We find the modified Friedmann equations and then from the equations we find the effective density and pressure for Einstein-Aether gravity sector. These can be treated as dark energy provided some restrictions on the free function $F(K)$, where $K$ is proportional to $H^{2}$. Assuming two types of the power law solutions of the scale factor, we have reconstructed the unknown function $F(K)$ from HDE and NADE and their entropy-corrected versions (ECHDE and ECNADE). We also obtain the EoS para…
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…
EFT of Dark Energy with Cosmic Chronometers: Reconstructing Background EFT Functions
Department of Physics, College of Humanities and Sciences, Nihon University（日本大学人文科学系）；Center for Gravitational Physics and Quantum Information, Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所引力物理与量子信息中心）
We give an outline of an algorithm designed to reconstruct the background cosmological metric within the class of spherically symmetric dust universes that may include a cosmological constant. Luminosity and age data are used to derive constraints on the geometry of the universe up to a redshift of $z = 1.75$. It is shown that simple radially inhomogeneous void models that are sometimes used as alternative explanations for the apparent acceleration of the late time Universe cannot be ruled out by these data alone.
The peculiar velocity of the Local Group, reconstructed from inhomogeneities in the local density field, differs in direction and magnitude from the velocity inferred from the Cosmic Microwave Background dipole. We investigate whether generalized theories of gravity, which predict a modified growth of perturbations, are able to alleviate this discrepancy. We introduce a general formalism for calculating the real-space peculiar-velocity field for modified gravity and theories with interactions in the dark sector. For different classes of theories - scalar tensor and higher-dimensional gravity -…
We present a method for populating dark matter simulations with haloes of mass below the resolution limit. It is based on stochastically sampling a field derived from the density field of the halo catalogue, using constraints from the conditional halo mass function n(m|δ). We test the accuracy of the method and show its application in the context of building mock galaxy samples. We find that this technique allows precise reproduction of the two-point statistics of galaxies in mock samples constructed with this method. Our results demonstrate that the full information content of a simulation ca…
We show that the shape of the inflationary landscape potential may be constrained by analyzing cosmological data. The quantum fluctuations of fields orthogonal to the inflationary trajectory may have probed the structure of the local landscape potential, inducing non-Gaussianity (NG) in the primordial distribution of the curvature perturbations responsible for the cosmic microwave background (CMB) anisotropies and our Universe's large-scale structure. The resulting type of NG (tomographic NG) is determined by the shape of the landscape potential, and it cannot be fully characterized by 3- or 4…
We consider the cosmology of modified gravity models in which Newton's constant is distorted by a function of the inverse d'Alembertian acting on the Ricci scalar. We derive a technique for choosing the distortion function so as to fit an arbitrary expansion history. This technique is applied numerically to the case of LambdaCDM cosmology, and the result agrees well with a simple hyperbolic tangent.
This brief contribution is devoted to phenomenological consequences of deviations from Lorentz invariance in gravity and dark matter. We will discuss main effects on cosmological observables and current constraints derived from astrophysical and cosmological data.
We investigate some cosmological models arising from a non-minimal coupling of a fermionic field to gravity in the geometrical setting of Einstein-Cartan-Sciama-Kibble gravity. The role played by the non-minimal coupling together with torsion in facing problems such as cosmological singularity, inflation and dark energy is discussed.
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.
A large number of cosmological parameters have been suggested for obtaining information on the nature of dark energy. In this work, we study the efficacy of these different parameters in discriminating theoretical models of dark energy, using both currently available supernova (SNe) data, and simulations of future observations. We find that the current data does not put strong constraints on the nature of dark energy, irrespective of the cosmological parameter used. For future data, we find that the although deceleration parameter can accurately reconstruct some dark energy models, it is unabl…
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.
We investigate the cosmological perturbations around FLRW solutions to non- linear massive gravity with a new effective coupling to matter proposed recently. Unlike the case with minimal matter coupling, all five degrees of freedom in the gravity sector propagate on generic self-accelerating FLRW backgrounds. We study the stability of the cosmological solutions and put constraints on the parameters of the theory by demanding the correct sign for the kinetic terms for scalar, vector and tensor perturbations.
We study dynamics of induced gravity cosmological models with sixth degree potential, that have found using the superpotential method. The important property of these models are existence of exact cosmological solutions that tend to fixed points. The stability of these cosmological solutions have been obtained. In particular, we find conditions under which solutions with a non-monotonic Hubble parameter that tend to a fixed point are attractors.
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…
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.
We perform a detailed dynamical analysis of various cosmological scenarios in extended (varying-mass) nonlinear massive gravity. Due to the enhanced freedom in choosing the involved free functions, this cosmological paradigm allows for a huge variety of solutions that can attract the universe at late times, comparing to scalar-field cosmology or usual nonlinear massive gravity. Amongst others, it accepts quintessence, phantom, or cosmological-constant-like late-time solutions, which moreover can alleviate the coincidence problem. These features seem to be general and non-sensitive to the impos…
We use the ideas of entropic gravity to derive the FRW cosmological model and show that for late time evolution we have an effective cosmological constant. By using the first law of thermodynamics and the modified entropy area relationship derived from the supersymmetric Wheeler-DeWitt equation of the Schwarzschild black hole, we obtain modifications to the Friedmann equations that in the late time regime gives an effective positive cosmological constant. Therefore, this simple model can account for the dark energy component of the universe by providing an entropic origin to the cosmological c…
We have discussed a particular class of exact cosmological solutions of the 4-dimensional low energy string gravity in the string frame. In the vacuum without matter and the 2-form fields, the exact cosmological solutions always give monotonically shrinking universes if the dilaton field is not a constant. However, in the presence of the 2-form fields and/or the radiation-like fluid in the string frame, the exact cosmological solutions show a minimum size of the universe in the evolution, but with an initial cosmological curvature singularity in the string frame.
We study cosmological applications of extended vector-tensor theories, whose Lagrangians contain up to two derivatives with respect to metric and vector field. We derive background equations under the assumption of homogeneous and isotropic universe and study the nature of cosmological perturbations on top of the background. We found an example of healthy cosmological solutions in non-trivial degenerate theory of gravity for the first time, where those perturbations do not suffer from any instabilities, that is, ghost and gradient instabilities.
We consider linear perturbations about a homogeneous and isotropic cosmological background in the projectable version of Hořava-Lifshitz gravity. Starting from the action for cosmological perturbations, we identify the canonically normalized fluctuation variables. We find that - in contrast to what happens in the non-projectable version of the theory - the extra scalar cosmological perturbation mode is already dynamical at the level of linear perturbations. For values of the parameter $λ$ in the range $1/3 < λ< 1$, the extra mode is ghost-like, for values $1 < λ$ and $λ< 1/3$ it is tachyonic. …
We consider the evolution of cosmological gravitational waves in scalar-tensor theory and $F(R)$ gravity theory as typical models of the modified gravity. Although the propagation speed is not changed from the speed of light, the propagation phase changes when we compare the propagation in these modified gravity theories with the propagation in the $Λ$CDM model. The phase change might be detected in future observations.
A ghost-free theory of gravity with two dynamical metrics both coupled to matter is shown to be consistent and viable. Its cosmological implications are studied, and the models, in particular in the context of partially massless gravity, are found to explain the cosmic acceleration without resorting to dark energy.
We discuss a possible mechanism to screen a cosmological constant in non-local gravity. We find that in a simple model of of non-local gravity with the Lagrangian of the form, $R+f(\Box^{-1}R)-2Λ$ where $f(X)$ is a quadratic function of $X$, there is a flat spacetime solution despite the presence of the cosmological constant $Λ$. Unfortunately, however, we also find that this solution contains a ghost in general. Then we discuss the condition to avoid a ghost and find that one can avoid it only for a finite range of `time'. Nevertheless our result suggests the possibility of solving the cosmol…
In this paper, we will show that the equations of motion of the quadratic in curvature, ghost free, infinite derivative theory of gravity will not permit an anisotropic collapse of a homogeneous Universe for a Kasner-type vacuum solution.
We investigate perturbations of a class of spherically symmetric solutions in massive gravity and bi-gravity. The background equations of motion for the particular class of solutions we are interested in reduce to a set of the Einstein equations with a cosmological constant. Thus, the solutions in this class include all the spherically symmetric solutions in general relativity, such as the Friedmann-Lemaître-Robertson-Walker solution and the Schwarzschild (-de Sitter) solution, though the one-parameter family of two parameters of the theory admits such a class of solutions. We find that the eq…
We investigate the corresponding relation between $f(R)$ gravity and an interacting holographic dark energy. By obtaining conditions needed for some observational evidence such as, positive acceleration expansion of universe, crossing the phantom divide line and validity of thermodynamics second law in an interacting HDE model and corresponding it with $f(R)$ mode of gravity we find a viable $f(R)$ model which can explain the present universe. We also obtain the explicit evolutionary forms of the corresponding scalar field, potential and scale factor of universe.
The current paper provides a comprehensive examination of a dark energy cosmological model in the classical regime, in which a generic scalar field is regarded as a dark energy source. Einstein's field equations are solved in model independent way i.e. using a scheme of cosmological parametrization. A parametrization of the density parameter as a function of the cosmic scale factor has been investigated in this line. The result is noteworthy because it shows a smooth transition from a decelerating to an accelerating phase in the recent past. The model parameters involved in the functional form…
In the framework of the recently proposed models of massive gravity, defined with respect to a de Sitter reference metric, we obtain new homogeneous and isotropic solutions for arbitrary cosmological matter and arbitrary spatial curvature. These solutions can be classified into three branches. In the first two, the massive gravity terms behave like a cosmological constant. In the third branch, the massive gravity effects can be described by a time evolving effective fluid with rather remarkable features, including the property to behave as a cosmological constant at late time.
Reconstructing the Gaussian initial conditions at the beginning of the Universe from the survey data in a forward modeling framework is a major challenge in cosmology. This requires solving a high dimensional inverse problem with an expensive, non-linear forward model: a cosmological N-body simulation. While intractable until recently, we propose to solve this inference problem using an automatically differentiable N-body solver, combined with a recurrent networks to learn the inference scheme and obtain the maximum-a-posteriori (MAP) estimate of the initial conditions of the Universe. We demo…
Reconstructing Barrow Holographic Dark Energy in $f(Q,T)$ Gravity and Cosmic Constraint
State Key Laboratory of Radio Astronomy and Technology, Xinjiang Astronomical Observatory, Chinese Academy of Sciences（中国科学院新疆天文台射电天文技术与重点实验室）；School of Astronomy and Space Science, University of Chinese Academy of Sciences（中国科学院大学天文与空间科学学院）；School of Physics and Electronics, Henan University（河南大学物理与电子学院）；School of Physical Science and Technology, Xinjiang University（新疆大学物理科学与技术学院）；School of Physics and Astronomy, China West Normal University（西华师范大学物理学与电子信息学院）
We review recent developments on cosmology in extended teleparallel gravity, called "$F(T)$ gravity" with $T$ the torsion scalar in teleparallelism. We explore various cosmological aspects of $F(T)$ gravity including the evolution of the equation of state for the universe, finite-time future singularities, thermodynamics, and four-dimensional effective $F(T)$ gravity theories coming from the higher-dimensional Kaluza-Klein (KK) and Randall-Sundrum (RS) theories.
We study linear cosmological perturbations in the ``healthy extension'' of Horava-Lifshitz gravity which has recently been analyzed \cite{BPS2}. We find that there are two degrees of freedom for scalar metric fluctuations, but that one of them decouples in the infrared limit. Also, for appropriate choices of the parameters defining the Lagrangian, the extra mode can be made well-behaved even in the ultraviolet.
We propose a new method to recover the cosmological initial conditions of the presently observed galaxy distribution, which can serve to run constrained simulations of the Local Universe. Our method, the Reverse Zeldovich Approximation (RZA), can be applied to radial galaxy peculiar velocity data and extends the previously used Constrained Realizations (CR) method by adding a Lagrangian reconstruction step. The RZA method consists of applying the Zeldovich approximation in reverse to galaxy peculiar velocities to estimate the cosmic displacement field and the initial linear matter distribution…
We study the generation and propagation of gravitational waves in scalar-tensor gravity using numerical relativity simulations of scalar field collapses beyond spherical symmetry. This allows us to compare the tensor and additional massive scalar waves that are excited. As shown in previous work in spherical symmetry, massive propagating scalar waves decay faster than 1/r and disperse, resulting in an inverse chirp. These effects obscure the ringdown in any extracted signal by mixing it with the transient responses of the collapse during propagation. In this paper we present a simple method to…
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 use the 2% distance measurement from our reconstructed baryon acoustic oscillations (BAOs) signature using the Sloan Digital Sky Survey (SDSS) Data Release 7 (DR7) Luminous Red Galaxies (LRGs) from Padmanabhan et al. (2012) and Xu et al. (2012) combined with cosmic microwave background (CMB) data from Wilkinson Microwave Anisotropy Probe (WMAP7) to measure parameters for various cosmological models. We find a 1.7% measurement of H_0 = 69.8 +/- 1.2 km/s/Mpc and a 5.0% measurement of Omega_m = 0.280 +/- 0.014 for a flat Universe with a cosmological constant. These measurements of H_0 and Omeg…
Reconstructions of the primordial power spectrum (PPS) of curvature perturbations from cosmic microwave background anisotropies and large-scale structure data suggest that the usually assumed power-law PPS has localised features (up to $\sim 10\%$ in amplitude), although of only marginal significance in the framework of $Λ$CDM cosmology. On the other hand if the underlying cosmology is assumed to be Einstein-de Sitter, larger features in the PPS (up to $\sim 20\%$) are required to accurately fit the observed acoustic peaks. Within the context of single clock inflation, we show that any given r…
The primordial spectrum of cosmological tensor perturbations is considered as a possible probe of quantum gravity effects. Together with string theory, loop quantum gravity is one of the most promising frameworks to study quantum effects in the early universe. We show that the associated holonomy correction should modify the potential seen by gravitational waves during the inflationary amplification. The resulting power spectrum should exhibit a characteristic tilt. This opens a new window for cosmological tests of quantum gravity.
We investigate the cosmological perturbations in the context of a Scalar-Tensor-Vector theory of Gravity known as MOG in the literature. Recent investigations show that MOG reproduces a viable background cosmological evolution comparable to $Λ$CDM. However, the matter-dominated era is slightly different. In this paper, we study the linear matter perturbations and estimate the relevant modified gravity parameters. We show that MOG reduces the growth rate of the perturbations and comparing with the RSD data reveals that MOG suggests a higher value for $σ_8$, compare to $Λ$CDM. This point, consti…
We investigate anisotropic cosmological solutions of the theory with non-minimal couplings between electromagnetic fields and gravity in $Y(R) F^2$ form. After we derive the field equations by the variational principle, we look for spatially flat cosmological solutions with magnetic fields or electric fields. Then we give exact anisotropic solutions by assuming the hyperbolic expansion functions. We observe that the solutions approach to the isotropic case in late-times.
