We propose a new cosmological framework in which the strength of the gravitational force acted on dark matter at late time can be weaker than that on the standard matter fields without introducing extra gravitational degrees of freedom. The framework integrates dark matter into a type-II minimally modified gravity that was recently proposed as a dark energy mimicker. The idea that makes such a framework possible consists of coupling a dark matter Lagrangian and a cosmological constant to the metric in a canonically transformed frame of general relativity (GR). On imposing a gauge fixing constraint, which explicitly breaks the temporal diffeomorphism invariance, we keep the number of gravitational degrees of freedom to be two, as in GR. We then make the inverse canonical transformation to bring the theory back to the original frame, where one can add the standard matter fields. This framework contains two free functions of time which specify the generating functional of the above mentioned canonical transformation and which are then used in order to realize desired time evolutions of both the Hubble expansion rate $H(z)$ and the effective gravitational constant for dark matter $G_{\rm eff}(z)$. The aim of this paper is therefore to provide a new framework to address the two puzzles present in today's cosmology, i.e. the $H_0$ tension and the $S_8$ tension, simultaneously. When the dark matter is cold in this framework, we dub the corresponding cosmological model the V Canonical Cold Dark Matter (VCCDM), as the cosmological constant $Λ$ in the standard $Λ$CDM is replaced by a function $V(ϕ)$ of an auxiliary field $ϕ$ and the CDM is minimally coupled to the metric in a canonically transformed frame.
Minimally modified gravity is a class of models with only the two tensor degrees of freedom as in general relativity. Using the framework with auxiliary constraints these models can maintain a dynamical cosmological background. The form of the constraints is thereby restricted by the requirement of dynamical dark energy and the avoidance of a breakdown of perturbation theory. Studying the linear perturbations around the FLRW background the results are, however, quite insensitive to the details of the constraints leading to a modified effective gravitational constant or a non-vanishing sound sp…
We investigate the Hamiltonian structure of a class of gravitational theories whose actions are linear in the lapse function. We derive the necessary and sufficient condition for a theory in this class to have two or less local physical degrees of freedom. As an application we then find several concrete examples of modified gravity theories in which the total number of local physical degrees of freedom in the gravity sector is two.
We study the phenomenology of a class of minimally modified gravity theories called $f(\mathcal{H})$ theories, in which the usual general relativistic Hamiltonian constraint is replaced by a free function of it. After reviewing the construction of the theory and a consistent matter coupling, we analyze the dynamics of cosmology at the levels of both background and perturbations, and present a concrete example of the theory with a $3$-parameter family of the function $f$. Finally, we compare this example model to Planck data as well as some later-time probes, showing that such a realization of …
The self-consistent matter coupling is found in a broad class of minimally modified gravity theories which was discovered recently. All constraints in the theories remain first class and thus a graviton has only 2 local degrees of freedom. The cosmological solution of one of the examples in this class, the so-called square root gravity, exhibits a singularity freeness at high energy limit. At low energy limit, the theory smoothly connects to GR. A general feature of the theories in this class, with the self-consistent matter coupling discovered in our current work, is the non-trivial interacti…
We propose a modified gravity theory that propagates only two local gravitational degrees of freedom and that does not have an Einstein frame. According to the classification in JCAP 01 (2019) 017 [arXiv:1810.01047 [gr-qc]], this is a type-II minimally modified gravity theory. The theory is characterized by the gravitational constant $G_{\rm N}$ and a function $V(ϕ)$ of a non-dynamical auxiliary field $ϕ$ that plays the role of dark energy. Once one fixes a homogeneous and isotropic cosmological background, the form of $V(ϕ)$ is determined and the theory no longer possesses a free parameter or…
We study cosmology in a class of minimally modified gravity (MMG) with two local gravitational degrees of freedom. We classify modified gravity theories into type-I and type-II: theories of type-I have an Einstein frame and can be recast by change of variables as general relativity (GR) with a non-minimal matter coupling, while theories of type-II have no Einstein frame. Considering a canonical transformation of the lapse, the 3-dimensional induced metric and their conjugate momenta we generate type-I MMG. We then show that phenomenological deviations from GR, such as the speed of gravitationa…
We explore general scalar-tensor models in the presence of a kinetic mixing between matter and the scalar field, which we call Kinetic Matter Mixing. In the frame where gravity is de-mixed from the scalar this is due to disformal couplings of matter species to the gravitational sector, with disformal coefficients that depend on the gradient of the scalar field. In the frame where matter is minimally coupled, it originates from the so-called beyond Horndeski quadratic Lagrangian. We extend the Effective Theory of Interacting Dark Energy by allowing disformal coupling coefficients to depend on t…
We have investigated inflationary model constructed from minimally modified gravity (MMG) theories. The MMG theory in the form of $f({\bf H}) \propto {\bf H}^{1+p}$ gravity where, ${\bf H}$ is the Hamiltonian constraint in the Einstein gravity and $p$ is constant, has been studied. An inflation is difficult to be achieved in this theory of gravity unless an additional scalar field playing a role of inflaton is introduced in the model. We have found that the inflaton with exponential potential can drive inflation with graceful exist different from the case of Einstein gravity. The slow-roll par…
This paper is devoted to the study of Noether gauge symmetries of $f(T)$ gravity minimally coupled with a canonical scalar field. We explicitly determine the unknown functions of the theory $f(T),V(ϕ), W(ϕ)$. We have shown that there are two invariants for this model, one of which defines the Hamiltonian $H$ under time invariance (energy conservation) and the other is related to scaling invariance. We show that the equation of state parameter in the present model can cross the cosmological constant boundary. The behavior of Hubble parameter in our model closely matches to that of $Λ$CDM model,…
Modified Chaplygin gas as an exotic fluid has been introduced in [34]. Essential features of the modified Chaplygin gas as a cosmological model are discussed. Observational constraints on the parameters of the model have been included. The relationship between the modified Chaplygin gas and a homogeneous minimally coupled scalar field are reevaluated by constructing its self-interacting potential. In addition, we study the role of the tachyonic field in the modified Chaplygin gas cosmological model and the mapping between scalar field and tachyonic field is also considered.
Joint Constraints on Neutrinos and Dynamical Dark Energy in Minimally Modified Gravity
Universidade Federal do Rio Grande do Sul（南里奥格兰德联邦大学）；Instituto Nacional de Pesquisas Espaciais（国家空间研究所）；Presidency University（总统大学）；Durban University of Technology（德班理工大学）；Liaoning Normal University（辽宁师范大学）
We study observational constraints on the modified symmetric teleparallel gravity, the non-metricity $f(Q)$ gravity, which reproduces background expansion of the universe. For this purpose, we use Hubble measurements, Baryonic Acoustic Oscillations (BAO), 1048 Pantheon supernovae type Ia data sample which integrate SuperNova Legacy Survey (SNLS), Sloan Digital Sky Survey (SDSS), Hubble Space Telescope (HST) survey, Panoramic Survey Telescope and Rapid Response System (Pan-STARRS1). We confront our cosmological model against observational samples to set constraints on the parameters using Marko…
In this paper we show that the baryon-to-photon ratio $η$ is in general not conserved before decoupling in non-minimally coupled theories of gravity. We use big-bang nucleosynthesis and cosmic microwave background limits on the baryon-to-photon ratio $η$ to derive new constraints on modified gravity theories with a universal non-minimal coupling between matter and curvature, showing that they rule out a specific class of models previously considered in the literature as a substitute for the dark matter. We also compare these new constraints with the ones obtained from the COBE-FIRAS limits on …
Minimally modified gravity with Laplacian auxiliary constraints and an inflationary realization
The Institute for Fundamental Study (The Tah Poe Academia Institute), Naresuan University（那莱王大学基础研究所（塔波学术学院））；Center for Gravitational Physics and Quantum Information, Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理中心引力物理与量子信息）
$Λ_{\rm s}$CDM cosmology from a type-II minimally modified gravity
Istanbul Technical University（伊斯坦布尔理工大学）；Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所）；University of Sheffield（谢菲尔德大学）；Plaksha University（普拉克斯哈大学）；Indira Gandhi University（英迪拉甘地大学）；Universidade Federal do Rio Grande do Sul（南里奥格兰德联邦大学）；Instituto Nacional de Pesquisas Espaciais（国家空间研究院）；Universidad Nacional Autónoma de México（墨西哥国立自治大学）
本文提出$Λ_{\ m s}$VCDM模型，通过平滑AdS到dS转变过程，解决宇宙学张力问题，并探讨不同过渡历史对背景和扰动演化的影响。
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.
We study a model of quintessential inflation constructed in $R^2$ modified gravity with a non-minimally coupled scalar field, in the Palatini formalism. Our non-minimal inflaton field is characterised by a simple exponential potential. We find that successful quintessential inflation can be achieved with no fine-tuning on the model parameters. Predictions on the characteristics of dark energy will be tested by observations in the near future, while contrast with existing observations provides insights on the modified gravity background, such as the value of the non-minimal coupling and its run…
We present an accurate non-linear matter power spectrum prediction scheme for a variety of extensions to the standard cosmological paradigm, which uses the tuned halo model previously developed in Mead (2015b). We consider dark energy models that are both minimally and non-minimally coupled, massive neutrinos and modified gravitational forces with chameleon and Vainshtein screening mechanisms. In all cases we compare halo-model power spectra to measurements from high-resolution simulations. We show that the tuned halo model method can predict the non-linear matter power spectrum measured from …
We employ the superpotential technique for the reconstruction of cosmological models with a non-minimally coupled scalar field evolving on a spatially flat Friedmann-Robertson-Walker background. The key point in this method is that the Hubble parameter is considered as a function of the scalar field and this allows one to reconstruct the scalar field potential and determine the dynamics of the field itself, without a priori fixing the Hubble parameter as a function of time or of the scale factor. The scalar field potentials that lead to de Sitter or asymptotic de Sitter solutions, and those th…
Inflationary dynamics of non-minimally coupled $f(R)$ matter-curvature theories
Universidade do Porto（波尔图大学）；Centro de Física das Universidades do Minho e do Porto（米尼奥与波尔图大学物理中心）；Faculdade de Ciências e Tecnologia da Universidade de Coimbra（科英布拉大学科学与技术学院）
本研究探讨了非最小耦合 f(R) 理论对膨胀动力学的影响，发现负耦合模型可容纳稳定 de Sitter 解，并约束非最小耦合尺度高于 10^13 GeV。
The $E_G$ statistic is a powerful probe for detecting deviations from GR by combining weak lensing (WL), real-space clustering and redshift space distortion (RSD) measurements thus probing both the lensing and the growth effective Newton constants ($G_L$ and $G_{eff}$). We construct an up to date compilation of $E_G$ statistic data including both redshift and scale dependence ($E_G(R,z)$). We combine this $E_G$ data compilation with an up to date compilation of $fσ_8$ data from RSD observations to identify the current level of tension between the Planck/$Λ$CDM standard model based on general r…
Is Phantom Divide Crossing in General Relativity Completely Impossible? Shortcomings in canonical and minimally coupled scalar field and Possible Solutions in $k$-essence Models
High Energy Accelerator Research Organization (KEK)（高能加速器研究机构）；Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, Nagoya University（名古屋大学小林-益川粒子宇宙起源研究所）；ICREA（加泰罗尼亚高级研究中心）；Institute of Space Sciences (IEEC-CSIC)（空间科学研究所）；Institut d’Estudis Espacials de Catalunya (IEEC)（加泰罗尼亚空间研究学院）；Aristotle University of Thessaloniki（塞萨洛尼基亚里士多德大学）；Khazar University（哈扎尔大学）
We investigate the cosmological dynamics of non-minimally coupled scalar field system described by $F(ϕ)R$ coupling with $F(ϕ)=(1-ξϕ^N)R$($N\ge2$) and the field potential, $V(ϕ)=V_0ϕ^n$. We use a generic set of dynamical variables to bring out new asymptotic regimes of the underlying dynamics. However, our dynamical variables miss the most important fixed point$-$ the de Sitter solution. We make use of the original form of system of equations to investigate the issues related to this important solution. In particular, we show that the de-Sitter solution which is a dynamical attractor of the sy…
The electrodynamics with a Chern-Simons term $p_μA_ν\widetilde{F}^{μν}$ violates Lorentz and $CPT$ symmetries with a non-vanishing $p_μ$. For a fixed vector $p_μ$, in this paper we point out that the energy-momentum tensor of this theory coupled to the gravity minimally is symmetric but not divergence free, which consequently makes the gravitational field equation inconsistent. To preserve the consistency, we introduce a Chern-Simons term in the gravity sector with the coefficient determined by the Lorentz and $CPT$ violating term in the electromagnetic field. Further we study the phenomenolog…
The existence and the stability conditions for some exact relativistic solutions of special interest are studied in a higher-order modified teleparallel gravitational theory. The theory with the use of a Lagrange multiplier is equivalent with that of General Relativity with a minimally coupled noncanonical field. The conditions for the existence of de Sitter solutions and ideal gas solutions in the case of vacuum are studied as also the stability criteria. Furthermore, in the presence of matter the behaviour of scaling solutions is given. Finally, we discuss the degrees of freedom of the field…
We study new FRW type cosmological models of modified gravity treated on the background of Palatini approach. These models are generalization of Einstein gravity by the presence of a scalar field non-minimally coupled to the curvature. The models employ Starobinsky's term in the Lagrangian and dust matter. Therefore, as a by-product, an exhausted cosmological analysis of general relativity amended by quadratic term is presented. We investigate dynamics of our models, confront them with the currently available astrophysical data as well as against LCDM model. We have used the dynamical system m…
In the present study, we consider an extended form of teleparallel Lagrangian $f(T,ϕ,X)$, as function of a scalar field $ϕ$, its kinetic term $X$ and the torsion scalar $T$. We use linear perturbations to obtain the equation of matter density perturbations on sub-Hubble scales. The gravitational coupling is modified in scalar modes with respect to the one of General Relativity, albeit vector modes decay and do not show any significant effects. We thus extend these results by involving multiple scalar field models. Further, we study conformal transformations in teleparallel gravity and we obtai…
In the context of modified teleparallel gravity, we study the generation of primordial density fluctuations in a general scalar-torsion theory whose Lagrangian density is an arbitrary function $f(T,ϕ)$ of the torsion scalar $T$ and a scalar field $ϕ$, plus the kinetic term of this latter. It is well known that generic modifications of teleparallel gravity are not invariant under six-parameter local Lorentz transformations. In order to restore the local Lorentz symmetry, we have incorporated six additional degrees of freedom in the form of Goldstone modes of the symmetry breaking through a Lore…
We investigate the cosmological applications of a bi-scalar modified gravity that exhibits partial conformal invariance, which could become full conformal invariance in the absence of the usual Einstein-Hilbert term and introducing additionally either the Weyl derivative or properly rescaled fields. Such a theory is constructed by considering the action of a non-minimally conformally-coupled scalar field, and adding a second scalar allowing for a nonminimal derivative coupling with the Einstein tensor and the energy-momentum tensor of the first field. At a cosmological framework we obtain an e…
In this paper we investigate the global dynamics for the minimally coupled scalar field representation of the modified Chaplygin gas in the context of flat FLRW cosmology. The tool for doing this is a new set of bounded variables that lead to a regular dynamical system. It is shown that the exact modified Chaplygin gas perfect fluid solution appears as a straight line in the associated phase plane. It is also shown that no other solutions stay close to this solution during their entire temporal evolution, but that there exists an open subset of solutions that stay arbitrarily close during an i…
We study canonical transformations of general relativity (GR) to provide a novel matter coupling to gravity. Although the transformed theory is equivalent to GR in vacuum, the equivalence no longer holds if a matter field minimally couples to the canonically transformed gravitational field. We find that a naive matter coupling to the transformed field leads to the appearance of an extra mode in the phase space, rendering the theory inconsistent. We then find a consistent and novel way of matter coupling: after imposing a gauge fixing condition, a matter field can minimally couple to gravity wi…
The aim of this paper is to constrain modified gravity with redshift space distortion observations and supernovae measurements. Compared with a standard LCDM analysis, we include three additional free parameters, namely the initial conditions of the matter perturbations,the overall perturbation normalization, and a scale-dependent Y parameter modifying the Poisson equation, in an attempt to perform a more model-independent analysis. First, we constrain the Poisson parameter Y (also called Geff ) by using currently available fsigma_8 data and the recent SN catalog JLA. We find that the inclusio…
Classical generalization of general relativity is considered as gravitational alternative for unified description of the early-time inflation with late-time cosmic acceleration. The structure and cosmological properties of number of modified theories, including traditional $F(R)$ and Hořava-Lifshitz $F(R)$ gravity, scalar-tensor theory, string-inspired and Gauss-Bonnet theory, non-local gravity, non-minimally coupled models, and power-counting renormalizable covariant gravity are discussed. Different representations and relations between such theories are investigated. It is shown that some ve…
Non-Minimally Coupled Warm Inflation in the Defining Frame
Center for Physical Sciences and Technology (FTMC)（立陶宛物理与工程技术中心）；Faculdade de Ciências e Tecnologia and CFisUC, Departamento de Física, Universidade de Coimbra（科英布拉大学科学与技术学院及CFisUC物理系）
We compute the three-point correlation function of primordial scalar density perturbations in a general single-field inflationary scenario, where a scalar field phi has a direct coupling with the Ricci scalar R and the Gauss-Bonnet term GB. Our analysis also covers the models in which the Lagrangian includes a function non-linear in the field kinetic energy X=-(nabla phi)^2/2, and a Galileon-type field self-interaction G(phi, X)*(Box phi), where G is a function of phi and X. We provide a general analytic formula for the equilateral non-Gaussianity parameter f_{NL}^{equil} associated with the b…
ACT Data and Positive Running of the Spectral Index for Scalar Theory and Modified Gravity
ICREA（加泰罗尼亚高级研究院）；Institute of Space Sciences (IEEC-CSIC)（空间科学研究所）；Department of Physics, Aristotle University of Thessaloniki（萨洛尼卡亚里士多德大学物理系）；Center for Theoretical Physics, Khazar University（阿塞拜疆可汗大学理论物理中心）
Motivated by their potential role as dark matter, we study the cosmological evolution of light scalar and vector fields non-minimally coupled to gravity. Our focus is on a situation where the dominant contribution to the energy density arises from the misalignment mechanism. In addition, we also discuss the possibility that dark matter is generated in a stochastic scenario or from inflationary fluctuations. Even small deviations in the non-minimal couplings from the standard scenarios lead to significant qualitative and quantitative changes. This is due to the curvature-coupling driven superho…
We present a thorough stability analysis of modified gravity theories in the presence of matter fields. We use the Effective Field Theory framework for Dark Energy and Modified Gravity to retain a general approach for the gravity sector and a Sorkin-Schutz action for the matter one. Then, we work out the proper viability conditions to guarantee in the scalar sector the absence of ghosts, gradient and tachyonic instabilities. The absence of ghosts can be achieved by demanding a positive kinetic matrix, while the lack of a gradient instability is ensured by imposing a positive speed of propagati…
We consider the non-minimal model of gravity in $Y(R) F^2$-form. We investigate a particular case of the model, for which the higher order derivatives are eliminated but the scalar curvature $R$ is kept to be dynamical via the constraint $Y_RF_{mn}F^{mn} =-\frac{2}{κ^2}$. The effective fluid obtained can be represented by interacting electromagnetic field and vacuum depending on $Y(R)$, namely, the energy density of the vacuum tracks $R$ while energy density of the conventional electromagnetic field is dynamically scaled with the factor $\frac{Y(R)}{2}$. We give exact solutions for anisotropic…
We have succeeded in establishing a cosmological model with a non-minimally coupled scalar field $ϕ$ that can account not only for the spatial periodicity or the picket-fence structure exhibited by the galaxy $N$-$z$ relation of the 2dF survey, but also for the spatial power spectrum of the cosmic microwave background radiation (CMB) temperature anisotropy observed by the WMAP satellite. The scalar field of our model universe starts from an extremely small value at around the nucleosynthesis epoch, remains in that state for sufficiently long periods, allowing sufficient time for the CMB temper…
Realization of quintom dark energy after DESI DR2 in Nieh-Yan modified teleparallel gravity
University of Science and Technology of China（中国科学技术大学）；Interdisciplinary Center for Theoretical Study, University of Science and Technology of China（中国科学技术大学交叉理论研究中心）；Peng Huanwu Center for Fundamental Theory（彭桓武基础理论中心）
