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 interaction among different components of matter sector. We have also checked the Hamiltonian structure of a scalar QED coupling to the square root gravity in the same manner. All constraints in the theory are first class too and thus the local U(1) gauge symmetry in scalar QED is preserved.
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 obtain traversable wormhole and time machine solutions of the field equations of an alternative of gravity with non-minimally curvature-matter coupling. Our solutions exhibit a non-trivial redshift function and allow for matter that satisfy the dominant energy condition.
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 …
Static, spherically symmetric solutions representing stars made of barotropic perfect fluid are studied in the context of two theories of type-II minimally modified gravity, VCDM and VCCDM. Both of these theories share the property that no additional degree of freedom is introduced in the gravity sector, and propagate only two gravitational waves besides matter fields, as in General Relativity (GR). We find that, on imposing physical boundary conditions on the Misner-Sharp mass of the system, the solutions in V(C)CDM exactly coincide with the ones in GR, namely they also satisfy the Tolman-Opp…
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…
The first order Plebanski formulation of (complex) general relativity (GR) in terms of self-dual 2-forms admits a generalization, proposed by Krasnov, that is qualitatively different from other possible generalizations of GR in terms of metric variables. In this paper, we investigate, within a minimal modification, and in a perturbative approach, the geometrical meaning of the field variables used in the Krasnov generalization, and compare them to the field variables used in the Plebanski formulation.
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 theories are modifications of general relativity with two local gravitational degrees of freedom in four dimensions. Their construction relies on the breaking of 4D diffeomorphism invariance keeping however the symmetry under 3D diffeomorphisms. Here, we construct these theories from a Hamiltonian point of view. We start with the phase space of general relativity in the ADM formalism. Then, we find the conditions that the Hamiltonian must satisfy for the theory to propagate (up to) two gravitational degrees of freedom with the assumptions that the lapse and the shift…
Working directly with a general Hamiltonian for the spacetime metric with the $3+1$ decomposition and keeping only the spatial covariance, we investigate the possibility of reducing the number of degrees of freedom by introducing an auxiliary constraint. The auxiliary constraint is considered as part of the definition of the theory. Through a general Hamiltonian analysis, we find the conditions for the Hamiltonian as well as for the auxiliary constraint, under which the theory propagates two tensorial degrees of freedom only. The class of theories satisfying these conditions can be viewed as a…
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 constr…
We study a large family of metric-affine theories with a projective symmetry, including non-minimally coupled matter fields which respect this invariance. The symmetry is straightforwardly realised by imposing that the connection only enters through the symmetric part of the Ricci tensor, even in the matter sector. We leave the connection completely free (including torsion) and obtain its general solution as the Levi-Civita connection of an auxiliary metric, showing that the torsion only appears as a projective mode. This result justifies the widely used condition of setting vanishing torsion …
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…
In the context of the recently proposed type-II minimally modified gravity theory, i.e. a metric theory of gravity with two local physical degrees of freedom that does not possess an Einstein frame, we study spherically symmetric vacuum solutions to explore the strong gravity regime. Despite the absence of extra degrees of freedom in the gravity sector, the vacuum solutions are locally different from the Schwarzschild or Schwarzschild-(A)dS metric in general and thus the Birkhoff theorem does not hold. The general solutions are parameterized by several free functions of time and admit regular …
We discuss non-minimally coupled cosmologies involving different geometric invariants. Specifically, actions containing a non-minimally coupled scalar field to gravity described, in turn, by curvature, torsion and Gauss--Bonnet scalars are considered. We show that couplings, potentials and kinetic terms are determined by the existence of Noether symmetries which, moreover, allows to reduce and solve dynamics. The main finding of the paper is that different non-minimally coupled theories, presenting the same Noether symmetries, are dynamically equivalent. In other words, Noether symmetries are …
The slow-roll field equations for the case of non-minimally coupled scalar fields are obtained in two ways: first using the direct generalization of slow-roll conditions in the minimal coupling case to non-minimal one; and, second, conformal transforming the slow-roll field equations in the Einstein frame to the Jordan frame and then applying the generalized slow-roll conditions. We compare the difference of two methods in calculation of the spectral index, $n_s$, for a model example. The second method seems to be more precise.
If one assumes a particular form of non-minimal coupling, called the conformal coupling, of a perfect fluid with gravity in the fluid-gravity Lagrangian then one gets modified Einstein field equation. In the modified Einstein equation, the effect of the non-minimal coupling does not vanish if one works with spacetimes for which the Ricci scalar vanishes. In the present work we use the Schwarzschild metric in the modified Einstein equation, in presence of non-minimal coupling with a fluid, and find out the energy-density and pressure of the fluid. In the present case the perfect fluid is part o…
We consider a non-minimally coupled curvature-matter gravity model (NMC) with a Weyl connection, a theory referred to as non-minimally coupled Weyl connection gravity (NMCWCG). The Weyl connection is an affine connection that is not compatible with the metric, and involves a vector field. Assuming a vacuum expectation value for the vector field and a matter Lagrangian that only contains the contributions of the vacuum energy, we show that the model admits solutions in the space-form with a reference curvature that can be fine-tuned to much smaller values than the contribution of the matter fie…
We study theories of gravity with non-minimal coupling between polarized media with pole-dipole and quadrupole moments and an arbitrary function of the space-time curvature scalar $R$ and the squares of the Ricci and Riemann curvature tensors. We obtain the general form of the equation of motion and show that an induced quadrupole moment emerges as a result of the curvature tensor dependence of the function coupled to the matter. We derive the explicit forms of the equations of motion in the particular cases of coupling to a function of the curvature scalar alone, coupling to an arbitrary func…
We show that effective theories of matter that classically violate the null energy condition cannot be minimally coupled to Einstein gravity without being inconsistent with both string theory and black hole thermodynamics. We argue however that they could still be either non-minimally coupled or coupled to higher-curvature theories of gravity.
We study the Hamiltonian formalism of the non-minimally coupled Weyl connection gravity (NMCWCG) in order to check whether Ostrogradsky instabilities are present. The Hamiltonian of the NMCWCG theories is obtained by foliating space-time into a real line (representing time) and \mbox{3-dimensional} space-like hypersurfaces, and by considering the spatial metric and the extrinsic curvature of the hypersurfaces as the canonical coordinates of the theory. Given the fact that the theory we study contains an additional dynamical vector field compared to the usual NMC models, which do not have Ostro…
We study the quasi-normal modes of asymptotically anti-de Sitter black holes in a class of shift-symmetric Horndeski theories where a gravitational scalar is derivatively coupled to the Einstein tensor. The space-time differs from exact Schwarzschild-anti-de Sitter, resulting in a different effective potential for the quasi-normal modes and a different spectrum. We numerically compute this spectrum for a massless test scalar coupled both minimally to the metric, and non-minimally to the gravitational scalar. We find interesting differences from the Schwarzschild-anti-de Sitter black hole found…
We derive the general formulae for the the scalar and tensor spectral tilts to the second order for the inflationary models with non-minimally derivative coupling without taking the high friction limit. The non-minimally kinetic coupling to Einstein tensor brings the energy scale in the inflationary models down to be sub-Planckian. In the high friction limit, the Lyth bound is modified with an extra suppression factor, so that the field excursion of the inflaton is sub-Planckian. The inflationary models with non-minimally derivative coupling are more consistent with observations in the high fr…
We discuss the consistency of a recently proposed class of theories described by an arbitrary function of the Ricci scalar, the trace of the energy-momentum tensor and the contraction of the Ricci tensor with the energy-momentum tensor. We briefly discuss the limitations of including the energy-momentum tensor in the action, as it is a non fundamental quantity, but a quantity that should be derived from the action. The fact that theories containing non-linear contractions of the Ricci tensor usually leads to the presence of pathologies associated with higher-order equations of motion will be s…
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）
Properties of soliton stars that could be expected to naturally arise out of a first order phase transition in non-minimally coupled scalar-field-induced gravity theories are investigated. Of particular interest are configurations, similar to Lee-Wick stars, with vanishing effective gravitational constant in the interiors.
We present consistent supersymmetric theories invariant under the generalization of the Galilean shift symmetry to ${\cal{N}}=1$ superspace. These theories are constructed via the decoupling limit of certain non-minimally derivative coupled supergravities, thus they correspond to the supersymmetrization of the so-called covariant Galileon. Specifically, these theories are constructed in the linearized ${\cal{N}}=1$ new-minimal supergravity set-up where the chiral supermultiplet is minimally coupled to gravity via the standard R-current contact term, and, at the same time, non-minimally derivat…
In a recent paper [1], it was introduced a new class of gravitational theories with two local degrees of freedom. The existence of these theories apparently challenges the distinctive role of general relativity as the unique non-linear theory of massless spin-2 particles. Here we perform a comprehensive analysis of these theories with the aim of (i) understanding whether or not these are actually equivalent to general relativity, and (ii) finding the root of the variance in case these are not. We have found that a broad set of seemingly different theories actually pass all the possible tests o…
In the bibliography a certain confusion arises in what regards to the classification of the gravitational theories into scalar-tensor theories and general relativity with a scalar field either minimally or non-minimally coupled to matter. Higher-derivatives Horndeski and beyond Horndeski theories that at first sight do not look like scalar-tensor theories only add to the confusion. To further complicate things, the discussion on the physical equivalence of the different conformal frames in which a given scalar-tensor theory may be formulated, makes even harder to achieve a correct classificati…
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。
In modified gravity, the one-loop matter power spectrum exhibits an ultraviolet divergence as shown in the framework of the degenerate higher-order scalar-tensor theory. To address this problem, we extend the effective field theory of large scale structure to modified gravity theories. We find that new counterterms appear and renormalize the ultraviolet divergence as a natural consequence of non-linearity in the modified Poisson equation. The renormalized one-loop matter power spectrum is useful to test modified gravity theories by comparing to observations.
We consider the variational principle in the covariant formulation of modified teleparallel theories with second order field equations. We vary the action with respect to the spin connection and obtain a consistency condition relating the spin connection with the tetrad. We argue that since the spin connection can be calculated using an additional reference tetrad, modified teleparallel theories can be interpreted as effectively bigravity theories. We conclude with discussion about the relation of our results and those obtained in the usual, non-covariant, formulation of teleparallel theories …
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）
Theories with a non-minimal coupling between the space-time curvature and matter fields introduce an extra force due to the non-conservation of the matter energy momentum. In the present work the theoretical consistency of such couplings is studied using a scalar field Lagrangian to model the matter content. The conditions that the coupling does not introduce ghosts, classical instabilities or superluminal propagation of perturbations are derived. These consistency conditions are then employed to rule out or severely restrict the forms of the non-minimal coupling functions considered in the pr…
We consider background dynamics of generalized Galileon theories in the context of inflation, where gravity and inflaton are non-minimally coupled to each other. In the inflaton oscillation regime, the Hubble parameter and energy density oscillate violently in many cases, in contrast to the Einstein gravity with minimally coupled inflaton. However, we find that there is an adiabatic invariant in the inflaton oscillation regime in any generalized Galileon theory. This adiabatic invariant is useful in estimating the expansion law of the universe and also the particle production rate due to the o…
We systematically review some standard issues and also the latest developments of modified gravity in cosmology, emphasizing on inflation, bouncing cosmology and late-time acceleration era. Particularly, we present the formalism of standard modified gravity theory representatives, like $F(R)$, $F(\mathcal{G})$ and $F(T)$ gravity theories, but also several alternative theoretical proposals which appeared in the literature during the last decade. We emphasize on the formalism developed for these theories and we explain how these theories can be considered as viable descriptions for our Universe.…
In this work, we propose different models of extended theories of gravity, which are minimally coupled to the SM fields, to explain the possibility of a dark matter (DM) candidate, without ad-hoc additions to the Standard Model (SM). We modify the gravity sector by allowing quantum corrections motivated from local $f(R)$ gravity, and non-minimally coupled gravity with SM sector and dilaton field. Using an effective field theory (EFT) framework, we constrain the scale of the EFT and DM mass. We consider two cases-Light DM (LDM) and Heavy DM (HDM), and deduce upper bounds on the DM annihilation …
We discuss spherically symmetric black holes in the modified self-dual theory of gravity recently studied by Krasnov, obtained adding a Weyl-curvature dependent `cosmological term' to the Plebanski lagrangian for general relativity. This type of modified gravity admits two different types of singularities: one is a true singularity for the theory where the fundamental fields of the theory, as well as the (auxiliary) spacetime metric, become singular, and the other one is a milder "non-metric singularity" where the metric description of the spacetime breaks down but the fundamental fields thems…
We explore alternate theories of gravity where the gravitational term in the Lagrangian $\frac{R}{8πG}$ is replaced by a function $f_1(R)$ and the matter Lagrangian is multiplied by a function $f_2(R)$. We argue that nuclear physics can provide strong experimental constraints on such theories. In particular using energy conditions on the pressure in the $^4$He nucleus, for $f_1(R)=\frac{R}{8πG}$ and $f_2(R)=1+λR$, we find a limit of $|λ| < 5\times 10^{-12}\, \hbox{m}^2$, more than thirty orders of magnitude stronger than the previous limit.
We study the spherically symmetric collapse of a cloud of dust in VCDM, a class of gravitational theories with two local physical degrees of freedom. We find that the collapse corresponds to a particular foliation of the Oppenheimer-Snyder solution in general relativity (GR) which is endowed with a constant trace for the extrinsic curvature relative to the time $t$ constant foliation. For this solution, we find that the final state of the collapse leads to a static configuration with the lapse function vanishing at a radius inside the apparent horizon. Such a point is reached in an infinite ti…
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…
We review thermodynamic properties of modified gravity theories such as $F(R)$ gravity and $f(T)$ gravity, where $R$ is the scalar curvature and $T$ is the torsion scalar in teleparallelism. In particular, we explore the equivalence between the equations of motion for modified gravity theories and the Clausius relation in thermodynamics. In addition, thermodynamics of the cosmological apparent horizon is investigated in $f(T)$ gravity. We show both equilibrium and non-equilibrium descriptions of thermodynamics. It is demonstrated that the second law of thermodynamics in the universe can be met…
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…
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）
In this article, we propose different background models of extended theories of gravity, which are minimally coupled to the SM fields, to explain the possibility of genesis of dark matter without affecting the SM particle sector. We modify the gravity sector by allowing quantum corrections motivated from (1) local $f(R)$ gravity and (2) non-minimally coupled gravity with SM sector and dilaton field. Next we apply conformal transformation on the metric to transform the action back to the Einstein frame. We also show that an effective theory constructed from these extended theories of gravity an…
Most no-hair theorems involve the assumption that the scalar field is independent of time. Recently in [Phys. Rev. D90 (2014) 041501(R)] the existence of time-dependent scalar hair outside a stationary black hole in general relativity was ruled out. We generalize this work to modified gravities and non-minimally coupled scalar field with an additional assumption that the spacetime is axisymmetric. It is shown that in higher-order gravity such as metric $f(R)$ gravity the time-dependent scalar hair doesn't exist. While in Palatini $f(R)$ gravity and non-minimally coupled case the time-dependent…
