Luca Fabbri
We consider how the principles of causality and equivalence restrict the background in which matter field theories are defined; those constraints develop in restrictions for these matter field theories: the simplest matter field theory aside, all other less simple matter field theories are too complex therefore resulting to be inconsistent in general instances.
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The aim of this paper is to clarify the relation between three different approaches of theories with a minimal length scale: A modification of the Lorentz-group in the 'Deformed Special Relativity', theories with a 'Generalized Uncertainty Principle' and those with 'Modified Dispersion Relations'. It is shown that the first two are equivalent, how they can be translated into each other, and how the third can be obtained from them. An adequate theory with a minimal length scale requires all three features to be present.
We investigate the stability criterions for perfect fluid in $f(R)$ theories which is an important generalization of general relativity. Firstly, using Wald's general variation principle, we recast Seifert's work and obtain the dynamical stability criterion. Then using our generalized thermodynamical criterion, we obtain the concrete expressions of the criterion. We show that the dynamical stability criterion is exactly the same as the thermodynamical stability criterion. This result suggests that there is an inherent connection between the thermodynamics and gravity in $f(R)$ theories. It sho…
Kurtosis consistency relation in large-scale structure as a probe of gravity theories
本文基于物质密度涨落构建峰度一致性关系，推导出DHOST理论框架下两个独立的一致性关系，为约束和检验修正引力理论提供了新探针。
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…
Matter coupling in modified gravity theories is a nontrivial issue when the gravitational Lagrangian possesses a degeneracy structure to avoid the problem of the Ostrogradsky ghost. Recently, this issue was addressed for bosonic matter fields in the generalized disformal Horndeski class, which is so far the most general class of ghost-free scalar-tensor theories obtained by performing a higher-derivative generalization of invertible disformal transformations on Horndeski theories. In this paper, we clarify the consistency of fermionic matter coupling in the generalized disformal Horndeski theo…
The dynamics of physical theories is usually described by differential equations. Difference equations then appear mainly as an approximation which can be used for a numerical analysis. As such, they have to fulfill certain conditions to ensure that the numerical solutions can reliably be used as approximations to solutions of the differential equation. There are, however, also systems where a difference equation is deemed to be fundamental, mainly in the context of quantum gravity. Since difference equations in general are harder to solve analytically than differential equations, it can be he…
On the self-consistency of compact objects in Lorentz-violating gravity theories
本文研究洛伦兹破缺引力理论中致密天体的自洽性，提出需同时满足场方程与几何约束的框架，并证明此前若干解在物理上不可接受。
Generalized Second Law for Non-minimally Coupled Matter Theories
本文将广义第二定律的线性化半经典证明推广到物质部分非最小耦合的高阶曲率引力理论，通过在有效场论框架中求值物质路径积分并结合线性化第二定律完成证明。
We identify classical solutions of a generalised group field theory model in 3 dimensions, and study the corresponding perturbations, deriving their effective dynamics. We discuss their interpretation as emergent matter fields. This allows us, on the one hand to test the proposed mechanism for emergence of matter as a phase of group field theory, and on the other hand to expose some limitations of the generalised group field theory formalism.
Consistency of matter models with asymptotically safe quantum gravity
本文基于截断重整化群流给出渐近安全量子引力对物质场数量与类型的限制，包括自旋3/2场，并指出其可容纳标准模型但严格限制新物质，从而可由对撞机实验检验。
Are $f(R, {\rm Matter})$ theories really relevant to cosmology?
本文论证了包含 Standard Model 的 $f(R, \ ext{Matter})$ 理论因存在 ghost states 或已被实验排除而与宇宙学无关，不包含 SM 的此类理论则应归为标量-张量等理论另行研究。
Validity of the Background Subtraction Method for Black Hole Thermodynamics in Matter-Coupled Gravity Theories
本文研究背景减法方法在物质耦合引力理论中的有效性，通过两个例子验证了其与Iyer-Wald形式的等价性，并指出特殊物质场可能导致的细微问题。
Invertible disformal transformations are a useful tool to investigate ghost-free scalar-tensor theories. By performing a higher-derivative generalization of the invertible disformal transformation on Horndeski theories, we construct a novel class of ghost-free scalar-tensor theories, which we dub generalized disformal Horndeski theories. Specifically, these theories lie beyond the quadratic/cubic DHOST class. We explore cosmological perturbations to identify a subclass where gravitational waves propagate at the speed of light and clarify the conditions for the absence of ghost/gradient instabi…
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 perturbation theory for large-scale structure in the most general scalar-tensor theories propagating a single scalar degree of freedom, which include Horndeski theories and beyond. We model the parameter space using the effective field theory of dark energy. For Horndeski theories, the gravitational field and fluid equations are invariant under a combination of time-dependent transformations of the coordinates and fields. This symmetry allows one to construct a physical adiabatic mode which fixes the perturbation-theory kernels in the squeezed limit and ensures that the well-known con…
In this brief reply we respond to the note of Bertolami and Gomes (arXiv:2005.03968) on our recent paper (arXiv:2003.10154).
This paper pushes back against the Democritean-Newtonian tradition of assuming a strict conceptual dichotomy between spacetime and matter. Our approach proceeds via the more narrow distinction between modified gravity/spacetime (MG) and dark matter (DM). A prequel paper argued that the novel field $Φ$ postulated by Berezhiani and Khoury's 'superfluid dark matter theory' is as much (dark) matter as anything could possibly be, but also$-$below the critical temperature for superfluidity$-$as much (of a modification of) spacetime as anything could possibly be. Here we introduce and critically eval…
We investigate the potential of cosmological observations, such as galaxy surveys, for constraining degenerate higher-order scalar-tensor (DHOST) theories, focusing in particular on the linear growth of the matter density fluctuations. We develop a formalism to describe the evolution of the matter density fluctuations during the matter dominated era and in the early stage of the dark energy dominated era in DHOST theories, and give an approximate expression for the gravitational growth index in terms of several parameters characterizing the theory and the background solution under consideratio…
We consider alternative theories of gravity with a direct coupling between matter and the Ricci scalar We study the relation between these theories and ordinary scalar-tensor gravity, or scalar-tensor theories which include non-standard couplings between the scalar and matter. We then analyze the motion of matter in such theories, its implications for the Equivalence Principle, and the recent claim that they can alleviate the dark matter problem in galaxies.
Matter really does matter, or Why $f(R,{\rm Matter})$ type theories are significant for gravitational physics and cosmology
本研究针对 Lacombe 等人对 $f(R,{\rm Matter})$ 修正引力理论的质疑展开反驳，指出其采用的无质量标量场物质源局限性强，通过理论基础梳理、能标分析及与观测数据、$\Lambda$CDM 范式的对比，证明该质疑并非定论性批评。
In this work we show the existence of traversable wormhole and time-machine solutions in a modified theory of gravity where matter and curvature are nonminimally coupled. Those solutions present a nontrivial redshift function and exist even in the presence of ordinary matter which satisfies the dominant energy condition.
We examine the role of consistency with causality and quantum mechanics in determining the properties of gravitation. We begin by examining two different classes of interacting theories of massless spin 2 particles -- gravitons. One involves coupling the graviton with the lowest number of derivatives to matter, the other involves coupling the graviton with higher derivatives to matter, making use of the linearized Riemann tensor. The first class requires an infinite tower of terms for consistency, which is known to lead uniquely to general relativity. The second class only requires a finite nu…
We present a general framework to include ordinary fermionic matter in the metric--affine gauge theories of gravity. It is based on a nonlinear gauge realization of the affine group, with the Lorentz group as the classification subgroup of the matter and gravitational fields.
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…
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 discuss possible instabilities in higher-derivative matter fields theories. These theories has two free parameters $β_1$ and $β_4$. By using dynamical system approach we explicitly demonstrate that for stability of Minkowski space in expanding Universe it is need condition $β_4<0$. By using quantum field theory approach we also find additional restriction for parameters $β_1>-\frac{1}{3}β_4$ which is need to avoid tachyon-like instability.
$ω(ϕ) \to \infty$ limit of scalar tensor theories are studied for traceless matter source. It is shown that the limit $ω(ϕ) \to \infty$ does not reduce a scalar tensor theory to general relativity. An exact radiation solution of scalar tensor cosmology under Nordtvedt conditions is obtained for flat Friedmann universe.
We study f(R)-gravity with torsion in presence of the most general ELKO matter, checking the consistency of the conservation laws with the matter field equations; we discuss some mathematical features of the field equations in connection with a cosmological application.
Consistency of higher derivative couplings to matter fields in scalar-tensor gravity
本文研究广义非形式 Horndeski 理论与最小耦合物质场的一致性，证明为避免 Ostrogradsky 鬼场，所有高导数非形式变换项均须排除。
Preserving the Energy-Momentum Tensor in f(R, Matter) Theories
本文提出基于Herglotz变分原理的f(R, Matter)理论，通过适当选择Herglotz贡献恢复能量动量张量协变守恒。
We investigate the skewness of galaxy number density fluctuations as a possible probe to test gravity theories. We find that the specific linear combination of the skewness parameters corresponds to the coefficients of the second-order kernels of the density contrast, which can be regarded as the consistency relation and used as a test of general relativity and modified gravity theories. We also extend the analysis of the skewness parameters from real space to redshift space and derive the redshift-space skewness consistency relation.
Recently there has been a proposal for modified gravitational f(R) actions which include a direct coupling between the matter action and the Ricci scalar, R. Of particular interest is the specific case where both the action and the coupling are linear in R. It is shown that such an action leads to a theory of gravity which includes higher order derivatives of the matter fields without introducing more dynamics in the gravity sector and, therefore, cannot be a viable theory for gravitation.
We suggest a limit of Einstein equations incorporating the state $g_{μν}=0$ as a solution. The large scale behavior of this theory has interesting properties. For a spherical source, the velocity profile for circular motions is of the form observed in galaxies (approximately flat). For FRW cosmologies, the Friedman equation contains an additional contribution in the matter sector.
We study the symmetries enjoyed by the Newtonian equations of motion of the non-relativistic dark matter fluid coupled to gravity which give rise to the phenomenon of gravitational instability. We also discuss some consistency relations involving the soft limit of the (n + 1)-correlator functions of matter and galaxy overdensities.
A new class of modified gravity theories with a healthy higher order derivative terms of a function of the matter Lagrangian $f(L_m)$ is considered. Generally the energy momentum tensor is not conserved, leading to the fifth force similar to $f(R,T)$ theories. We will however show that in the FRW background there exists two possibilities corresponding to conservative and non-conservative cases. Cosmological implications of both cases with different functions of the matter Lagrangian $f$ will be investigated in details and we will show that current observational data can be satisfied in this mo…
We study the matter density perturbations in modified teleparallel gravity theories, where extra degrees of freedom arise from the local Lorentz violation in the tangent space. We formulate a vierbein perturbation with variables addressing all the 16 components of the vierbein field. By assuming the perfect fluid matter source, we examine the cosmological implication of the 6 unfamiliar new degrees of freedom in modified $f(T)$ gravity theories. We find that despite the new modes in the vierbein scenario provide no explicit significant effect in the small-scale regime, they exhibit some deviat…
We derive the Layzer-Irvine equation for alternative gravitational theories with non-minimal coupling between curvature and matter for an homogeneous and isotropic Universe. As an application, we study the case of Abell 586, a relaxed and spherically symmetric galaxy cluster, assuming some matter density profiles.
We consider a class of condensed matter theories in a Newtonian framework with a Lagrange formalism related in a natural way with the classical conservation laws \partial_t ρ+ \partial_i (ρv^i) = 0 \partial_t (ρv^j) + \partial_i (ρv^i v^j + p^{ij}) = 0 We show that for an algebraically defined ``effective Lorentz metric'' g_{μν} and ``effective matter fields'' ϕthese theories are equivalent to material models of a metric theory of gravity with Lagrangian L = L_{GR} + L_{matter} - (8πG)^{-1}(Υg^{00}-Ξ(g^{11}+g^{22}+g^{33}))\sqrt{-g} which fulfils the Einstein equivalence principle and leads to …
We uncover two mechanisms that can render Kerr black holes unstable in scalar-tensor gravity, both associated to the presence of matter in the vicinity of the black hole and the fact that this introduces an effective mass for the scalar. Our results highlight the importance of understanding the structure of spacetime in realistic, astrophysical black holes in scalar-tensor theories.
In this contribution one examines the generalization of the $f(R)$ theories of gravity where one introduces a non-minimal coupling between curvature and matter. This model has new and interesting features. %, specially concerning the energy exchange between the matter fields and the curvature. However, as any modified gravity theories, these may give origin to anomalies which might turn the theory physically meaningless. In this respect, one undertakes a study on the energy conditions and the Dolgov-Kawasaki criterion specific of this new model.
The importance of the first-class constraint algebra of general relativity is not limited just by its self-contained description of the gauge nature of spacetime, but it also provides conditions to properly evolve the geometry by selecting a gauge only once throughout the whole evolution of a gravitational system. This must be a property of all background independent theories. In this paper we consider gravitational theories which arise from deformations of the fundamental canonical variables of general relativity where the proposed deformations are inspired by modifications of gravity. These …
Consistency of EFT illuminated via relative entropy: A case study in scalar field theory
本文分析了标量场理论中的相对熵，发现基于算符和圈展开的微扰计算可能破坏其非负性，从而提出用相对熵符号来识别EFT描述的一致性，并在单场暴胀模型中导出了非线性参数$f_{\ m NL}$的约束关系。
We give a brief exposition of the approach based on the methods of spectral geometry and the spectral action principle to construction and analysis of models on a foliated space-time.
The chiral Lagrangian including more than two spin-3/2 fields becomes complex in general when the self-dual connection satisfies its equation of motion, and the imaginary part of the chiral Lagrangian gives the additional equation for spin-3/2 fields which gives rise to the inconsistency. This inconsistency can be removed by taking the tetrad to be complex and defining the total Lagrangian which is the sum of the chiral Lagrangian and its complex conjugate. It is possible to establish the right (left)-handed supersymmetry in its total Lagrangian as in the case of the chiral Lagrangian. We also…
In this work, one examines how the presence of a non-minimal coupling between the spacetime curvature and matter affects the evolution of cosmological perturbations around a homogeneous and isotropic Universe and hence the formation of large-scale structure. This framework places constraints on the terms which arise due to the coupling with matter and, in particular, on the modification in the growth of matter density perturbations. One obtains approximate analytical solutions for the evolution of matter overdensities during the matter dominated era and shows that these favor the presence of a…
The First Law of Black Hole Thermodynamics in Arbitrary Gravity and Matter Theories Using Differential Forms
研究利用微分形式推导任意引力和物质理论中黑洞热力学第一定律，给出统一方法，适用于含挠率和一般物质场的广泛理论并得出具体表达式。
Recently, in the context of $f(R)$ modified theories of gravity, a new type of model has been proposed where one directly couples the scalar curvature to matter. As any model in $f(R)$ theory, there are certain conditions which have to be satisfy in order to ensure that the model is viable and physically meaningful. In this paper, one considers this new class of models with curvature-matter coupling and study them from the point of view of the energy conditions and of their stability under the Dolgov-Kawasaki criterion.
Theories of gravity with nonminimal matter-curvature coupling and the de Sitter swampland conjectures
本文研究非最小物质-曲率耦合引力理论中单标量场暴胀与德西特沼泽地猜想的相容性，发现一般暴胀解的慢滚条件与该猜想不相容。
In this paper, we investigate the conservation laws of different type of particles in theories with a universal gravity/matter coupling. The result brings new insights about previous studies on universal gravity/matter theories. Especially, the paper demonstrates that for perfect fluids, there is an equivalence between the assumption $Ł_m=-ε$, where $ε$ is the total energy density; and the assumption that the matter fluid current is conserved ($\nabla_σ(ρu^σ)=0$, where $ρ$ is the rest mass density). However, the main result is given in the general case where one does not make any assumption on…
We study matter density perturbations up to third order and the one-loop matter power spectrum in degenerate higher-order scalar-tensor (DHOST) theories beyond Horndeski. We systematically solve gravitational field equations and fluid equations order by order, and find three novel shape functions characterizing the third-order solution in DHOST theories. A complete form of the one-loop matter power spectrum is then obtained using the resultant second- and third-order solutions. We confirm the previous result that the convergence condition of the loop integrals in the infrared limit becomes mor…
We study the late time cosmological evolution of $f(R)$ theories of modified gravity, with the matter content of the universe being that of collisional self interacting matter. We assume that the universe is described by a flat Friedmann-Lemaitre-Robertson-Walker metric and that it is matter and dark energy dominated. The results of our numerical analysis for a collisional matter $f(R)$ theory are compared with those resulting from pressure-less matter $f(R)$ theory and from the $\mathrmΛ\mathrm{CDM}$ model. As we shall demonstrate, the resulting picture can vary from model to model, indicatin…
We propose a method to study and constrain modified gravity theories for dark matter using CMB temperature anisotropies and polarization. We assume that the theories considered here have already passed the matter power-spectrum test of large-scale structure. With this requirement met, we show that a modified gravity theory can be specified by parametrizing the time evolution of its dark-matter density contrast, which is completely controlled by the dark matter stress history. We calculate how the stress history with a given parametrization affects the CMB observables, and a qualitative discuss…
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