Unimodular Cosmological models
Enrique Alvarez, Jesus Anero
本文指出在幺模引力框架中，宇宙加速膨胀的观测事实不能作为宇宙学常数或类似精髓存在的证据。
本文声称，在幺模引力框架下，宇宙指数膨胀的观测事实不能被视为存在宇宙学常数或类似精髓（quintessence）的证据。
It is claimed that in the unimodular gravity framework the observational fact of exponential expansion of the universe cannot be taken as evidence for the presence for a cosmological constant or similar quintessence.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
Resolution of the cosmological constant problem by unimodular gravity and signature reversal symmetry
本文通过单模引力和符号反转对称性解决宇宙学常数问题的第二部分，将四维时空视为高维bulk中的膜，从而解释宇宙学常数的微小值。
Unimodular gravity (UG) is an important theory which may explain the smallness of the cosmological constant. To get insight into the covariant quantization of UG, we discuss the BRST quantization of General Relativity (GR) with a cosmological constant in the unimodular gauge. We develop a novel way to gauge fix the transverse diffeomorphism (TDiff) and then further to fulfill the unimodular gauge. This process requires the introduction of an additional pair of BRST doublets which decouple from the physical sector together with the other three pairs of BRST doublets for the TDiff. We show that …
It is well known that the problem of the cosmological constant appears in a new light in Unimodular Gravity. In particular, the zero momentum piece of the potential does not automatically produce a corresponding cosmological constant. Here we show that quantum corrections do not renormalize the classical value of this observable.
Unimodular gravity is based on a modification of the usual Einstein-Hilbert action that allows one to recover general relativity with a dynamical cosmological constant. It also has the interesting property of providing, as the momentum conjugate to the cosmological constant, an emergent clock variable. In this paper we investigate the cosmological reduction of unimodular gravity, and its quantization within the framework of flat homogeneous and isotropic loop quantum cosmology. It is shown that the unimodular clock can be used to construct the physical state space, and that the fundamental fea…
The problem of the cosmological constant appears in a new light in Unimodular Gravity. In particular, the zero momentum piece of the potential (that is, the constant piece independent of the matter fields) does not automatically produce a cosmological constant proportional to it. The aim of this paper is to give some details on a calculation showing that quantum corrections do not renormalize the classical value of this observable.
It is shown that the one-loop effective action of unimodular gravity is the same as that of ordinary gravity, restricted to unimodular metrics. The only difference is in the treatment of the global scale degree of freedom and of the cosmological term. A constant vacuum energy does not gravitate, addressing one aspect of the cosmological constant problem.
Perturbative analysis of singularity-free cosmological solutions in unimodular Kaluza-Klein theory
本文研究了单模Kaluza-Klein理论中无奇点宇宙解的微扰分析，探讨了其稳定性及与标量场和物质源的关系。
We show that the conclusion that matter stress-energy tensor satisfies the usual covariant continuity law, and the cosmological constant is still a constant of integration arrived at by Finkelstein et al (42, 340, 2001) is not valid.
Unimodular gravity is classically equivalent to General Relativity. This equivalence extends to actions which are functions of the curvature scalar. At the quantum level, the dynamics could differ. Most importantly, the cosmological constant is not a coupling in the unimodular action, providing a new vantage point from which to address the cosmological constant fine-tuning problem. Here, a quantum theory based on the asymptotic safety scenario is studied, and evidence for an interacting fixed point in unimodular f(R) gravity is found. We study the fixed point and its properties, and also discu…
We study cosmological perturbation theory within the framework of unimodular gravity. We show that the Lagrangian constraint on the determinant of the metric required by unimodular gravity leads to an extra constraint on the gauge freedom of the metric perturbations. Although the main equation of motion for the gravitational potential remains the same, the shift variable, which is gauge artifact in General Relativity, cannot be set to zero in unimodular gravity. This non-vanishing shift variable affects the propagation of photons throughout the cosmological evolution and therefore modifies the…
We review selected aspects of unimodular gravity and we discuss its viability as a solution of the old cosmological constant problem. In unimodular gravity the cosmological constant is promoted to a global degree of freedom. We highlight the importance of correctly setting up its initial data in order to achieve a resolution of the cosmological constant problem on a semi-classical level. We review recent path integral analysis of quantum aspects of unimodular gravity to note that the semi-classical findings carry over to the quantum level as well. We point out that a resolution of the problem …
Unimodular Quadratic Gravity and the Cosmological Constant
本文将幺模约束施加于非微扰、背景无关的量子二次引力，证明其会改变部分暴胀量子可观测量，并提出由单次大爆炸中不同时代构成的多重宇宙以人择解释暗能量尺度。
Unimodular Gravity is one of the oldest geometric gravity theory alternative to General Relativity. Essentially, it is based on the Einstein-Hilbert Lagrangian with an additional constraint on the determinant of the metric. It can be explicitly shown that Unimodular Gravity can be recast as General Relativity in presence of a cosmological constant. This fact has led to many discussions on the equivalence of both theories at classical and quantum levels. Here we present an analysis focused on the classical scalar perturbations around a cosmological background. The discussion is extended for the…
Generalized Unimodular Gravity and Cosmological Perturbations
重新审视广义单模引力理论，通过纯几何方式获得宇宙的常规物质成分，为暗区研究提供新视角，并在背景和扰动分析中恢复广义相对论结果但解释不同。
We consider a model of gravity and matter fields which is invariant only under unimodular general coordinate transformations (GCT). The determinant of the metric is treated as a separate field which transforms as a scalar under unimodular GCT. Furthermore we also demand that the theory is invariant under a new global symmetry which we call generalized conformal invariance. We study the cosmological implications of the resulting theory. We show that this theory gives a fit to the high-z supernova data which is identical to the standard Big Bang model. Hence we require some other cosmological ob…
We propose the unimodular-mimetic $F(R)$ gravity theory, to resolve cosmological constant problem and dark matter problem in a unified geometric manner. We demonstrate that such a theory naturally admits accelerating universe evolution. Furthermore, we construct unimodular-mimetic $F(R)$ inflationary cosmological scenarios compatible with the Planck and BICEP2/Keck-Array observational data. We also address the graceful exit issue, which is guaranteed by the existence of unstable de Sitter vacua.
Unimodular relativity is a theory of gravity and space-time with a fixed absolute space-time volume element, the modulus, which we suppose is proportional to the number of microscopic modules in that volume element. In general relativity an arbitrary fixed measure can be imposed as a gauge condition, while in unimodular relativity it is determined by the events in the volume. Since this seems to break general covariance, some have suggested that it permits a non-zero covariant divergence of the material stress-energy tensor and a variable cosmological ``constant.'' In Lagrangian unimodular rel…
We compare the path integral for transition functions in unimodular gravity and in general relativity. In unimodular gravity the cosmological constant is a property of states that are specified at the boundaries whereas in general relativity the cosmological constant is a parameter of the action. Unimodular gravity with a nondynamical background spacetime volume element has a time variable that is canonically conjugate to the cosmological constant. Wave functions depend on time and satisfy a Schrödinger equation. On the contrary, in the covariant version of unimodular gravity with a 3-form gau…
We extend the idea of unimodular gravity to the modified $f(R,T)$ theories. A new class of cosmological solutions, that the unimodular constraint on the metric imposes on the $f(R,T)$ theories, are studied. This extension is done in both Jordan and Einstein frames. We show that while the Lagrange multiplier (that imposes the unimodular constraint on the action) depends on the cosmic time in Jordan frame and therefore, can act as an evolving scalar field in the universe history, in the Einstein frame it acts as a cosmological constant. Then a general reconstruction method is used to realize an …
The so-called unimodular version of General Relativity is revisited. Unimodular gravity is constructed by fixing the determinant of the metric, what leads to the trace-free part of the equations instead of the usual Einstein field equations. Then, a cosmological constant naturally arises as an integration constant. While unimodular gravity turns out equivalent to General Relativity (GR) at the classical level, it provides important differences at the quantum level. Here we extend the unimodular constraint to some extensions of General Relativity that have drawn a lot of attention over the last…
In this paper we investigate how to realize various quite well known cosmological bouncing models in the context of the recently developed unimodular $F(R)$ gravity. Particularly, we shall study the matter bounce scenario, the singular bounce, the superbounce and a symmetric bounce scenario. We present the behavior of the Hubble radius for each of the bouncing models we shall take into account and we investigate which era of the bouncing model is responsible for the cosmological perturbations. As we shall demonstrate, the various bouncing models do not behave in the same way, so the cosmologic…
Unimodular-like times, evolution and Brans-Dicke Gravity
本文将类幺模理论中的自然常数视为相空间变量，考察其正则时间与 Brans-Dicke 标量场框架的耦合，筛选兼具参数共变和能量守恒破缺特征的理论。
We study some aspects of cosmological inflation in the framework of unimodular $f(R)$ gravity. To be more clarified, we consider a generic $f(R)$ of the type $f(R)=R+αR^{n}$. By considering Einstein frame counterpart of the unimodular $f(R)$ gravity, we set the scalaron to be responsible for cosmological inflation in this setup. We confront our model parameters space with observational data and impose some constraints on the value of $n$ in this manner. We show that for the number of e-folds $N=60$, the model is consistent with observation if $1.89<n<1.918$.
We investigate path integral quantization of two versions of unimodular gravity. First a fully diffeomorphism-invariant theory is analyzed, which does not include a unimodular condition on the metric, while still being equivalent to other unimodular gravity theories at the classical level. The path integral has the same form as in general relativity (GR), except that the cosmological constant is an unspecified value of a variable, and it thus is unrelated to any coupling constant. When the state of the universe is a superposition of vacuum states, the path integral is extended to include an in…
We combine the unimodular gravity and mimetic gravity theories into a unified theoretical framework, which is proposed to provide a suggestive proposal for a framework that may assist in the discussion and solution search of the cosmological constant problem and of the dark matter issue. After providing the formulation of the unimodular mimetic gravity and investigating all the new features that the vacuum unimodular gravity implies, by using the underlying reconstruction method, we realize some well known cosmological evolutions, with some of these being exotic for the ordinary Einstein-Hilbe…
Revisiting Unimodular Quantum Cosmology
本文重新审视迷你超空间中幺模引力的量子化分析，将其扩展到幻影标量场与Brans-Dicke标量张量理论，论证仅幻影场可获非平凡演化，标度因子呈现反弹接德西特膨胀，重现广义相对论量子宇宙学场景。
This chapter provides an introduction to Unimodular Gravity both at the classical and quantum level, discussing the rôle it might play in the partial solution of the Cosmological Constant problem. The main objective of this work is to serve as a conceptual introduction to Unimodular gravity without disregarding computational detail. In that sense, techniques used at the research level are presented and applied in detail.
A cosmological time variable is emerged from the hamiltonian formulation of unimodular theory of gravity to measure the evolution of dynamical observables in the theory. A set of constants of motion has been identified for the theory on the null hypersurfaces that its evolution is with respect to the volume clock introduced by the cosmological time variable.
Unimodular gravity is an interesting approach to address the cosmological constant problem, since the vacuum energy density of quantum fields does not gravitate in this framework, and the cosmological constant appears as an integration constant. These features arise as a consequence of considering a constrained volume element 4-form that breaks the diffeomorphisms invariance down to volume preserving diffeomorphisms. In this work, the first-order formulation of unimodular gravity is presented by considering the spin density of matter fields as a source of spacetime torsion. Even though the mos…
Comment on Cosmological constraints on unimodular gravity models with diffusion (arXiv:2211.07424): thermodynamic inadmissibility of the H0 tension resolution mechanism
该文指出，基于扩散的UG模型无法满足热力学第二定律，证明了其无法同时满足第二定律和产生正的有效宇宙学常数项，从而无法缓解H0张力。
The recently suggested generalized unimodular gravity theory, which was originally put forward as a model of dark energy, can serve as a model of cosmological inflation driven by the effective perfect fluid -- the dark purely gravitational sector of the theory. Its excitations are scalar gravitons which can generate, in the domain free from ghost and gradient instabilities, the red tilted primordial power spectrum of CMB perturbations matching with observations. The reconstruction of the parametric dependence of the action of the theory in the early inflationary Universe is qualitatively sketc…
We revisit a mechanism proposed by Hawking to resolve the cosmological constant problem (and the controversy it generated) to identify possibly more palatable alternatives and explore new connections and interpretations. In particular, through the introduction of a new action coupling the four-form field strength $F = dA$ to the cosmological constant via a dynamical field $λ(x)$, a novel Baum-Hawking-Coleman type mechanism is presented. This mechanism can be seen as a generalisation of Unimodular Gravity. A theory with a similar coupling to "$F^2$" is also presented, with promising results. We…
Geometrical Trinity of Unimodular Gravity
本文通过Weyl补偿子形式构造Weyl横向微分同胚不变的远平行引力，证明其非线性等价于单模引力，并结合对称远平行引力实现单模引力的三种几何表示。
Redshifting the Cosmological Constant in Unimodular Gravity via Nonlinear Quantum Mechanics
针对幺模引力中“影子”宇宙学常数的初始条件微调问题，本文基于非线性量子力学向哈密顿量引入度规期望值相关状态依赖项，使影子能量密度随宇宙膨胀红移并在晚期可忽略，且该红外修正与引力测试一致，还提出了检验方案。
In this review we discuss emergence of unimodular gravity (or, more precisely, Weyl transverse gravity) from thermodynamics of spacetime. By analyzing three different ways to obtain gravitational equations of motion by thermodynamic arguments, we show that the results point to unimodular rather than fully diffeomorphism invariant theories and that this is true even for modified gravity. The unimodular character of dynamics is especially evident from the status of cosmological constant and energy-momentum conservation.
Nonexistence of a parent theory for general relativity and unimodular gravity
本文研究广义相对论与单模引力是否存在以完整微分同胚和外尔变换为规范对称性的母理论，通过引入 Stueckelberg 场发现 UG 中宇宙学常数对应的额外全局自由度阻碍了母理论的构造。
Gödel-type universes in unimodular gravity
本研究在幺模引力框架下检验哥德尔型解的有效性，发现该理论中宇宙学常数为积分常数，且特定引力源下因果与非因果区域均允许存在。
Unimodular quantum cosmology in the connection representation: A minimal model
该研究在连接表象中对单模引力进行量子化，揭示了正宇宙学常数下波函数在零体积处消失的现象，并探讨了半经典几何波动与宇宙学常数问题的关系。
de Sitter Space Decay and Cosmological Constant Relaxation in Unimodular Gravity with Charged Membranes
本文证明在含带电膜的单模引力中德西特空间不稳定并衰变，通量不可公度时形成离散态集，且近闵可夫斯基空间为唯一长时吸引子，从而无需人择原理即可自然得到微小宇宙学常数。
We propose a unimodular version of the Brans-Dicke theory designed with a constrained Lagrangian formulation. The resulting field equations are traceless. The vacuum solutions in the cosmological background reproduce the corresponding solutions of the usual Brans-Dicke theory but with a cosmological constant term. A perturbative analysis of the scalar modes is performed and stable and unstable configurations appear in contrast with the Brans-Dicke case for which only stable configurations occur. On the other hand, tensorial modes in this theory remains the same as in the traditional Brans-Dick…
Unimodular gravity is classically equivalent to standard Einstein gravity, but differs when it comes to the quantum theory: The conformal factor is non-dynamical, and the gauge symmetry consists of transverse diffeomorphisms only. Furthermore, the cosmological constant is not renormalized. Thus the quantum theory is distinct from a quantization of standard Einstein gravity. Here we show that within a truncation of the full Renormalization Group flow of unimodular quantum gravity, there is a non-trivial ultraviolet-attractive fixed point, yielding a UV completion for unimodular gravity. We disc…
In this work we review the issue of imposing the conservation of the energy-momentum tensor as a necessary condition to recover the equivalence between the unimodular gravity and General Relativity (GR) equipped with a cosmological constant. This procedure is usually interpreted as an {\it ad hoc} imposition on the unimodular theory's structure. Whereas the consequences of avoiding the conservation of the total energy-momentum tensor has been already introduced in the literature, it has been not widely explored so far. We study an expanding universe sourced by a single effective perfect fluid …
A unimodular Kaluza-Klein theory
本文探讨了在包含标量场的5维 Kaluza-Klein 理论中施加幺模条件的可能性，通过在5维中表述变分原理并降维，提出并讨论了相应的宇宙学模型。
Cosmological aspects of the unimodular-mimetic $f(\mathcal{G})$ gravity
本研究提出单模-模拟$f(\mathcal{G})$引力，通过重构方案和逆向技术导出具体函数，验证其与BICEP2/Keck及Planck数据兼容，能描述混合膨胀、幂律演化及对称反弹，并解释符合观测的暴胀。
On the Stability of Non-Singular Solutions in Effective Theory from Kaluza-Klein Unimodular Gravity
该研究探讨了五维Kaluza-Klein单模引力约化后所得标量-张量理论中真空反弹解的四维正则性，发现引力波传播存在不稳定性，并与含宇宙学常数的四维量子模型进行了对比。
Gauge fixing in cosmological perturbations of Unimodular Gravity
本研究在幺模引力框架下推导牛顿与同步规范的等价形式，首次证明二者可自洽固定但异于广义相对论，揭示了其对冷暗物质密度扰动的影响并验证了萨克斯-沃尔夫效应。
Unimodular Gravity is an alternative to General Relativity (GR) which, however, is so closely related to the latter that one can wonder to what extent they are different. The different behavior of the cosmological constant in the semiclassical regimes of both frameworks suggests the possible existence of additional contrasting features. UG and GR are based on two different gauge symmetries: UG is based on transverse diffeomorphisms and Weyl rescalings (WTDiff transformations), whereas GR is based on the full group of diffeomorphisms. This difference is related to the existence of a fiduciary b…
Black hole singularity resolution in unimodular gravity from unitarity
本文通过要求幺模引力自然时间坐标下的幺正性，研究平面AdS黑洞内部的量子动力学，发现经典奇点与视界被高度量子区域取代，并论证幺模时间幺正性普遍导致黑洞奇点消解。
Classically, unimodular gravity is known to be equivalent to General Relativity (GR), except for the fact that the effective cosmological constant $Λ$ has the status of an integration constant. Here, we explore various formulations of unimodular gravity beyond the classical limit. We first consider the non-generally covariant action formulation in which the determinant of the metric is held fixed to unity. We argue that the corresponding quantum theory is also equivalent to General Relativity for localized perturbative processes which take place in generic backgrounds of infinite volume (such …
Holographic Ricci dark energy in Nonconservative Unimodular Gravity
本文在非保守单模引力框架下构建了基于Ricci标量截断的全息暗能量宇宙学模型，引入物质与暗能量相互作用项求解参数，统计表明其虽不及ΛCDM模型但具竞争力。
We propose a mechanism for generating an inflationary phase in the early universe without resorting to any type of scalar field(s). Instead, this accelerated expansion is driven by a dynamical "cosmological constant" in the framework of unimodular gravity. The time dependent cosmological constant can be related to an energy diffusion term that arises naturally in unimodular gravity due to its restrictive diffeomorphism invariance. We derive the generic conditions required for any type of diffusion to generate a realistic inflationary epoch. Furthermore, for a given parameterization of inflatio…
Unimodular Gravity is normally assumed to be equivalent to General Relativity for all matters but the character of the Cosmological Constant. Here we discuss this equivalence in the presence of a non-minimally coupled scalar field. We show that when we consider gravitation to be dynamical in a QFT sense, quantum corrections can distinguish both theories if the non-minimal coupling is non-vanishing. In order to show this, we construct a path integral formulation of Unimodular Gravity, fixing the complicated gauge invariance of the theory and computing all one-loop divergences. We find a combina…
We compute the lowest order gravitational UV divergent radiative corrections to the S matrix element of the $fermion + fermion\rightarrow fermion + fermion$ scattering process in the massive Yukawa theory, coupled either to Unimodular Gravity or to General Relativity. We show that both Unimodular Gravity and General Relativity give rise to the same UV divergent contribution in Dimensional Regularization. This is a nontrivial result, since in the classical action of Unimodular Gravity coupled to the Yukawa theory, the graviton field does not couple neither to the mass operator nor to the Yukawa…
Unimodular gravity is an appealing approach to address the cosmological constant problem. In this scenario, the vacuum energy density of quantum fields does not gravitate and the cosmological constant appears merely as an integration constant. Recently, it has been shown that energy diffusion that may arise in quantum gravity and in theories with spontaneous collapse is compatible with this framework by virtue of its restricted diffeomorphism invariance. New studies suggest that this phenomenon could lead to higher-order equations in the context of homogeneous and isotropic Universe, affecting…
We extend the formalism of the Einstein-Hilbert unimodular gravity in the context of modified $F(R)$ gravity. After appropriately modifying the Friedmann-Robertson-Walker metric in a way that it becomes compatible to the unimodular condition of having a constant metric determinant, we derive the equations of motion of the unimodular $F(R)$ gravity by using the metric formalism of modified gravity with Lagrange multiplier constraint. The resulting equations are studied in frames of reconstruction method, which enables us to realize various cosmological scenarios, which was impossible to realize…
We have investigated the vacuum maximally symmetric solutions of recently proposed density-metric unimodular gravity theory,the results are widely different from inflationary senario.The exponential dependence on time in deSitter space is substiuted by a power law. Open space-times with non-zero cosmological constant are excluded in this theory
Unimodular Gravity with Arbitrary Diffusion Function: A Dynamical System Reconstruction Approach
本研究在动力学系统重构框架下，于幺模引力中系统构建并分类扩散宇宙学，确定了相关不动点与标度解，实现无需宇宙学常数的晚期加速膨胀，提供了扩散宇宙学的全局探索方法。
Duru-Kleinert Path Integral in Unimodular Quantum Cosmology
本文采用Duru-Kleinert路径积分技术，研究单模量子宇宙学与氢原子的对应关系，推导量子化负宇宙学常数，计算宇宙从“无”的隧穿率及正宇宙学常数下的谱密度与Krylov复杂度。
A Five-dimensional Kaluza-Klein Approach to Unimodular Gravity
本文在含标量场的五维 Kaluza-Klein 理论中引入单模条件，在前期变分与维数约化及宇宙学模型基础上，进一步研究解的微扰性质与稳定性。
In our previous paper, we have presented a covariant BRST quantization of unimodular gravity which may account for the smallness of the cosmological constant, and have shown that the physical degrees of freedom in the theory are the same as general relativity. The formulation has been given by using rank-2 antisymmetric tensor fields for both ghosts and antighosts. Here we give an alternative formulation using a vector field for the antighost but keeping the same structure for the ghosts. This gives a significantly simpler covariant quantization with less ghosts and no tripole modes in the gho…
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。