Fotis Farakos
In this contribution we revisit higher curvature N=1 supergravity and discuss the quintessence phase that can appear due to the $R^4$ terms. In particular we focus on the bosonic supersymmetric completion within the old-minimal and the new-minimal formulations.
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The issue of Supersymmetry breaking in the context of Supergravity models of Quintessence is discussed.
We prove (in superspace) the equivalence between the higher-derivative N=1 supergravity, defined by a holomorphic function F of the chiral scalar curvature superfield, and the standard theory of a chiral scalar superfield with a chiral superpotential W, coupled to the (minimal) Poincare supergravity in four spacetime dimensions. The relation between the holomorphic functions F and W is found. It can be used as the technical framework for the possible scenario unifying the early Universe inflation and the present Universe acceleration. We speculate on the possible origin of our model as the eff…
The evolution of the quintessence field during a phase of chaotic inflation is studied. The inflaton and the quintesssence field are described in a supergravity framework where the coupling between the inflaton and quintessence is induced by non-renormalisable operators suppressed by the Planck mass. We show that the resulting quintessence potential during inflation possesses a time--dependent minimum playing the role of an attractor. The presence of this attractor forces the quintessence field to be small during inflation. These initial conditions are such that the quintessence field is on tr…
It was recently pointed out that the cosmological constant (even metastable one) belongs to the so-called "swampland" and hence cannot be obtained as the low-energy limit of string theory that requires $|\nabla V| > c V$. If true, the dark energy needs to be described by an evolving scalar field, i.e., quintessence with $w>-1$ within supergravity. However, the large hierarchy between the supersymmetry breaking scale and the energy scale of dark energy imposes a challenge on building quintessence models in supergravity as the quintessence field typically acquires a mass of order the gravitino m…
In the context of quintessence, the concept of tracking solutions allows to address the fine-tuning and coincidence problems. When the field is on tracks today, one has $Q\approx m_{\rm Pl}$ demonstrating that, generically, any realistic model of quintessence must be based on supergravity. We construct the most simple model for which the scalar potential is positive. The scalar potential deduced from the supergravity model has the form $V(Q)=\frac{Λ^{4+α}}{Q^α}e^{\fracκ{2}Q^2}$. We show that despite the appearence of positive powers of the field, the coincidence problem is still solved. If $α\…
Inspired by the stringy quintessence F-term problem we highlight a generic contribution to the effective moduli masses that arises due to kinetic mixings between the moduli and the quintessence sector. We then proceed to discuss few supergravity toy models that accommodate such effect, and point out possible shortcomings. Interestingly, in the standard 2-derivative supergravity action there is no term to mediate the supersymmetry breaking from the kinetic quintessence sector to the gaugini and generate Majorana masses. Therefore we also propose a 2-derivative supersymmetric invariant that play…
The status of exponential scalar potentials in supergravity is reviewed, and updated. One version of N=8 D=4 supergravity with a positive exponential potential, obtainable from a `non-compactification' of M-theory, is shown to have an accelerating cosmological solution that realizes `eternal quintessence'. Some implications for a de Sitter version of the domain wall/QFT correspondence are discussed.
Thermodynamics and optical aspects of ModMax black holes in higher order curvature gravity with quintessence dark energy
本文研究了将电磁场与暗能量耦合的高阶曲率引力中的ModMax黑洞，分析其热力学稳定性及相结构，探讨了高阶曲率修正和暗能量对黑洞阴影的影响。
We discuss the phenomenological model in which the potential energy of the quintessence field depends linearly on the energy density of the spatial curvature. We find that the pressure of the scalar field takes a different form when the potential of the scalar field also depends on the scale factor and the energy momentum tensor of the scalar field can be expressed as the form of a perfect fluid. A general coupling was proposed to explain the current accelerating expansion of the Universe and solve the fine-tuning problem.
In this paper we derive the most general curvature squared action coupled to an arbitrary number of vector multiplets in four dimensional $N=2$ supergravity using the dilaton Weyl multiplet. The action that we derive is encoded in a single holomorphic prepotential.
The issues of quintessence and cosmic acceleration can be discussed in the framework of $F(R, {\cal G})$ theories of gravity where $R$ is the Ricci curvature scalar and ${\cal G}$ is the Gauss-Bonnet topological invariant. It is possible to show that such an approach exhausts all the curvature content related to the Riemann tensor giving rise to a fully geometric approach to dark energy.
We study cosmological $α$-attractors in superconformal/supergravity models, where $α$ is related to the geometry of the moduli space. For $α=1$ attractors \cite{Kallosh:2013hoa} we present a generalization of the previously known manifestly superconformal higher curvature supergravity model \cite{Cecotti:1987sa}. The relevant standard 2-derivative supergravity with a minimum of two chiral multiplets is shown to be dual to a 4-derivative higher curvature supergravity, where in general one of the chiral superfields is traded for a curvature superfield. There is a degenerate case when both matter…
Supersymmetric Index for Half BPS Black Holes in N=2 Supergravity with Higher Curvature Corrections
本文在带有高曲率修正的 N=2 超引力中计算了半 BPS 黑洞的超对称指标，并证明其与携带相同电荷的超对称极端黑洞的简并度在引力层面上完全一致。
We find a class of d=4, N=2 supergravity with $R^2$-interactions that admits exact BPS black holes. The prepotential contains quadratic, cubic and chiral curvature-squared terms. Black hole geometry realizes stretched horizon, and consists of anti-de Sitter, intermediate and outermost flat regions. Mass and entropy depends on charges and are modified not only by higher curvature terms but also by quadratic term in the prepotential. Consequently, even for large charges, entropy is no longer proportional to mass-squared.
Criticality Quenching and Microstructure of Quintessence-AdS Black Holes
本文研究了在巨 canonical 集合中，包含五维反物质的 Reissner-Nordstrom 反德西特黑洞的热力学几何。通过 Ruppeiner 曲率标量分析，揭示了低电势下吸引相互作用主导，高电势下排斥相互作用占优的特性，并发现相互作用强度在相变中保持稳定。
We calculate the f(R) gravity function in the dual gravity description of the quintessence model with a quadratic (Linde) scalar potential and a positive cosmological constant. We find that in the large curvature regime relevant to chaotic inflation in early Universe, the dual f(R) gravity is well approximated by the (matter) loop-corrected Starobinsky inflationary model. In the small curvature regime relevant to dark energy in the present Universe, the f(R) gravity function reduces to the Einstein-Hilbert one with a positive cosmological constant.
The subject of this thesis is cosmological implications of string compactifications understood in a broad sense. In the first half of the thesis, we will begin by reviewing the four-dimensional description of the tree-level perturbative type IIB action. We will then review a number of open questions in cosmology and their relevance with regards to the remainder of the thesis. We will first explore some of these cosmological questions from the perspective of effective field theories motivated by supergravity. From the naturalness of dark energy and how to obtain a naturally light dark energy fi…
A cosmological constant in the regime of low space-time curvature is calculated in the recently proposed version of F(R) supergravity with a generic cubic function F. The F(R) supergravity is the N=1 supersymmetric extension of f(R) gravity. The cubic model is known to successfully describe a chaotic (slow-roll) inflation in the regime of high space-time curvature. We find that a simple extension of the same model allows a positive cosmological constant in the regime of low space-time curvature. The inflaton superfield in F(R) supergravity (like inflaton in f(R) gravity) violates the Strong En…
To curve, or not to curve: Is curvature-assisted quintessence observationally viable?
针对开放宇宙中新稳定不动点或可挽救陡峭势单场加速膨胀的观点，本文结合动力系统分析与贝叶斯参数推断，证明曲率辅助的 quintessence 及暴胀模型仍不具观测可行性。
In these lectures, after a short introduction to cosmology, we discuss the supergravity embedding of higher curvature models of inflation. The supergravity description of such models is presented for the two different formulations of minimal supergravity.
Inflationary slow-roll dynamics in Einstein gravity with a non-minimal scalar-curvature coupling can be equivalent to that in the certain f(R) gravity theory. We review the correspondence and extend it to N=1 supergravity. The non-minimal coupling in supergravity is rewritten in terms of the standard (`minimal') N=1 matter-coupled supergravity by using curved superspace. The established equivalence between two different inflationary theories means the same inflaton scalar potential, and does not imply the same post-inflationary dynamics and reheating.
We present the N = 2 supersymmetric completion of a scalar curvature squared term in a completely gauge independent form. We also elaborate on its component structure.
It is known that, for zero fermionic sector, the bosonic equations of Cremmer-Julia-Scherk eleven-dimensional supergravity can be collected in a compact expression which is a condition on the curvature of the generalized connection. Here we peresent the equation which collects all the bosonic equations of D=11 supergravity when the gravitino is nonvanishing.
Off-shell formulations of supergravities allow one to add closed-form higher-derivative super-invariants that are separately supersymmetric to the usual lower-derivative actions. In this paper we study four-dimensional off-shell N=1 supergravity where additional super-invariants associated with the square of the Weyl tensor and the square of the Ricci scalar are included. We obtain a variety of solutions where the metric describes domain walls, Lifshitz geometries, and also solutions of a kind known as gyratons. We find that in some cases the solutions can be supersymmetric for appropriate cho…
We examine the known Riemann curvature corrections to the supergravity action at order $α'^3$ under the T-duality transformations. Using the compatibility of the action with the linear T-duality and with the S-matrix calculations as guiding principles, we have found the couplings of four $B$-field strengths and the couplings of two Riemann curvatures and two $B$-field strengths at order $α'^3$. Using the S-matrix calculations we have also found new dilaton couplings in the string frame at this order.
Off-shell invariants of linearized $4D, \mathcal{N}=2$ supergravity in the harmonic approach
利用谐和超空间方法，在线性化层次上构造了推广标量曲率、里奇曲率和外尔张量的 $\mathcal{N}=2$ 超对称曲率，并基于这些超曲率构建了各种线性化 $4D, \mathcal{N}=2$ 爱因斯坦超引力不变量。
Curvatures and Non-metricities in the Non-Relativistic Limit of Bosonic Supergravity
本文提出非相对论极限下玻色超引力的度量类形式化方法，通过非度量性重构相对论张量，并建立弦牛顿-卡坦几何的体积元方法与该构造的等价性。
We examine the NS-NS corrections to the type II supergravity given by Gross and Sloan, under the linear T-duality transformations. We show that the gravity and the B-field couplings are invariant under off-shell T-duality, whereas the dilaton couplings are invariant under on-shell T-duality. Requiring the compatibility of the dilaton couplings with off-shell T-duality as a guiding principle, we extend them to include the appropriate Ricci curvature and the divergence of the B-field strength.
We investigate cosmological scenarios with a non-minimal derivative coupling between the scalar field and the curvature, examining both the quintessence and the phantom cases in zero and constant potentials. In general, we find that the universe transits from one de Sitter solution to another, determined by the coupling parameter. Furthermore, according to the parameter choices and without the need for matter, we can obtain a Big Bang, an expanding universe with no beginning, a cosmological turnaround, an eternally contracting universe, a Big Crunch, a Big Rip avoidance and a cosmological boun…
It is demonstrated that any realistic model of quintessence should be based on Supergravity since, when the scalar field is on tracks today, $Q\approx m_{\rm Pl}$. This improves the agreement between theoretical predictions and the current observations. In particular, a generic property is that ratio $ω_{\rm Q}\equiv p_{\rm Q}/ρ_{\rm Q}$ is pushed towards -1. A string-inspired model is proposed where the potential is given by $V(Q)= \frac{Λ^{4+α}}{Q^α}e^{\fracκ{2}Q^2}$. The model predicts $ω_{\rm Q}\approx -0.82$, a value less that one sigma from the current likehood value.
In the framework of linearized non-minimal supergravity (20/20), we present the embedding of the $R + R^2$ model and we analyze its field spectrum. As usual, the auxiliary fields of the Einstein theory now become propagating, giving rise to additional degrees of freedom, which organize themselves into on-shell irreducible supermultiplets. By performing the analysis both in component and superspace formulations we identify the new supermultiplets. On top of the two massive chiral superfields reminiscent of the old-minimal supergravity embedding, the spectrum contains also a consistent physical,…
We focus on non-linear realizations of local supersymmetry as obtained by using constrained superfields in supergravity. New constraints, beyond those of rigid supersymmetry, are obtained whenever curvature multiplets are affected as well as higher derivative interactions are introduced. In particular, a new constraint, which removes a very massive gravitino is introduced, and in the rigid limit it merely reduces to an explicit supersymmetry breaking. Higher curvature supergravities free of ghosts and instabilities are also obtained in this way. Finally, we consider direct coupling of the gold…
We revisit an emergent gravity scenario in $(4+1)$ dimensions underlying a propagating geometric torsion ${\cal H}_3$ with a renewed interest. We show that a pair-symmetric $4$th order curvature tensor is sourced by a two-form Neveu-Schwarz (NS) in a $U(1)$ gauge theoretic formulation. Interestingly the new space-time curvature governs a torsion free geometry sourced by a two-form NS field and shares the properties of the Riemann tensor. On the other hand, a completely anti-symmetric $4$th order tensor in the formulation is shown to incorporate a dynamical geometric torsion correction and is a…
We observe that the replacement of the Riemann curvature with the generalized Riemann curvature into the corrections to the type II supergravity at order $α'^3$ which are in terms of the contractions of four Riemann curvatures $R^4$, is not fully consistent with the S-matrix elements in the superstring theory. In particular, they produce non-zero S-matrix elements for odd number of B-field strengths which are not consistent with the string theory results. Using the consistency of the couplings with the linear T-duality as a guiding principle, we consider all T-duality invariant couplings and f…
On curvature-squared invariants of minimal five-dimensional supergravity from superspace
本文在最小五维超引力的离壳超空间框架中，系统构造并给出了三个四导数曲率平方不变量的显式表达，首次推导出任意组合变形后的主运动方程，并识别出可用于标量曲率平方超对称补全的新不变量。
We describe the supersymmetric completion of several curvature-squared invariants for ${\cal N}=(1,0)$ supergravity in six dimensions. The construction of the invariants is based on a close interplay between superconformal tensor calculus and recently developed superspace techniques to study general off-shell supergravity-matter couplings. In the case of minimal off-shell Poincaré supergravity based on the dilaton-Weyl multiplet coupled to a linear multiplet as a conformal compensator, we describe off-shell supersymmetric completions for all the three possible purely gravitational curvature-sq…
The superspace formulation of N=1 conformal supergravity in four dimensions is demonstrated to be equivalent to the conventional component field approach based on the superconformal tensor calculus. The detailed correspondence between two approaches is explicitly given for various quantities; superconformal gauge fields, curvatures and curvature constraints, general conformal multiplets and their transformation laws, and so on. In particular, we carefully analyze the curvature constraints leading to the superconformal algebra and also the superconformal gauge fixing leading to Poincare supergr…
In the new-minimal supergravity formulation we present the embedding of the $R+R^2$ Starobinsky model of inflation. Starting from the superspace action we perform the projection to component fields and identify the Starobinsky model in the bosonic sector. Since there exist no other scalar fields, this is by construction a single field model. This higher curvature supergravity also gives rise to a propagating massive vector. Finally we comment on the issues of higher order corrections and initial conditions.
In the N=1 four-dimensional new-minimal supergravity framework, we supersymmetrise the coupling of the scalar kinetic term to the Einstein tensor. This coupling, although introduces a non-minimal derivative interaction of curvature to matter, it does not introduce harmful higher-derivatives. For this construction, we employ off-shell chiral and real linear multiplets. Physical scalars are accommodated in the chiral multiplet whereas curvature resides in a linear one.
We evaluate one-loop amplitudes of N = 4 supergravity in D dimensions using the double-copy procedure that expresses gravity integrands in terms of corresponding ones in Yang--Mills theory.We organize the calculation in terms of a set of gauge-invariant tensors, allowing us to identify evanescent contributions. Among the latter, we find the matrix elements of supersymmetric completions of curvature-squared operators. In addition, we find that such evanescent terms and the U(1)-anomalous contributions to one-loop N = 4 amplitudes are tightly intertwined. The appearance of evanescent operators i…
Carrollian bosonic supergravity at order $α'$ and the universal cancellation of higher-curvature divergences
研究玻色子超引力的卡罗尔极限，通过纳入α'修正项证明其保持有限，构建有效作用量。建立通用标准确定高曲率贡献的有限性，应用此标准证明α'²和α'³修正的卡罗尔极限有限并推导其对作用量的贡献。
We investigate the effect of (Curvature)^2-terms on N=1 and N=2 supergravity in three dimensions. We use the off-shell component fields (e_μ^m, ψ_μ, S) for N=1 and (e_μ^m, ψ_μ, ψ_μ^*, A_μ, B, B^*) for N=2 supergravity. The S, A_μand B are respectively a real scalar, a real vector and a complex scalar auxiliary fields. Both for N=1 and N=2, only two invariant actions for (Curvature)^2-terms exist, while only the actions with (Scalar Curvature)^2 are free of negative energy ghosts. Interestingly, the originally non-physical graviton and gravitino fields start propagating, together with the scala…
Components of curvature-squared invariants of minimal supergravity in five dimensions
本文首次给出五维离壳最小超引力全部曲率平方不变量的超对称完备化分量结构，利用超空间与超共形张量计算技术构造离壳庞加莱超引力，并推导出变形后的运动方程及其协变后代。
The generic embedding of the $R+R^2$ higher curvature theory into old-minimal supergravity leads to models with rich vacuum structure in addition to its well-known inflationary properties. When the model enjoys an exact R-symmetry, there is an inflationary phase with a single supersymmetric Minkowski vacuum. This appears to be a special case of a more generic set-up, which in principle may include R-symmetry violating terms which are still of pure supergravity origin. By including the latter terms, we find new supersymmetry breaking vacua compatible with single-field inflationary trajectories.…
A scale invariant Goldstino theory coupled to Supergravity is obtained as a standard supergravity dual of a rigidly scale invariant higher--curvature Supergravity with a nilpotent chiral scalar curvature. The bosonic part of this theory describes a massless scalaron and a massive axion in a de Sitter Universe.
On five-dimensional curvature squared supergravity and holography
本文研究五维曲率平方不变量在N=1超引力中的构造，提出复合多重态结构，并计算其对黑洞的引力和CFT结果的修正，展现精确匹配。
Has DESI detected exponential quintessence?
本文利用 DESI DR2 数据对指数势单场精质场模型进行贝叶斯分析，发现其拟合优度显著优于 ΛCDM，并以约 3.5σ 显著性偏好非零 λ，同时暗示宇宙可能存在负曲率。
We consider the exact solutions of the supergravity theories in various dimensions in which the space-time has the form M_{d} x S^{D-d} where M_{d} is an Einstein space admitting a conformal Killing vector and S^{D-d} is a sphere of an appropriate dimension. We show that, if the cosmological constant of M_{d} is negative and the conformal Killing vector is space-like, then such solutions will have a conformal Penrose limit: M^{(0)}_{d} x S^{D-d} where M^{(0)}_{d} is a generalized d-dimensional AdS plane wave. We study the properties of the limiting solutions and find that M^{(0)}_{d} has 1/4 s…
Large curvature fluctuations from no-scale supergravity with a spectator field
本文在无标度超引力的SU(2,1)/SU(2)×U(1)对称框架下，提出将模场作为轻旁观者场，通过其暴胀后量子涨落产生大曲率扰动，从而在不微调参数且满足CMB约束的情况下解释原初黑洞的形成。
We compute the macroscopic entropy of the supersymmetric rotating dyonic strings carrying linear momentum in 6D (1,0) supergravity with curvature squared corrections. Our calculation is based on Sen's entropy function formalism applied to the near-horizon geometry of the string solution taking the form of an extremal BTZ$\times S^3$. The final entropy formula states that the two independent supersymmetric completions of Riemann tensor squared contribute equally to the entropy. A further $S^3$ compactification of the 6D theory results in a matter coupled 3D supergravity model in which the quant…
We construct dual supergravity descriptions of D3-branes wrapping associative 3-cycles $L$. We analyse the conditions for having five-dimensional background solutions of the form $AdS_2 \times L$ and show that they require $L$ to be of constant negative curvature type. This provides $AdS_2$ background solutions when $L$ is the hyperbolic space $H^3$ or its quotients by subgroups of its isometry group. We construct a regular numerical solution interpolating between $AdS_5$ in the UV and $AdS_2 \times H^3$ in the IR. The IR fixed point exists at the ``intersection'' of the Coulomb and Higgs bran…
Curvature divergences in 5d $\mathcal{N} = 1$ supergravity
研究五维 $\mathcal{N}=1$ 超重力中矢量模空间标量曲率发散现象，揭示强耦合奇点与 SCFT 和 LST 的关系。
The complete structure of curvature squared terms is analyzed in the context of chirally extended supergravity, with special emphasis on the gravitationally induced Fayet-Iliopoulos D--term. Coupling of (chiral) matter is discussed in relation with a possible extension to U(1) supergravity of the equivalence mechanism between $\cR+\al\cR^2$ and General Relativity coupled to a scalar.
We construct IIB supergravity (viewed as dilatonic gravity) background with non-trivial dilaton and with curved four-dimensional space. Such a background may describe another vacuum of maximally supersymmetric Yang-Mills theory or strong coupling regime of (non)-supersymmetric gauge theory with (power-like) running gauge coupling which depends on curvature. Curvature dependent quark-antiquark potential is calculated where the geometry type of hyperbolic (or de Sitter universe) shows (or not) the tendency of the confinement. Generalization of IIB supergravity background with non-constant axion …
Holographic Consequences of Heterotic String Theory beyond its Supergravity Approximation
本文研究了超越超引力近似的 heterotic 弦论修正对低能有效作用量的影响，发现紧致化引入的高阶导数耦合会移动稳定性界限、重整化群流及全息超导体的临界温度，其效果取决于通量或曲率主导。
Using the entropy function formalism we compute the entropy of extremal supersymmetric and non-supersymmetric black holes in N=2 supergravity theories in four dimensions with higher derivative corrections. For supersymmetric black holes our results agree with all previous analysis. However in some examples where the four dimensional theory is expected to arise from the dimensional reduction of a five dimensional theory, there is an apparent disagreement between our results for non-supersymmetric black holes and those obtained by using the five dimensional description. This indicates that for t…
We reconsider the well-known issue of string corrections to Supergravity theory. Our treatment is carried out to second order in the string slope parameter. We establish a procedure for solving the Bianchi identities in the non minimal case, and we solve a long standing problem in the perturbative expansion of D=10, N=1 string corrected Supergravity, obtaining the H sector tensors, torsions and curvatures.
In this paper we investigate the cosmological effects of modified gravity with string curvature corrections added to Einstein-Hilbert action in the presence of a dynamically evolving scalar field coupled to Riemann invariants. The scenario exhibits several features of cosmological interest for late universe. It is shown that higher order stringy corrections can lead to a class of dark energy models consistent with recent observations. The model can give rise to quintessence, deSitter or phantom dark energy, in last case without recourse to negative kinetic energy field. The detailed treatment …
We solve the non-minimal case of string corrected D=10, N=1 Supergravity as the low energy limit of string theory. We find a consistent set of solutions to the Bianchi identities in the H sector, and we also find the torsions and curvatures at second order in the string slope parameter. In so doing we solve a long standing problem in the non minimal case of the perturbative expansion.
Completing earlier work on three dimensional (3D) N=1 supergravity with curvature-squared terms, we construct the general supergravity extension of cosmological massive gravity theories. We expand about supersymmetric anti-de Sitter vacua, finding the conditions for bulk unitarity and the critical points in parameter space at which the spectrum changes. We discuss implications for the dual conformal field theory.
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