An exponential kind of quintessential inflation potential motivated by supergravity is studied. This type belongs to the class of α-attractor models. The model was studied for the first time by Dimopoulos and Owen in [J. Cosmol. Astropart. Phys. 06 (2017) 027], in which the authors introduced a negative cosmological constant in order to ensure a zero-vacuum energy density at late times. However, in this paper, we disregard this cosmological constant, showing that the obtained results are very close to the ones obtained recently in the context of Lorentzian quintessential inflation and thus depicting with great accuracy the early- and late-time acceleration of our Universe. The model is compatible with the recent observations. Finally, we review the treatment of the α-attractor and we show that our potential depicts the late time cosmic acceleration with an effective equation of state equal to -1.
We investigate a compelling model of quintessential inflation in the context of $α$-attractors, which naturally result in a scalar potential featuring two flat regions, the inflationary plateau and the quintessential tail. The "asymptotic freedom" of $α$-attractors, near the kinetic poles, suppresses radiative corrections and interactions, which would otherwise threaten to lift the flatness of the quintessential tail and cause a 5th-force problem respectively. Since this is a non-oscillatory inflation model, we reheat the Universe through instant preheating. The parameter space is constrained …
A novel approach to quintessential inflation model building is studied, within the framework of $α$-attractors, motivated by supergravity theories. Inflationary observables are in excellent agreement with the latest CMB observations, while quintessence explains the dark energy observations without any fine-tuning. The model is kept intentionally minimal, avoiding the introduction of many degrees of freedom, couplings and mass scales. In stark contrast to $Λ$CDM, for natural values of the parameters, the model attains transient accelerated expansion, which avoids the future horizon problem, whi…
Single-field models of $α$-attractor quintessential inflation provide a unified picture of the two periods of early- and late-time cosmic acceleration, where both inflation and dark energy are described by a single scalar degree of freedom rolling down a runaway potential. These theoretically well-motivated models have distinct observational predictions that are in agreement with existing cosmological data. We show that the next generation of large-scale structure surveys, even when no other cosmological data sets are considered, will strongly constrain the parameter space of these models, and…
University of Catania（卡塔尼亚大学）；INFN-Sezione di Catania（意大利国家核物理研究所卡塔尼亚分部）；Max-Planck-Institut für Physik (Werner-Heisenberg-Institut)（马克斯·普朗克物理学研究所（维尔纳·海森堡研究所））
In this paper, we apply reconstruction techniques to recover the potential parameters for a particular class of single-field models, the $α$-attractor (supergravity) models of inflation. This also allows to derive the inflaton vacuum expectation value at horizon crossing. We show how to use this value as one of the input variables to constrain the postaccelerated inflationary phase. We assume that the tensor-to-scalar ratio $r$ is of the order of $10^{-3}$ , a level reachable by the expected sensitivity of the next-generation CMB experiments.
Quintessential inflation utilises a single scalar field to account for the observations of both cosmic inflation and dark energy. The requirements for modelling quintessential inflation are described and two explicit successful models are presented in the context of $α$-attractors and Palatini modified gravity.
Recently a new kind of quintessential inflation coming from the Lorentzian distribution has been introduced in [1,2]. The model leads to a very simple potential, which basically depends on two parameters, belonging to the class of $α$-attractors and depicting correctly the early and late time accelerations of our universe. The potential emphasizes a {\it cosmological seesaw mechanism} (CSSM) that produces a large inflationary vacuum energy in one side of the potential and a very small value of dark energy on the right hand side of the potential. {Here we show that the model agrees with the rec…
The Planck value of the spectral index can be interpreted as $n_s = 1 - 2/N$ in terms of the number of e-foldings $N$. An appealing explanation for this phenomenological observation is provided by $α$-attractors: the inflationary predictions of these supergravity models are fully determined by the curvature of the Kahler manifold. We provide a novel formulation of $α$-attractors which only involves a single chiral superfield. Our construction involves a natural deformation of no-scale models, and employs these to construct a De Sitter plateau with an exponential fall-off. Finally, we show how …
We study a new model of quintessential inflation which is inspired by supergravity and string theory. The model features a kinetic pole, which gives rise to the inflationary plateau, and a runaway quintessential tail. We envisage a coupling between the inflaton and the Peccei-Quinn (PQ) field which terminates the roll of the runaway inflaton and traps the latter at an enhanced symmetry point (ESP), thereby breaking the PQ symmetry. The kinetic density of the inflaton is transferred to the newly created thermal bath of the hot big bang due to the decay of PQ particles. The model successfully ac…
In string-inspired supergravity theory, Kähler metric of chiral matter fields often has a pole. Such Kähler metric is interesting from the viewpoint of the framework of the pole inflation, where the scalar potential can be stretched out to be flat around the pole for a canonically normalized field and inflation can be realized. However, when Kähler metric has a pole, the scalar potential can also have a pole at the same point in supergravity theory. We study such supergravity models with the pole, and provide numerical analysis of inflationary dynamics and resultant density perturbation. In co…
We compute in detail how deviations from Einstein gravity at the inflation energy scale could appear as non-Gaussian features in the sky. To illustrate this we use multi-field $α-$attractor models in the framework of supergravity to realise inflation. We find no obvious obstacle for having choices of model's parameters that generate non-Gaussian features of the equilateral and local type at the $\cal O$(1) level in the $f_{\rm NL}$ non-Gaussianity parameter, thus being potentially detectable in future cosmological surveys. This non-Gaussianity has its origin in either the non-canonical kinetic…
Over the last few years, a large family of cosmological attractor models has been discovered, which can successfully match the latest inflation-related observational data. Many of these models can also describe a small cosmological constant $Λ$, which provides the most natural description of the present stage of the cosmological acceleration. In this paper, we study $α$-attractor models with dynamical dark energy, including the cosmological constant $Λ$ as a free parameter. Predominantly, the models with $Λ> 0$ converge to the asymptotic regime with the equation of state $w=-1$. However, there…
Fibre inflation is a specific string theory construction based on the Large Volume Scenario that produces an inflationary plateau. We outline its relation to $α$-attractor models for inflation, with the cosmological sector originating from certain string theory corrections leading to $α=2$ and $α=1/2$. Above a certain field range, the steepening effect of higher-order corrections leads first to the breakdown of single-field slow-roll and after that to the onset of 2-field dynamics: the overall volume of the extra dimensions starts to participate in the effective dynamics. Finally, we propose e…
I describe a simple class of $α$-attractors, generalizing the single-field GL model of inflation in supergravity. The new class of models is defined for $0<α\lesssim 1$, providing a good match to the present cosmological data. I also present a generalized version of these models which can describe not only inflation but also dark energy and supersymmetry breaking.
We describe a simple class of cosmological models called $α$ attractors, which provide an excellent fit to the latest Planck data. These theories are most naturally formulated in the context of supergravity with logarithmic Kahler potentials. We develop generalized versions of these models which can describe not only inflation but also dark energy and supersymmetry breaking.
We show that the inflaton coupling to all other fields is exponentially suppressed during inflation in the cosmological $α$-attractor models. In the context of supergravity, this feature is a consequence of the underlying hyperbolic geometry of the moduli space which has a flat direction corresponding to the inflaton field. A combination of these factors protects the asymptotic flatness of the inflaton potential.
In this PhD thesis, we investigate generic features of inflation which are strictly related to fundamental aspects of UV-physics scenarios, such as string theory or supergravity. After a short introduction to standard and inflationary cosmology, we present our research findings. On the one hand, we show that focusing on universality properties of inflation can yield surprisingly stringent bounds on its dynamics. This approach allows us to identify the regime where the inflationary field range is uniquely determined by both the tensor-to-scalar ratio and the spectral index. Then, we derive a no…
We define a general class of superconformal inflationary attractor models studied in our previous papers [1,2], which include, among others, inflationary models of 'induced gravity' which were argued to retain perturbative unitarity up to the Planck scale [3]. The choice of the function $f(ϕ)$ in superconformal attractors for the models introduced in [3] is $f(ϕ)= ϕ^n - ξ^{-1}$. We present both superconformal and supergravity versions of these models, which were derived in [1,2] for arbitrary $f(ϕ)$, together with the universal conditions required for stabilization of the extra three moduli pr…
We study a particular version of the theory of cosmological $α$-attractors with $α=1/3$, in which both the dilaton (inflaton) field and the axion field are light during inflation. The kinetic terms in this theory originate from maximal $\mathcal{N}=4$ superconformal symmetry and from maximal $\mathcal{N}=8$ supergravity. We show that because of the underlying hyperbolic geometry of the moduli space in this theory, it exhibits double attractor behavior: their cosmological predictions are stable not only with respect to significant modifications of the dilaton potential, but also with respect to…
In this paper we address the question how to discriminate whether the gauged isometry group G_Sigma of the Kahler manifold Sigma that produces a D-type inflaton potential in a Minimal Supergravity Model is elliptic, hyperbolic or parabolic. We show that the classification of isometries of symmetric cosets can be extended to non symmetric Sigma.s if these manifolds satisfy additional mathematical restrictions. The classification criteria established in the mathematical literature are coherent with simple criteria formulated in terms of the asymptotic behavior of the Kahler potential K(C) = 2 J(…
Inflationary $α$-attractor models in supergravity, which provide excellent fits to the latest observational data, are based on the Poincare disk hyperbolic geometry. We refine these models by constructing Kahler potentials with built-in inflaton shift symmetry and by making a canonical choice of the goldstino Kahler potential. The refined models are stable with respect to all scalar fields at all $α$, no additional stabilization terms are required. The scalar potential V has a nearly Minkowski minimum at small values of the inflaton field $φ$, and an infinitely long dS valley of constant depth…
In this paper we consider the $α-$attractor model and study inflation under a non-slow-roll dynamics. More precisely, we follow the approach recently proposed by Gong and Sasaki \cite{Gong:2015ypa} by means of assuming $N=N\left(ϕ\right)$. Within this framework we obtain a family of functions describing the local shape of the potential during inflation. We study a specific model and find an inflationary scenario predicting an attractor at $n_{s}\approx0.967$ and $r\approx5.5\times10^{-4}$. We further show that considering a non-slow-roll dynamics, the $α-$attractor model can be broaden to a wi…
We provide a unified description of cosmological $α$-attractors and late-time acceleration, in excellent agreement with the latest Planck data. Our construction involves two superfields playing distinctive roles: one is the dynamical field and its evolution determines inflation and dark energy, the other is nilpotent and responsible for a landscape of vacua and supersymmetry breaking. We prove that the attractor nature of the theory is enhanced when combining the two sectors: cosmological attractors are very stable with respect to any possible value of the cosmological constant and, interestin…
Cosmological alpha-attractors give a natural explanation for the spectral index n_s of inflation as measured by Planck while predicting a range for the tensor-to-scalar ratio r, consistent with all observations, to be measured more precisely in future detection of gravity waves. Their embedding into supergravity exploits the hyperbolic geometry of the Poincare disk or half-plane. These geometries are isometric under Mobius transformations, which include the shift symmetry of the inflaton field. We introduce a new Kahler potential frame that explicitly preserves this symmetry, enabling the infl…
Inflationary $α$-attractor models can be naturally implemented in supergravity with hyperbolic geometry. They have stable predictions for observables, such as $n_s=1-{2/ N_e} $, assuming that the potential in terms of the original geometric variables, as well as its derivatives, are not singular at the boundary of the hyperbolic disk, or half-plane. In these models, the potential in the canonically normalized inflaton field $φ$ has a plateau, which is approached exponentially fast at large $φ$. We call them exponential $α$-attractors. We present a closely related class of models, where the pot…
In this paper we consider a scalar field system with a class of potentials given by the expression, $V(ϕ)\propto ϕ^m {\rm exp}({-λϕ^n/{M^n_{Pl}}})$; $m\geqslant 0, n>1$ for which $Γ=V_{ϕϕ}V/V^2_ϕ\to 1 $ as $|ϕ|\to \infty$. We carry out dynamical analysis for the underlying system choosing a suitable set of autonomous variables and find all the fixed points. In particular, we show that the scaling solution is an attractor of the system in the asymptotic regime. We indicate the application of the solution to models of quintessential inflation.
The modified supergravity approach is applied to describe a formation of Primordial Black Holes (PBHs) after Starobinsky inflation. Our approach naturally leads to the two-(scalar)-field attractor-type double inflation, whose first stage is driven by scalaron and whose second stage is driven by another scalar field which belongs to a supergravity multiplet. The scalar potential and the kinetic terms are derived, the vacua are studied, and the inflationary dynamics of those two scalars is investigated. We numerically compute the power spectra and we find the ultra-slow-roll regime leading to an…
Effective supergravity inflationary models induced by anti-D3 brane interaction with the moduli fields in the bulk geometry have a geometric description. The Kähler function carries the complete geometric information on the theory. The non-vanishing bisectional curvature plays an important role in the construction. The new geometric formalism, with the nilpotent superfield representing the anti-D3 brane, allows a powerful generalization of the existing inflationary models based on supergravity. They can easily incorporate arbitrary values of the Hubble parameter, cosmological constant and grav…
We explore the Gravitational Waves (GW) phenomenology of a simple class of supergravity models that can explain and unify inflation and Primordial Black Holes (PBH) as Dark Matter (DM). Our (modified) supergravity models naturally lead to a two-field attractor-type double inflation, whose first stage is driven by Starobinsky scalaron and the second stage is driven by another scalar belonging to a supergravity multiplet. The PBHs formation in our supergravity models is efficient, compatible with all observational constraints, and predicts a stochastic GW background. We compute the PBH-induced G…
We propose a new broad class of multi-field non-canonical inflationary models as an extension of multi-field conformal cosmological attractors. This also generalizes the recently discovered class of non-canonical conformal attractors for single field inflation. Kinetic terms of this class of models are phenomenologically arising from ${\cal N}=1$ supergravity and from ${\cal N}=1$ superconformal theory, with two conformal scalar compensator fields in the latter. We show that the inflationary dynamics and predictions of this class of models are stable with respect to the significant modificatio…
We explore the dynamics of multi-field models of inflation in which the field-space metric is a hyperbolic manifold of constant curvature. Such models are known as $α$-attractors and their single-field regimes have been extensively studied in the context of inflation and supergravity. We find a variety of multi-field inflationary trajectories in different regions of parameter space, which is spanned by the mass parameters and the hyperbolic curvature. Amongst these is a novel dynamical attractor along the boundary of the Poincare disc which we dub "angular inflation". We calculate the evolutio…
We consider a broad class of inflationary models that arise naturally in supergravity. They are defined in terms of a parameter $α$ that determines the curvature and cutoff of these models. As a function of this parameter, we exhibit that the inflationary predictions generically interpolate between two attractor points. At small cutoff $α$, the resulting inflationary model is of plateau-type with $n_s = 1 - 2 / N$ and $r = 12 α/ N^2$. For $α= 1$, these predictions coincide with predictions of the Starobinsky model and Higgs inflation. In contrast, for large cutoff $α$, the theory asymptotes to…
Cosmological Constraints on Neutrino Masses in Quintessential Inflation
Observatório Nacional（国家天文台）；Universidade Federal do Rio Grande do Norte（北里奥格兰德联邦大学）；Università di Trento（特伦托大学）；Trento Institute for Fundamental Physics and Applications (TIFPA)-INFN（特伦托基础物理与应用研究所（TIFPA）-意大利国家核物理研究所）；International Institute of Physics, Universidade Federal do Rio Grande do Norte（北里奥格兰德联邦大学国际物理研究所）
Recently, Kallosh and Linde have drawn attention to a new family of superconformal inflationary potentials, subsequently called $α$-attractors. The $α$-attractor family can interpolate between a large class of inflationary models. It also has an important theoretical underpinning within the framework of supergravity. We demonstrate that the $α$-attractors have an even wider appeal since they may describe dark matter and perhaps even dark energy. The dark matter associated with the $α$-attractors, which we call $α$-dark matter ($α$DM), shares many of the attractive features of fuzzy dark matter…
We have presented previously a general treatment of Starobinsky-like inflation in no-scale supergravity where the tensor-to-scalar ratio $r = 3(1 - n_s)^2$, and $n_s$ is the tilt of the scalar perturbations. In particular, we have shown how this scenario can be unified with modulus fixing, supersymmetry breaking and a small cosmological constant. In this paper we extend these constructions to inflationary models based on generalized no-scale structures. In particular, we consider alternative values of the curvature parameter, $α< 1$, as may occur if not all the complex Kähler moduli contribute…
This paper provides a systematic study of supergravity contributions relevant for inflationary model building in Jordan frame supergravity. In this framework, canonical kinetic terms in the Jordan frame result in the separation of the Jordan frame scalar potential into a tree-level term and a supergravity contribution, which is potentially dangerous for sustaining inflation. We show that if the vacuum energy necessary for driving inflation originates dominantly from the F-term of an auxiliary field (i.e. not the inflaton), the supergravity corrections to the Jordan frame scalar potential are g…
We develop four-parameter supergravity models of inflation and dark energy, constrained so that ${δρ\over ρ}$, $n_s$ and the cosmological constant $Λ$ take their known observable values, but where the mass of gravitino $m_{3/2}$ and the tensor-to-scalar ratio $r$ are free parameters. We focus on generalized cosmological $α$-attractor models, with logarithmic Kahler potentials, a nilpotent goldstino and spontaneously broken supersymmetry at the de Sitter minimum. The future data on B-modes will specify the parameter $α$, measuring the geometry of the Kahler, manifold. The string landscape idea …
We have recently proposed attractor models for modulus fixing, inflation, supersymmetry breaking and dark energy based on no-scale supergravity. In this paper we develop phenomenological and cosmological aspects of these no-scale attractor models that underpin their physical applications. We consider models in which inflation is driven by a modulus field ($T$-type) with supersymmetry broken by a Polonyi field, or a matter field ($ϕ$-type) with supersymmetry broken by the modulus field. We derive the possible patterns of soft supersymmetry-breaking terms, which depend in $T$-type models whether…
Recent BICEP/Keck data on the cosmic microwave background, in combination with previous WMAP and Planck data, impose strong new constraints on the tilt in the scalar perturbation spectrum, $n_s$, as well as the tensor-to-scalar ratio, $r$. These constrain the number of e-folds of inflation, $N_*$, the magnitude of the inflaton coupling to matter, $y$, and the reheating temperature, $T_{\rm reh}$, which we evaluate in attractor models of inflation as formulated in no-scale supergravity. The 68% C.L. region of $(n_s, r)$ favours large values of $N_*, y$ and $T_{\rm reh}$ that are constrained by …
It is shown that, when the inflaton field modulates the gauge kinetic function of the gauge fields in supergravity realisations of inflation, the dynamic backreaction leads to a new inflationary attractor solution, in which the inflaton's variation suffers additional impedance. As a result, slow-roll inflation can naturally occur along directions of the scalar potential which would be too steep and curved to support it otherwise. This provides a generic solution to the infamous eta-problem of inflation in supergravity. Moreover, it is shown that, in the new inflationary attractor, the spectral…
