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 the Polonyi and/or matter fields are twisted or not, and in $ϕ$-type models on whether the inflaton and/or other matter fields are twisted or not. In $ϕ$-type models, we are able to directly relate the scale of supersymmetry breaking to the inflaton mass. We also discuss cosmological constraints from entropy considerations and the density of dark matter on the mechanism for stabilizing the modulus field via higher-order terms in the no-scale Kähler potential.
We have investigated the attractor structure for the CMB fluctuations in composite inflation scenario within the gauged Nambu-Jona-Lasinio (NJL) model. Such composite inflation represents an attractor which can not be found in a fundamental scalar model. As is known, the number of inflationary models contains the attractor classified by the $α$-attractor model. It is found that the attractor inflation in the gauged NJL model corresponds to the $α= 2$ case.
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 …
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 study reheating in $α$-attractor models of inflation in which the inflaton couples to other scalars or fermions. We show that the parameter space contains viable regions in which the inflaton couplings to radiation can be determined from the properties of CMB temperature fluctuations, in particular the spectral index. This may be the only way to measure these fundamental microphysical parameters, which shaped the universe by setting the initial temperature of the hot big bang and contain important information about the embedding of a given model of inflation into a more fundamental theory o…
Minimal chaotic models of D-term inflation predicts too large primordial tensor perturbations. Although it can be made consistent with observations utilizing higher order terms in the Kähler potential, expansion is not controlled in the absence of symmetries. We comprehensively study the conditions of Kähler potential for D-term plateau-type potentials and discuss its symmetry. They include the alpha-attractor model with a massive vector supermultiplet and its generalization leading to pole inflation of arbitrary order. We extend the models so that it can describe Coulomb phase, gauge anomaly …
The Swampland Distance Conjecture (SDC) constraints the dynamics emerging at infinite distances in field space of any effective field theory consistent with quantum gravity. It provides a relation between the cut-off in energies and the field range which, as we show, in the context of inflation it yields a universal upper bound on the inflaton excursion in terms of the tensor-to-scalar ratio, measured at typical CMB scales. In this note, we investigate the interplay between the SDC and the emergent inflationary physics around infinite distances singularities in string theory, with a special lo…
Once quantum corrections are taken into account, the strong coupling limit of the $ξ$-attractor models (in metric gravity) might depart from the usual Starobinsky solution and move into linear inflation. Furthermore, it is well known that the metric and Palatini formulations of gravity lead to different inflationary predictions in presence of non-minimally couplings between gravity and the inflaton. In this letter we show that for a certain class of non-minimally coupled models, loop corrections will lead to a linear inflation attractor regardless of the adopted gravity formulation.
We study the effects of the non-attractor initial conditions for the canonical single-field inflation. The non-attractor stage can last only several $e$-folding numbers, and should be followed by hilltop inflation. This two-stage evolution leads to large scale suppression in the primordial power spectrum, which is favored by recent observations. Moreover we give a detailed calculation of primordial non-Guassianity due to the "from non-attractor to slow-roll" transition, and find step features in the local and equilateral shapes. We conclude that a plateau-like inflaton potential with an initia…
A reformulation of inflationary model analyses appeared recently, in which inflationary observables are determined by the structure of a pole in the inflaton kinetic term rather than the shape of the inflaton potential. We comprehensively study this framework with an arbitrary order of the pole taking into account possible additional poles in the kinetic term or in the potential. Depending on the setup, the canonical potential becomes the form of hilltop or plateau models, variants of natural inflation, power-law inflation, or monomial/polynomial chaotic inflation. We demonstrate attractor beh…
Sneutrino inflation employs the fermionic partners of the inflaton and stabilizer field as right-handed neutrinos to realize the seesaw mechanism for light neutrino masses. We show that one can improve the latest version of this scenario and its consistency with the Planck data by embedding it in the theory of cosmological $α$-attractors.
We investigate the interplay between moduli dynamics and inflation, focusing on the KKLT-scenario and cosmological $α$-attractors. General couplings between these sectors can induce a significant backreaction and potentially destroy the inflationary regime; however, we demonstrate that this generically does not happen for $α$-attractors. Depending on the details of the superpotential, the volume modulus can either be stable during the entire inflationary trajectory, or become tachyonic at some point and act as a waterfall field, resulting in a sudden end of inflation. In the latter case there …
We introduce a novel non-minimal coupling between gravity and the inflaton sector. Remarkably, for large values of this coupling all models asymptote to a universal attractor. This behavior is independent of the original scalar potential and generalizes the attractor in the phi^4 theory with non-minimal coupling to gravity. The attractor is located in the `sweet spot' of Planck's recent results.
We describe an induced inflation, which refers to a class of inflationary models with a generalized non-minimal coupling $ξg(ϕ) R$ and a specific scalar potential. The defining property of these models is that the scalar field takes a vev in the vacuum and thus induces an effective Planck mass. We study this model as a function of the coupling parameter $ξ$. At large $ξ$, the predictions of the theory are known to have an attractor behavior, converging to a universal result independent on the choice of the function $g(ϕ)$. We find that at small $ξ$, the theory approaches a second attractor. Th…
This is the first of a three-part series of papers, in which we study the preheating phase for multifield models of inflation involving nonminimal couplings. In this paper, we study the single-field attractor behavior that these models exhibit during inflation and quantify its strength and parameter dependence. We further demonstrate that the strong single-field attractor behavior persists after the end of inflation. Preheating in such models therefore generically avoids the "de-phasing" that typically affects multifield models with minimally coupled fields, allowing efficient transfer of ener…
We discuss the phenomenology of the minimal inflation scenario. We concentrate on two aspects: inflationary trajectories and particle production. Our findings can be summarized in two main results: first, that inflationary trayectories that are very flat and provide enough number of e-foldings are natural in the scenario without fine tunning. We present a general formalism to identify attractors in multi-field inflation regardless of trajectories fulfilling the slow-roll conditions. We then explore particle production in the model and show how the inflaton naturally transmutes into a dark matt…
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…
Conformal scaling invariance should play an important role for understanding the origin and evolution of universe. During inflation period, it appears to be an approximate symmetry, but how it is broken remains uncertain. The appealing $α$-attractor inflation implements the spontaneous breaking of conformal symmetry and a mysterious SO(1,1) global symmetry. To better understand the SO(1,1) symmetry, here we present a systematic treatment of the inflation models with local conformal symmetry in a more general formalism. We find SO(2) is the other possible symmetry in the presence of Weyl gauge …
Non-attractor inflation is known as the only single field inflationary scenario that can violate non-Gaussianity consistency relation with the Bunch-Davies vacuum state and generate large local non-Gaussianity. However, it is also known that the non-attractor inflation by itself is incomplete and should be followed by a phase of slow-roll attractor. Moreover, there is a transition process between these two phases. In the past literature, this transition was approximated as instant and the evolution of non-Gaussianity in this phase was not fully studied. In this paper, we follow the detailed ev…
In this work we study the cosmological attractor models of inflation in connection with certain scalar-tensor theories of gravity, e.g $f(R)$ gravity and Brans-Dicke theory. For some particular choices of the functional degrees of freedom in these theories, one obtains Starobinsky like predictions in the ($n_s$-$r$) observable plane. We have demonstrated that these choices in the Lagrangian density of certain $f(R)$ and Brans-Dicke theories fulfil the condition of the cosmological attractors. That explains why known predictions of $f(R)$ and Brans-Dicke theories in certain cases appear to be t…
The inflationary attractor properties of the canonical scalar field and Born-Infeld field are investigated in the Randall-Sundrum II scenario with a Gauss-Bonnet term in the bulk action. We find that the inflationary attractor property will always hold for both the canonical and Born-Infeld fields for any allowed non-negative Gauss-Bonnet coupling. We also briefly discuss the possibility of explaining the suppressed lower multiples and running scalar spectral index simultaneously in the scenario of Gauss-Bonnet brane inflation.
We study the production of observable primordial local non-Gaussianity in two opposite regimes of canonical single field inflation: attractor (standard single field slow-roll inflation) and non attractor (ultra slow-roll inflation). In the attractor regime, the standard derivation of the bispectrum's squeezed limit using co-moving coordinates gives the well known Maldacena's consistency relation $f_{NL} = 5(1-n_{s})/12$. On the other hand, in the non-attractor regime, the squeezed limit offers a substantial violation of this relation given by $f_{NL} = 5/2$. In this work we argue that, indepen…
Recently, several broad classes of inflationary models have been discovered whose cosmological predictions are stable with respect to significant modifications of the inflaton potential. Some classes of models are based on a non-minimal coupling to gravity. These models, which we will call $ξ$-attractors, describe universal cosmological attractors (including Higgs inflation) and induced inflation models. Another class describes conformal attractors (including Starobinsky inflation and T-models) and their generalization to $α$-attractors. The aim of this paper is to elucidate the common denomin…
There are some motivations to consider inflation driven by a phantom field. Before entering into some specific models and perform data fitting, it is important first investigating some general features that any viable inflation model should hold. The inflationary attractor property is an important one of those features. In this paper we will show that the inflationary attractor property still holds for canonical and Born-Infeld phantom fields in the standard Friedmann-Robertson-Walker cosmology, however, it does not hold for canonical and Born-Infeld phantom fields in the Randall -Sundrum II c…
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 study multifield inflation in scenarios where the fields are coupled non-minimally to gravity via $ξ_I(ϕ^I)^n g^{μν}R_{μν}$, where $ξ_I$ are coupling constants, $ϕ^I$ the fields driving inflation, $g_{μν}$ the space-time metric, $R_{μν}$ the Ricci tensor, and $n>0$. We consider the so-called $α$-attractor models in two formulations of gravity: in the usual metric case where $R_{μν}=R_{μν}(g_{μν})$, and in the Palatini formulation where $R_{μν}$ is an independent variable. As the main result, we show that, regardless of the underlying theory of gravity, the field-space curvature in the Einst…
Inflationary scenarios motivated by the Minimal Supersymmetric Standard Model (MSSM) where five scalar fields are non-minimally coupled to gravity are considered. The potential of the model and the function of non-minimal coupling are polynomials of two Higgs doublet convolutions. We show that the use of the strong coupling approximation allows to obtain inflationary parameters in the case when a combination of the four scalar fields plays a role of inflaton. Numerical calculations show that the cosmological evolution leads to inflationary scenarios fully compatible with observational data for…
We revisit the notion of slow-roll in the context of general single-field inflation. As a generalization of slow-roll dynamics, we consider an inflaton $ϕ$ in an attractor phase where the time derivative of $ϕ$ is determined by a function of $ϕ$, $\dotϕ=\dotϕ(ϕ)$. In other words, we consider the case when the number of $e$-folds $N$ counted backward in time from the end of inflation is solely a function of $ϕ$, $N=N(ϕ)$. In this case, it is found that we need a new independent parameter to properly describe the dynamics of the inflaton field in general, in addition to the standard parameters c…
We study the complete evolution of a flat and homogeneous universe dominated by tachyonic matter. We demonstrate the attractor behaviour of the tachyonic inflation using the Hamilton-Jacobi formalism. We else obtain analytical approximations to the trajectories of the tachyon field in different regions. The numerical calculation shows that an initial non-vanishing momentum does not prevent the onset of inflation. The slow-rolling solution is an attractor.
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.
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 …
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…
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…
We discuss a new mechanism to enhance the spectrum of primordial tensor fluctuations in single field inflationary scenarios. The enhancement relies on a transitory non-attractor inflationary phase, which amplifies the would-be decaying tensor mode, and gives rise to a growth of tensor fluctuations at superhorizon scales. We show that the enhancement produced during this phase can be neatly treated via a tensor duality between an attractor and non-attractor phase, which we introduce. We illustrate the mechanism and duality in a kinetically driven scenario of inflation, with non-minimal coupling…
We demonstrate the attractor behavior of inflation driven by a scalar field or a tachyon field in the context of recently proposed four-dimensional effective gravity induced on the world-volume of a three-brane in five-dimensional Einstein gravity, and we obtain a set of exact inflationary solutions. Phase portraits indicate that an initial kinetic term decays rapidly and it does not prevent the onset of inflation. The trajectories more rapidly reach the slow-roll curve than in the standard cosmology.
In this work, we revisit the dynamics of pre-inflationary universe with a family of $α-$attractor potentials, in the framework of loop quantum cosmology, in which the big bang singularity is generically resolved purely with quantum geometric effects, and replaced by a quantum bounce. At the bounce, the background evolution is divided into two distinct classes, the first is dominated by the kinetic energy of the inflaton field and the second by the potential energy. In both classes, we find the physically viable initial conditions numerically that provide not only the slow-roll inflation, but a…
The large class of inflationary models known as $α$- and $ξ$-attractors gives identical cosmological predictions at tree level (at leading order in inverse power of the number of efolds). Working with the renormalization group improved action, we show that these predictions are robust under quantum corrections. This means that for all the models considered the inflationary parameters $(n_s,r)$ are (nearly) independent on the Renormalization Group flow. The result follows once the field dependence of the renormalization scale, fixed by demanding the leading log correction to vanish, satisfies a…
We investigate the inflationary attractors in models of inflation inspired from general conformal transformation of general scalar-tensor theories to the Einstein frame. The coefficient of the conformal transformation in our study depends on both the scalar field and its kinetic term. Therefore the relevant scalar-tensor theories display the subset of the class I of the degenerate higher-order scalar-tensor theories in which both the scalar field and its kinetic term can non-minimally couple to gravity. We find that if the conformal coefficient $Ω$ takes a multiplicative form such that $Ω\equi…
We study the stability of an inflaton condensate in the presence of attractive inflaton self-interactions, in order to determine analytical conditions on the self-interaction couplings under which the condensate undergoes fragmentation. As an application of our results, we consider the stability of the inflaton condensate in $α$-attractor inflation. We show that the stability of the condensate depends upon the value of $α$. For the T-model with $n = 1$, we find that it is unstable for $α\lesssim 10^{-4}$. In this case it is expected that inflation will be followed by an oscillon-dominated era.
We study the dynamics of ELKO in the context of accelerated phase of our universe. To avoid the fine tuning problem associated with the initial conditions, it is required that the dynamical equations lead to an early-time attractor. In the earlier works, it was shown that the dynamical equations containing ELKO fields do not lead to early-time stable fixed points. In this work, using redefinition of variables, we show that ELKO cosmology admits early-time stable fixed points. More interestingly, we show that ELKO cosmology admit two sets of attractor points corresponding to slow and fast-roll …
The possibility of linking inflation and late cosmic accelerated expansion using the $α$-attractor models has received increasing attention due to their physical motivation. In the early universe, $α$-attractors provide an inflationary mechanism compatible with Planck satellite CMB observations and predictive for future gravitational wave CMB modes. Additionally $α$-attractors can be written as quintessence models with a potential that connects a power law regime with a plateau or uplifted exponential, allowing a late cosmic accelerated expansion that can mimic behavior near a cosmological con…
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…
Cosmological $α$-attractors stand out as particularly compelling models to describe inflation in the very early universe, naturally meeting tight observational bounds from cosmic microwave background (CMB) experiments. We investigate $α$-attractor potentials in the presence of an inflection point, leading to enhanced curvature perturbations on small scales. We study both single- and multi-field models, driven by scalar fields living on a hyperbolic field space. In the single-field case, ultra-slow-roll dynamics at the inflection point is responsible for the growth of the power spectrum, while …
We propose a curvaton model in which the initial condition of the curvaton oscillation is determined by its attractor behavior during inflation. Assuming a chaotic inflation model, we find that the initial condition determined by the attractor behavior is appropriate to generate a sizable non-Gaussianity contribution to the curvature perturbation, which will be tested in the foreseeable future. Implications on the thermal history of the universe and on particle physics models are also discussed.
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…
We study the stability of a scalar inflaton field and analyze its point attractors in the phase space. We show that the value of the inflaton field in the vacuum is a bifurcation parameter and prove the possible existence of a limit cycle by using analytical and numerical arguments.
We discuss the introduction of a non minimal coupling between the inflaton and gravity in terms of the recently proposed $β$-function formalism for inflation\cite{Binetruy:2014zya}. Via a field redefinition we reduce to the case of minimally coupled theories. The universal attractor at strong coupling has a simple explanation in terms of the new field. Generalizations are discussed and the possibility of evading the universal attractor is shown.
We offer a geometric interpretation of attractor theories with singular kinetic terms as a union of multiple canonical models. We demonstrate that different domains (separated by poles) can drastically differ in their phenomenology. We illustrate this with the help of a "master model" that leads to distinct predictions depending on which side of the pole the field evolves before examining the more realistic example of $α$-attractor models. Such models lead to quintessential inflation within the poles when featuring an exponential potential. However, beyond the poles, we discover a novel behavi…
