From the assumption that the slow roll parameter $ε$ has a Lorentzian form as a function of the e-folds number $N$, a successful model of a quintessential inflation is obtained. The form corresponds to the vacuum energy both in the inflationary and in the dark energy epochs. The form satisfies the condition to climb from small values of $ε$ to $1$ at the end of the inflationary epoch. At the late universe $ε$ becomes small again and this leads to the Dark Energy epoch. The observables that the models predicts fits with the latest Planck data: $r \sim 10^{-3}, n_s \approx 0.965$. Naturally a large dimensionless factor that exponentially amplifies the inflationary scale and exponentially suppresses the dark energy scale appears, producing a sort of {\it{cosmological see saw mechanism}}. We find the corresponding scalar Quintessential Inflationary potential with two flat regions - one inflationary and one as a dark energy with slow roll behavior.
From the assumption that the slow roll parameter $ε$ has a Lorentzian form as a function of the e-folds number $N$, a successful model of a quintessential inflation is obtained, as succinctly studied in \cite{Benisty:2020xqm}. The form corresponds to the vacuum energy both in the inflationary and in the dark energy epochs and satisfies the condition to climb from small values of $ε$ to $1$ at the end of the inflationary epoch. We find the corresponding scalar Quintessential Inflationary potential with two flat regions. Moreover, a reheating mechanism is suggested with numerical estimation for …
In this paper, we focus on general features of quintessential inflation which is an effort to unify inflation and dark energy using a single scalar field. We describe a class of models of quintessential inflation which can give rise to the tensor to scalar ratio of perturbations consistent with recent BICEP2 measurements. The scale of inflation in the model is around the GUT scale and there is large parameter space consistent with the recent findings.
We introduce warm quintessential inflation and study it in the weak dissipative regime. We consider the original quintessential inflation model, which approximates quartic chaotic inflation at early times and thawing quartic inverse-power-law quintessence at present. We find that the model successfully accounts for both inflation and dark energy observations, while it naturally reheats the Universe, thereby overcoming a major problem of quintessential inflation model-building.
We investigate two classes of models of quintessential inflation, based upon canonical as well as noncanonical scalar fields. In particular, introducing potentials steeper than the standard exponential, we construct models that can give rise to a successful inflationary phase, with signatures consistent with Planck 2015 results. Additionally, using nonminimal coupling of the scalar field with massive neutrino matter, we obtain the standard thermal history of the Universe, with late-time cosmic acceleration as the last stage of evolution. In both cases, inflation and late-time acceleration are …
Quintessential inflation refers to an attempt to unify inflation and late-time cosmic acceleration using a single scalar field. In this letter we consider two different classes of quintessential inflation, one of which is based upon a Lagrangian with non-canonical kinetic term $k^2(ϕ)\partial^μϕ\partial_μϕ$ and a steep exponential potential while the second class uses the concept of steep brane world inflation. We show that in both cases the Lyth bound can be evaded, despite the large tensor-to-scalar ratio of perturbations. The post-inflationary dynamics is consistent with nucleosynthesis con…
We investigate the generation of gravitational waves in the hybrid quintessential inflationary model. The full gravitational-wave energy spectrum is calculated using the method of continuous Bogoliubov coefficients. The post-inflationary kination period, characteristic of quintessential inflationary models, leaves a clear signature on the spectrum, namely, a peak at high frequencies. The maximum of the peak is firmly located at the MHz-GHz region of the spectrum and corresponds to $Ω_{GW} \simeq 10^{-12}$. This peak is substantially smaller than the one appearing in the gravitational-wave ener…
We study a model of quintessential inflation constructed in $R^2$ modified gravity with a non-minimally coupled scalar field, in the Palatini formalism. Our non-minimal inflaton field is characterised by a simple exponential potential. We find that successful quintessential inflation can be achieved with no fine-tuning on the model parameters. Predictions on the characteristics of dark energy will be tested by observations in the near future, while contrast with existing observations provides insights on the modified gravity background, such as the value of the non-minimal coupling and its run…
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 dep…
We study in detail a new model of quintessential inflation where the inflaton field is coupled to the Gauss-Bonnet term. This coupling ensures that the variation of the field is kept sub-Planckian, which avoids the 5th force problem as well as the lifting of the flatness of the quintessential tail in the runaway scalar potential due to radiative corrections. We find that the inflationary predictions of the model are in excellent agreement with CMB observations, while the coincidence requirement of dark energy is satisfied with natural values of the parameters, overcoming thereby the extreme fi…
This pedagogical review is devoted to quintessential inflation, which refers to unification of inflation and dark energy using a single scalar field. We present a brief but concise description of the concepts needed to join the two ends, which include discussion on scalar field dynamic, conformal coupling, instant preheating and relic gravitational waves. Models of quintessential inflation broadly fall into two classes, depending upon the early and late time behavior of the field potential. In the first type we include models in which the field potential is steep for most of the history of the…
We investigate in detail a family of quintessential inflation models in the context of $R+R^2$ Palatini modified gravity. We find that successful inflation and quintessence are obtained with an inflaton scalar potential that is approximately quadratic in inflation and inverse quartic in quintessence. We show that corrections for the kination period due to Palatini modified gravity are subdominant, while the setup does not challenge constraints on modified gravity from solar system observations and microscopic experiments, in contrast to the metric case. We obtain concrete predictions regarding…
Quintessential inflation unifies inflation and late time acceleration by a single scalar field. Such a scenario, with canonical and non-canonical scalar fields, has been discussed . The scalar field behaves as an inflaton field during inflation and as a quintessence field during late time. Also the predictions of the models has been compared with the recent Planck data.
We first study dark energy models with a minimally-coupled scalar field and exponential potentials, admitting exact solutions for the cosmological equations: actually, it turns out that for this class of potentials the Einstein field equations exhibit alternative Lagrangians, and are completely integrable and separable (i.e. it is possible to integrate the system analytically, at least by quadratures). We analyze such solutions, especially discussing when they are compatible with a late time quintessential expansion of the universe. As a further issue, we discuss how such quintessential scalar…
A quintessential Inflation (QI) scenario from Mimetic Dark Matter (MDM) is presented in this paper. This scenario, which is based on the MDM model presented by Chamseddine and Mukhanov \cite{chams}, uses a potential that is defined on three time intervals:the first during inflation, the second $10^{-65}s$ after the end of inflation and the third after that. The resulting energy density of the universe is constant during inflation, followed by that of a matter/radiation dominated universe, and finally ends with a constant energy density corresponding to dark energy. The scale factor has an acce…
In this paper we study a class of quintessential Einstein Gauss-Bonnet models, focusing on their early and late-time phenomenology. With regard to the early-time phenomenology, we formalize the slow-roll evolution of these models and we calculate in detail the spectral index of the primordial curvature perturbations and the tensor-to-scalar ratio. As we demonstrate, the resulting observational indices can be compatible with both the Planck and the BICEP2/Keck-Array observational constraints on inflation. With regard to the late-time behavior, by performing a numerical analysis we demonstrate t…
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…
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…
By making use of a class of steep exponential type of potentials, which has been recently used to describe quintessential inflation, we show how a unified picture for both inflation, dark energy and dark matter can emerge entirely through dissipative effects. Dissipation provides a way for extending the applicability of a larger class of these potentials in the sense of leading to a consistent early Universe inflationary picture and producing observables in agreement with the Planck legacy data. Likewise, dissipative effects lead to dark matter production with consistent abundances and, toward…
We study a model of quintessential inflation in the context of Palatini gravity. As a representative example, we consider the Peebles-Vilenkin model of quintessential inflation with a small non-minimal coupling to gravity, which is consistent with the most recent Planck measurements. At the end of inflation, the inflaton field passes through a tachyonic region and it leads to explosive particle production through the tachyonic preheating process. After preheating, the Universe becomes dominated by the kinetic energy of the inflaton and enters a period of kination. Eventually, the total energy …
We study quintessential inflation using a generalized exponential potential $V(ϕ)\propto exp(-λϕ^n/Mpl^n), n>1$, the model admits slow-roll inflation at early times and leads to close-to-scaling behaviour in the post inflationary era with an exit to dark energy at late times. We present detailed investigations of the inflationary stage in the light of the Planck 2015 results, study post-inflationary dynamics and analytically confirm the existence of an approximately scaling solution. Additionally, assuming that standard massive neutrinos are non-minimally coupled, makes the field $ϕ$ dominant …
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 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 …
We construct a model of quintessential inflation in Palatini $R^2$ gravity employing a scalar field with a simple exponential potential and coupled to gravity with a running non-minimal coupling. At early times, the field acts as the inflaton, while later on it becomes the current dark energy. Combining the scalar sector with an ideal fluid, we study the cosmological evolution of the model from inflation all the way to dark energy domination. We interpret the results in the Einstein frame, where a coupling emerges between the fluid and the field, feeding energy from the former to the latter du…
We investigate a single field model in the context of the constant-roll inflation in which inflaton moves down to the minimum point of the potential with a constant rate of rolling. We use a quintessential inflationary model obtained by a Lorentzian function which is dependent on the number of e-folds. We present the inflationary analysis for the model and find the observational constraints on the parameters space using the observations of CMB anisotropies \textit{i.e.} the Planck and Keck/array datasets. We find the observationally acceptable values of the Width of the Lorentzian function as …
We study relic gravitational waves in the paradigm of quintessential inflation. In this framework, irrespective of the underlying model, inflation is followed by the kinetic regime. Thereafter, the field energy density remains sub-dominant before the onset of acceleration. We carry out model independent analysis to obtain the temperature at the end of inflation and the estimate for upper bound on the Hubble parameter to circumvent the problem due to relic gravitational waves. In this process, we used Planck 2015 data to constrain the inflationary phase. We demonstrate that the required tempera…
We provide a detailed study of gravitational reheating in quintessential inflation generalizing previous analyses only available for the standard case when inflation is followed by an era dominated by the energy density of radiation. Quintessential inflation assumes a common origin for inflation and the dark energy of the Universe. In this scenario reheating can occur through gravitational particle production during the inflation-kination transition. We calculate numerically the amount of the radiation energy density, and determine the temperature $T_*$ at which radiation starts dominating ove…
Incorporating three generations of right-handed Majorana neutrinos to quintessential inflation, we construct a model which simultaneously explains inflation, dark energy, dark matter and baryogenesis. These neutrinos have hierarchical masses $M_3 \sim 10^{13}$GeV, $M_2 \sim 10^{11}$GeV, $M_1 \sim 10$keV and are produced by gravitational particle production in the kination regime after inflation. The heaviest, the intermediate, and the lightest account for reheating, CP violation of leptogenesis, and dark matter, respectively. This model can be tested in various ways with forthcoming observatio…
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.
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…
A model is presented in which a single scalar field is responsible for both primordial inflation at early times and then dark energy at late times. This field is coupled to a second scalar field which becomes unstable and starts to oscillate after primordial inflation, thus driving a reheating phase that can create a high post-inflation temperature. This model easily avoids overproduction of gravity waves, which is a problem in the original quintessential inflation model in which reheating occurs via gravitational particle production.
We study a two-field quintessential Higgs inflation model in which a quintessence field with an exponential potential $e^{-βϕ/M_P}$ is coupled to the Higgs field from the beginning of inflation. The Higgs field itself is also non-minimally coupled to gravity. The inflationary predictions of this model for $n_s$ and $r$ are in good agreement with Planck 2018 data. We calculate the observables $n_s$ and $r$ against the free parameter $β$. Comparing these parameters with the observed $n_s$ and $r$ in Planck 2018 paper, we find $β\lesssim 8\times 10^{-3}$ that strongly disfavors the Swampland conj…
In this paper, we investigate a scenario of variable gravity and apply it to the unified description of inflation and late time cosmic acceleration dubbed quintessential inflation. The scalar field called "cosmon" which in this model unifies both the concepts reduces to inflaton at early epochs. We calculate the slow-roll parameters, the Hubble parameter at the end of inflation, the reheating temperature,the tensor-to-scalar ration and demonstrate the agreement of the model with observations and the Planck data.As for the post inflationary dynamics, cosmon tracks the background before it exits…
The combination of non-minimal couplings to gravity with the post-inflationary kinetic-dominated era typically appearing in quintessential inflation scenarios may lead to the spontaneous symmetry breaking of internal symmetries and its eventual restoration at the onset of radiation domination. On general grounds, the breaking of these symmetries leads to the generation of short-lived topological defects that tend to produce gravitational waves until the symmetry is restored. We study here the background of gravitational waves generated by a global cosmic string network following the dynamical …
Constraining Quintessential Inflation with ACT: A Gauss-Bonnet Gateway
Institute for Theoretical Physics and Cosmology, Zhejiang University of Technology（浙江工业大学理论物理与宇宙学研究所）；Department of Physics, Islamic University of Science and Technology（伊斯兰科技大学物理系）；Department of Physics, School of Advanced Sciences, Vellore Institute of Technology (VIT)（维罗尔理工学院高级科学学院物理系）；Centre for Cosmology and Science Popularization (CCSP), SGT University（SGT大学宇宙学与科学普及中心）
Quasi-pole quintessential inflation in metric-affine gravity
Consortium for Fundamental Physics, School of Physics and Astronomy, Lancaster University（兰开斯特大学物理与天文学院基础物理学联盟）；National Institute of Chemical Physics and Biophysics（国家化学物理和生物物理研究所）；Tallinn University of Technology（塔尔图理工大学）
We examine the possibility of achieving quintessential inflation, where the same field serves as both inflaton and quintessence, in the context of a five-dimensional braneworld. Braneworld cosmology provides an appropriate environment as it permits inflation with much steeper potentials than the conventional scenario, which is favourable to a late-time quintessence. We explore a wide space of models, together with contemporary observational data, to determine in which contexts such a picture is possible. We find that such a scenario, although attractive, is in fact impossible to achieve for th…
We consider the framework of quintessential inflation in the warm background which is caused by the dissipation of the scalar field energy density into relativistic degrees of freedom. The dissipation process has important consequences for the evolution both at the levels of background as well as perturbation and allows us to easily satisfy the observational constraints.~Our numerical analysis confirms that the model conforms to observational constraints even if the field-radiation coupling strength is weak. In the warm background, we investigate the post inflationary evolution of relic gravit…
We review the well-known Peebles-Vilenkin (PV) quintessential inflation model and discuss its possible improvements in agreement with the recent observations. The improved PV model depends only on two parameters: the inflaton mass $m$, and another smaller mass $M$; where the latter has to be chosen in order to undertake that, at present time, the dark energy density of the universe is approximately about 70\% of the total energy budget of the universe. The value of the inflaton mass $m$ is calculated using the observational value of the power spectrum of the scalar perturbations, and the value…
With the help of the tachyonic trapping mechanism one can potentially solve a number of problems affecting quintessential inflation models. In this mechanism we introduce a trapping field with a spontaneous symmetry breaking potential. When the quintessential inflaton passes the critical point, a sudden burst of particle production is able to reheat the Universe and trap the inflaton away from theminimum of its potential. However, self-interactions of the trapping field suppress particle production and reduce the efficiency of this process. We develop a method to compute the magnitude of the s…
Quintessential inflation provides a unified description of inflation and dark energy in terms of a single scalar degree of freedom, the cosmon. We present here a comprehensive overview of this appealing paradigm, highlighting its key ingredients and keeping a reasonable and homogeneous level of details. After summarizing the cosmological evolution in a simple canonical case, we discuss how quintessential inflation can be embedded in a more general scalar-tensor formulation and its relation to variable gravity scenarios. Particular emphasis is placed on the role played by symmetries. In particu…
In this paper, we consider a scenario of spontaneous baryogenesis in a framework of warm quintessential inflation where the residual inflaton field, left out after warm inflation, plays the role of quintessence field at late times and is coupled to a non-conserved baryonic current. Assuming a four fermion $(B-L)$ violating effective interaction, we have demonstrated that the required baryon asymmetry can be produced successfully in this case. We show that the post-inflationary evolution, with the underlying scalar field potential, $V(ϕ)=V^4_0 \exp{(-αϕ^n/M_{\rm Pl}^4 ) }$, $n>1$ well suited to…
If the inflaton and the quintessence fields are identified, the background geometry evolves through a stiff epoch undershooting the expansion rate of a radiation-dominated plasma. For some classes of inflationary potentials this scenario is at odds with the current observational evidence since the corresponding tensor-to-scalar ratio is too large. Quintessential inflation is analyzed when the gravitational action is supplemented by a contribution quadratic in the Einstein-Hilbert term. In the Palatini formulation the addition such a term does not affect the scalar modes during the inflationary…
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）
We calculate the baryon asymmetry value generated in the Scalar Field Condensate (SCF) baryogenesis model obtained in several inflationary scenarios and different reheating models. We provide analysis of the baryon asymmetry value obtained for more than 70 sets of parameters of the SCF model and the following inflationary scenarios, namely: new inflation, chaotic inflation, Starobinsky inflation, MSSM inflation, quintessential inflation. We considered both cases of efficient thermalization after inflation and also delayed thermalization. We have found that SFC baryogenesis model produces baryo…
