We have tested some simple quintessential inflation models, imposing that they match with the recent observational data provided by the BICEP and Planck's team and leading to a reheating temperature, which is obtained via gravitational particle production after inflation, supporting the nucleosynthesis success. Moreover, for the models coming from supergravity one needs to demand low temperatures in order to avoid problems such as the gravitino overproduction or the gravitational production of moduli fields, which are obtained only when the reheating temperature is due to the production of massless particles with a coupling constant very close to its conformal value.
We study the consequences of reheating in quintessential inflation. From simple inflationary quintessential models introduced in cite{hap, hap2}, we show that when the reheating is due to the production of heavy massive particles conformally coupled with gravity, a viable model which matches with the current observational data cite{Ade, Planck, bicep2} is only possible for reheating temperatures that range between $1$ GeV and $10^4$ GeV. On the other hand, when the universe reheats via the production of massless particles, the viability of the model is only possible when those particles are ne…
In this paper, we consider a model of quintessential inflation based upon inverse hyperbolic potential. We employ curvaton mechanism for reheating which is more efficient than gravitational particle production; the mechanism complies with nucleosynthesis constraint due to relic gravity waves. We obtain a lower bound on the coupling constant $g$ that governs the interaction of curvaton with matter fields. We study curvaton decay before domination and decay after domination and plot the allowed region in the parameter space in both cases.
We compute the gravitational production of conformally coupled superheavy particles during the phase transition from the end of inflation to the beginning of kination for $α$-attractors potentials in the context of Quintessential Inflation ($α$-QI), showing that the maximum value of the reheating temperature, independently of the value of the parameter $α$, is near $10^9$ GeV. This result, which contradicts the usual belief that the reheating via the production of superheavy massive particles leads to an inefficient reheating temperature, is due to the fact that in our numerical calculations w…
One of the most important issues in an inflationary theory as standard or quintessential inflation is the mechanism to reheat the universe after the end of the inflationary period in order to match with the Hot Big Bang universe. In quintessential inflation two mechanisms are frequently used, namely the reheating via gravitational particle production which is, as we will see, very efficient when the phase transition from the end of inflation to a kinetic regime (all the energy of the inflaton field is kinetic) is very abrupt, and the so-called instant preheating which is used for a very smooth…
An improved version of the well-known Peebles-Vilenkin model unifying early inflationary era to current cosmic acceleration, is introduced in order to match with the theoretical values of the spectral quantities provided by it with the recent observational data about the early universe. Since the model presents a sudden phase transition, we consider the simplest way to reheat the universe - via the gravitational production of heavy massive particles - which assuming that inflation starts at GUT scales $\sim 10^{16}$ GeV, allows us to use the Wentzel-Kramers-Brillouin (WKB) approximation and co…
We compute numerically the reheating temperature due to the gravitational production of conformally coupled superheavy particles during the phase transition from the end of inflation to the beginning of kination in two different Quintessential Inflation (QI) scenarios, namely Lorentzian Quintessential Inflation (LQI) and $α$-attractors in the context of Quintessential Inflation ($α$-QI). Once these superheavy particles have been created, they must decay into lighter ones to form a relativistic plasma, whose energy density will eventually dominate the one of the inflaton field in order to rehea…
In quintessence scalar field theories, the presence of scaling solutions are important during the radiation and matter epoch due to having their attractor character. Usually, it is assumed that the initial conditions of the quintessence field are in the basin of attraction of the scaling solutions. However, in order to reproduce the current cosmic acceleration, at late times, a mechanism to exit this behavior is needed. In the present work we show that the quintessential inflation models could be an excellent candidate to exhibit the above behavior. However, the crucial point of quintessential…
We will show that for exponential type potentials, which are used to depict quintessential inflation, the solutions whose initial conditions take place during the slow roll phase in order to describe correctly the inflationary period do not belong to the basin of attraction of the scaling solution -a solution of the scalar field equation whose energy density scale as the one of the fluid component of the universe during radiation or the matter domination period-, meaning that a late time mechanism to exit this behavior and depict correctly the current cosmic acceleration is not needed.
We present for smooth non-oscillating backgrounds an analytic formula which calculates the energy density of massive and massless particles created via gravitational particle production, thus giving the corresponding reheating temperature. It can be applied to models of Quintessential Inflation such as $α$-attractors, and shows that for masses larger than the Hubble rate at the end of inflation, namely $H_{END}$, the reheating temperature is exponentially suppressed. On the contrary, for masses of the order of $H_{END}$ one obtains a maximum reheating temperature of the order of $10^7$ GeV. Fi…
The gravitational production of superheavy dark matter is studied in the context of quintessential inflation. The superheavy particles, whose decay products are baryonic matter and are the responsible for the reheating of the universe after the end of the inflationary period, are not conformally coupled with gravity. On the contrary, dark matter is assumed to be conformally coupled with gravity. We show that the viability of these scenarios requires the mass of the superheavy dark matter to be greater than 8 x 10^{15} GeV.
The diagonalization method, introduced by a group of Russian scientists at the beginning of seventies, is used to compute the energy density of superheavy massive particles produced due to a sudden phase transition from inflation to kination in quintessential inflation models, the models unifying inflation with quintessence originally proposed by Peebles-Vilenkin. These superheavy particles must decay in lighter ones to form a relativistic plasma, whose energy density will eventually dominate the one of the inflaton field, in order to have a hot universe after inflation. In the present article…
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 incorporation of bulk viscosity process to General Relativity leads to the appearance of nonsingular backgrounds that, at early and late times, depict an accelerated universe. These backgrounds could be analytically calculated and mimicked, in the context of General Relativity, by a single scalar field whose potential could also be obtained analytically. We will show that, we can build viable backgrounds that, at early times, depict an inflationary universe leading to a power spectrum of cosmological perturbations which match with current observational data, and after leaving the inflation…
In the framework of a flat Friedmann-Lema{\^ı}tre-Robertson-Walker (FLRW) geometry, we present a nonsingular model (no big bang singularity at finite time) of our universe describing its evolution starting from its early inflationary era up to the present accelerating phase. We found that a hydrodynamical fluid with nonlinear equation of state could result in such a non singular scenario, which after the end of this inflationary stage, suffers a sudden phase transition and enters into the stiff matter dominated era, and the universe becomes reheated due to a huge amount of particle production.…
We study quintessential inflation with an inverse hyperbolic type potential $V(ϕ) = {V_0}/{\cosh \left( {ϕ^n}/{λ^n} \right)}$, where $V_0$, $λ$ and "n" are parameters of the theory. We obtain a bound on $λ$ for different values of the parameter n. The spectral index and the tensor-to-scalar-ratio fall in the $1 σ$ bound given by the Planck 2015 data for $n \geq 5$ for certain values of $λ$. However for $3 \leq n < 5$ there exist values of $λ$ for which the spectral index and the tensor-to-scalar-ratio fall only within the $2 σ$ bound of the Planck data. Furthermore, we show that the scalar fie…
The present work is a sequel of our previous work Phys.Rev.D { 93}, 084018 (2016) [arXiv:1601.08175 [gr-qc]] cite{hap} which depicted a simple version of an inflationary quintessential model whose inflationary stage was described by a Higgs type potential and the quintessential phase was responsible due to an exponential potential. Additionally, the model predicted a nonsingular universe in past which was geodesically past incomplete. Further, it was also found that the model is in agreement with the Planck 2013 data when running is allowed. But, this model was found to be unsuccessful with Pl…
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…
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 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.
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…
We have tested some simple $Λ$CDM (the same test is also valid for quintessence) inflation models, imposing that they match with the recent observational data provided by the BICEP and Planck's team and leading to a reheating temperature, which is obtained via gravitational particle production after inflation, supporting the nucleosynthesis success.
We compute numerically the reheating temperature due to the gravitational production of conformally coupled superheavy particles during the phase transition from the end of inflation to the beginning of kination in two different Quintessential Inflation (QI) scenarios, namely Lorentzian Quintessential Inflation (LQI) and $α$-attractors in the context of Quintessential Inflation ($α$-QI). Once these superheavy particles have been created, they must decay into lighter ones to form a relativistic plasma, whose energy density will eventually dominate the one of the inflaton field in order to rehea…
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 …
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.
First, we propose a scale-invariant modified gravity interacting with a neutral scalar "inflaton" and a Higgs-like SU(2)xU(1) iso-doublet scalar field based on the formalism of non-Riemannian (metric-independent) spacetime volume-elements. This model describes in the physical Einstein frame a quintessential inflationary scenario driven by the "inflaton" together with gravity-inflaton assisted dynamical spontaneous SU(2)xU(1) symmetry breaking in the post-inflationary universe, whereas SU(2)xU(1) symmetry remains intact in the inflationary epoch. Next, we find the explicit representation of the…
The end of inflation is connected to the standard cosmological scenario through reheating. During reheating, the inflaton oscillates around the minimum of the potential and thus decays into the daughter particles that populate the Universe at later times. Using cosmological evolution for observable CMB scales from the time of Hubble crossing to the present time, we translate the constraint on the spectral index $n_s$ from Planck data to the constraint on the reheating scenario in the context of Kähler Moduli Inflation. In addition, we extend the de-facto analysis generally done only for the pi…
A new model for inflation using modified gravity in the Palatini formalism is constructed. Here non-minimal coupling of scalar field h with the curvature R as a general function f(R,h) is considered. Explicit inflation models for some choices of f(R,h) are developed. By writing an equivalent scalar-tensor action for this model and going over to Einstein frame, slow roll parameters are constructed. There exists a large parameter space which satisfies values of n_s and limits on r compatible with Planck 2018 data. Further, we calculate reheating temperature and the number of e-folds at the end o…
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 …
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…
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 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…
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…
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…
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 …
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 la…
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 …
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）
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 …
We explore the possibility of baryogenesis in the framework of quintessential inflation. We focus on the model independent features of the underlying paradigm and demonstrate that the required baryon asymmetry can successfully be generated in this scenario. To this effect, we use the effective field theory framework with desired terms in the Lagrangian necessary to mimic baryon number violation \textit{à la} spontaneous baryogenesis which can successfully evade Sakharov's requirement allowing us to generate the observed baryon asymmetry in the equilibrium process. Our estimates are independent…
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…
