The intermediate, logamediate and exponential inflationary models in the context of Galileon inflation or G-inflation are studied. By assuming a coupling of the form $G(ϕ,X)\proptoϕ^ν\,X^{n}$ in the action, we obtain different analytical solutions from the background cosmological perturbations assuming the slow-roll approximation. General conditions required for these models of G-inflation to be realizable are determined and discussed. In general, we analyze the condition of inflation and also we use recent astronomical and cosmological observations for constraining the parameters appearing in these G-inflationary models.
In a logamediate inflationary universe model we introduce the curvaton field in order to bring this inflationary model to an end. In this approach we determine the reheating temperature. We also outline some interesting constraints on the parameters that describe our models. Thus, we give the parameter space in this scenario.
Warm inflationary universe models in the context of logamediate expansion are studied. General conditions required for these models to be realizable and discussed. This study is done in the weak and strong dissipative regimes. The parameters of our models are constrained from the observational data.
A logamediate inflationary model in the presence of the tachyon scalar field will be studied. Considering slow-roll inflation, the equations of motion of the universe and the tachyon field will be derived. In the context of perturbation theory, some important perturbation parameters will be obtained and using numerical calculations the consistency of our model with observational data will be illustrated.
We study a general form for the dissipative coefficient $Γ(T,ϕ)=C_ϕ\,T^{m}/ϕ^{m-1}$ in the context of warm intermediate and logamediate inflationary universe models. We analyze these models in the weak and strong dissipative regimes. In the slow-roll approximation, we describe in great detail the characteristics of these models. In both regimes, we use recent data from the WMAP nine-year data and Planck data to constrain the parameters appearing in our models.
We investigate the power-law, intermediate, and logamediate inflationary models in the framework of DBI non-canonical scalar field with constant sound speed. In the DBI setting, we first represent the power spectrum of both scalar density and tensor gravitational perturbations. Then, we derive different inflationary observables including the scalar spectral index $n_s$, the running of the scalar spectral index $dn_s/d\ln k$, and the tensor-to-scalar ratio $r$. We show that the 95\% CL constraint of the Planck 2015 T+E data on the non-Gaussianity parameter $f_{\rm NL}^{\rm DBI}$ leads to the so…
We study logamediate inflation in the context of $f(T)$ teleparallel gravity. $f(T)$-gravity is a generalization of the teleparallel gravity which is formulated on the Weitzenböck spacetime, characterized by the vanishing curvature tensor (absolute parallelism) and the non-vanishing torsion tensor. We consider an $f(T)$-gravity model which is sourced by a canonical scalar field. Assuming a power-law $f(T)$ function in the action, we investigate an inflationary universe with a logamediate scale factor. Our results show that, although logamediate inflation is completely ruled out by observationa…
According to a Barrow's solution for the scale factor of the universe, the main properties of the tachyon inflation model in the framework of RSII braneworld are studied. Within this framework the basic slow-roll parameters are calculated analytically. We compare this inflationary scenario against the latest observational data. The predicted spectral index and the tensor-to-scalar fluctuation ratio are in excellent agreement with those of {\it Planck 2015}. The current predictions are consistent with those of viable inflationary models.
A computation of the inflationary observables n_{s} and r is made for `logamediate' inflation where the cosmological scale factor expands as $a=\exp (A(\ln t)^λ)$, and is compared to their predicted values in the intermediate inflationary theory, where $a=\exp (Bt^{f})$. Both versions prove to be consistent with observational measurements of the cosmic background radiation. It is shown that the dynamics of a single inflaton field can be mimicked by a system of several fields in an analogous manner to that created by the joint evolution of the fields in assisted power-law inflation.
Tachyon inflationary universe model on the brane in the context of warm inflation is studied. In slow-roll approximation and in longitudinal gauge, we find the primoradial perturbation spectrums for this scenario. We also present the general expressions of the tensor-scalar ratio, scalar spectral index and its running. We develop our model by using exponential potential, the characteristics of this model are calculated in great details. We also study our model in the context of intermediate (where scale factor expands as: $a=a_0\exp(At^f)$) and logamediate (where the scale factor expands as: $…
In this paper we study non-abelian gauge field inflation (gauge-flation) model in the context of intermediate and logamediate scenario. Important parameters of this model are presented for these two cases. Numerical study shows that the intermediate and logamediate gauge-flation are compatible with WMAP9 observational data. For intermediate inflation, where the cosmological scale factor expands as: $a(t)=a_0\exp(At^f)$ ($A>0, 0<f<1$), $N\geq 100$ cases lead to $0.02<r<0.11$ ($r$ is tensor-scalar ratio) and $N\simeq50 $ case leads to $n_s\simeq 0.96$ ($n_s$ is spectral index). These constraints…
This paper is devoted to study the warm inflation using vector fields in the background of locally rotationally symmetric Bianchi type I universe model. We formulate the field equations, slow-roll and perturbation parameters (scalar and tensor power spectra as well as their spectral indices) under slow-roll approximation. We evaluate all these parameters in terms of directional Hubble parameter during intermediate and logamediate inflationary regimes by taking the dissipation factor as a function of scalar field as well as a constant. In each case, we calculate the observational parameter of i…
The $β$-exponential inflation is driven by a class of primordial potentials, derived in the framework of braneworld scenarios, that generalizes the well-known power law inflation. In this paper we update previous constraints on the minimal coupled $β$-exponential model [1] and extend the results also deriving the equations for the non-minimal coupled scenario. The predictions of both models are tested in light of the latest temperature and polarization maps of the Cosmic Microwave Background and clustering data. We also compare the predictions of these models with the standard $Λ$CDM cosmology…
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…
In this paper we shall consider an exponential inflationary model in the context of vacuum $F(R)$ gravity. By using well-known reconstruction techniques, we shall investigate which $F(R)$ gravity can realize the exponential inflation scenario at leading order in terms of the scalar curvature, and we shall calculate the slow-roll indices and the corresponding observational indices, in the context of slow-roll inflation. We also provide some general formulas of the slow-roll and the corresponding observational indices in terms of the $e$-foldings number. In addition, for the calculation of the s…
A generic feature of viable $F(R)$ gravity is investigated: It is demonstrated that during the matter dominated era the large frequency oscillations of the effective dark energy may influence the behavior of higher derivatives of the Hubble parameter with the risk to produce some singular unphysical solutions at high redshift. This behavior is explicitly analyzed for realistic $F(R)$ models, in particular, exponential gravity and a power form model. To stabilize such oscillations, we consider the additional modification of the models via a correction term which does not destroy the viability p…
In this paper we study a tachyon cosmological model based on dynamics of a 3-brane in the second Randall-Sundrum (RSII) model extended to include matter in the bulk. The presence of matter in the bulk changes warp factor which leads to modification of inflationary dynamics. The additional brane behaves effectively as a tachyon. We calculate numerically observation parameters of inflation: the scalar spectral index ($n_s$) and the tensor-to-scalar ratio ($r$) for the exponential potential of tachyon field.
We confront quasi-exponential models of inflation with WMAP seven years dataset using Hamilton Jacobi formalism. With a phenomenological Hubble parameter, representing quasi exponential inflation, we develop the formalism and subject the analysis to confrontation with WMAP seven using the publicly available code CAMB. The observable parameters are found to fair extremely well with WMAP seven. We also obtain a ratio of tensor to scalar amplitudes which may be detectable in PLANCK.
A disformal coupling between two scalar fields is considered in the context of cosmological inflation. The coupling introduces novel derivative interactions mixing the kinetic terms of the fields but without introducing superluminal or unstable propagation of the two scalar fluctuation modes. Though the typical effect of the disformal coupling is to inhibit one of the fields from inflating the universe, the energy density of the other field can drive viable near Sitter -inflation in the presence of nontrivial disformal dynamics, in particular when one assumes exponential instead of power-law f…
We analyse $f(R)$ theories of gravity from a dynamical system perspective, showing how the $R^2$ correction in Starobinsky's model plays a crucial role from the viewpoint of the inflationary paradigm. Then, we propose a modification of Starobinsky's model by adding an exponential term in the $f(R)$ Lagrangian. We show how this modification could allow to test the robustness of the model by means of the predictions on the scalar spectral index $n_s$.
The 2015 Planck data release tightened the region of the allowed inflationary models. Inflationary models with convex potentials have now been ruled out since they produce a large tensor to scalar ratio. Meanwhile the same data offers interesting hints on possible deviations from the standard picture of CMB perturbations. Here we revisit the predictions of the theory of the origin of the universe from the landscape multiverse for the case of exponential inflation, for two reasons: firstly to check the status of the anomalies associated with this theory, in the light of the recent Planck data; …
A model where the inflationary phase emerges as a response to protect the Fischler-Susskind holographic bound is described. A two fluid model in a closed universe inflation picture is assumed, and a discussion on conditions under which is possible to obtain an additional exponential expansion phase as those currently observed is given.
We heal the cosmological constant problem by means of a \emph{cancellation mechanism} that adopts a phase transition during which quantum fluctuations are eliminated. To this purpose, we propose that a generalized scalar (dark) matter field with a non-vanishing pressure term can remove the vacuum energy contribution, if its corresponding thermodynamics is written in terms of a \emph{quasi-quintessence} representation. In such a picture, pressure differs from quintessence as it shows a zero kinetic contribution. Using this field, we investigate a metastable transition phase, in which the univer…
We introduce super exponential inflation ($ω< -1$) from a 5D Riemann-flat canonical metric on which we make a dynamical foliation. The resulting metric describes a super accelerated expansion for the early universe well-known as super exponential inflation that, for very large times, tends to an asymptotic de Sitter (vacuum dominated) expansion. The scalar field fluctuations are analyzed. The important result here obtained is that the spectral index for energy density fluctuations is not scale invariant, and for cosmological scales becomes $n_s(k<k_*) \simeq 1$. However, for astrophysical scal…
In this paper we investigate how to describe in a unified way a constant-roll inflationary era with a dark energy era, by using the theoretical framework of $F(R)$ gravity. To this end, we introduce some classes of appropriately chosen $F(R)$ gravity models, and we examine in detail how the unification of early and late-time acceleration eras can be achieved. We study in detail the inflationary era, and as we demonstrate it is possible to achieve a viable inflationary era, for which the spectral index of primordial curvature perturbations and the scalar-to-tensor ratio can be compatible with t…
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.
This paper is devoted to the analysis of a class of $F(R)$ gravity, where additional logarithmic corrections are assumed. The gravitational action includes an exponential term and a $R^2$ inflationary term, both with logarithmic corrections. This model can unify an early time inflationary era and also the late time acceleration of the universe expansion. This model is deeply analysed, confronting with recent observational data coming from the largest Pantheon Type Ia supernovae sample, the latest measurements of the Hubble parameter $H(z)$, manifestations of Baryon Acoustic Oscillations and Co…
We have investigated inflationary model constructed from minimally modified gravity (MMG) theories. The MMG theory in the form of $f({\bf H}) \propto {\bf H}^{1+p}$ gravity where, ${\bf H}$ is the Hamiltonian constraint in the Einstein gravity and $p$ is constant, has been studied. An inflation is difficult to be achieved in this theory of gravity unless an additional scalar field playing a role of inflaton is introduced in the model. We have found that the inflaton with exponential potential can drive inflation with graceful exist different from the case of Einstein gravity. The slow-roll par…
We investigate how a Type IV future singularity can be included in the cosmological evolution of a well-known exponential model of inflation. In order to achieve this we use a two scalar field model, in the context of which the incorporation of the Type IV singularity can be consistently done. In the context of the exponential model we study, when a Type IV singularity is included in the evolution, an instability occurs in the slow-roll parameters, and in particular on the second slow-roll parameter. Particularly, if we abandon the slow-roll condition for both the scalars we shall use, then th…
We consider issues related to tachyonic inflation with exponential potential. We find exact solution of evolution equations in the slow roll limit in FRW cosmology. We also carry out similar analysis in case of Brane assisted tachyonic inflation. We investigate the phase space behavior of the system and show that the dust like solution is a late time attractor. The difficulties associated with reheating in the tachyonic model are also indicated.
In this paper we investigate extended inflation with an exponential potential $V(σ)= V_0 e^{-κσ}$, which provides a simple cosmological scenario where the distribution of the constants of Nature is mostly determined by $κ$. In particular, we show that this theory predicts a uniform distribution for the Planck mass at the end of inflation, for the entire ensemble of universes that undergo stochastic inflation. Eternal inflation takes place in this scenario for a broad family of initial conditions, all of which lead up to the same value of the Planck mass at the end of inflation. The predicted v…
In the present work we study a warm inflationary model defined by a quasi-exponential inflaton potential and an inflaton decay rate proportional to the Hubble rate. The model is characterized by three free parameters. We compute the power spectrum, the scalar spectral index as well as the tensor-to-scalar ratio within the framework of the model, and we compare with the latest Planck data. On the $r-n_s$ plane we show both the theoretical curves and the contour plots allowed by observations, and we constrain the parameters of the model accordingly. The non-linear parameter $f_{NL}$, correspondi…
The curvature perturbations produced during an early era of inflation are known to have quasi-Gaussian distribution functions close to their maximum, where they are well constrained by measurements of the cosmic microwave background anisotropies and of the large-scale structures. In contrast, the tails of these distributions are poorly known, although this part is the relevant one for rare, extreme objects such as primordial black holes. We show that these tails are highly non-Gaussian, and cannot be described with standard non-Gaussian expansions, that are designed to approximate the distribu…
In this work we consider Randall-Sundrum braneworld type scenarios, in which the spacetime is described by a five-dimensional manifold with matter fields confined in a domain wall or three-brane. We present the results of a systematic analysis, using dynamical systems techniques, of the qualitative behaviour of Friedmann-Lemaitre-Robertson-Walker type models, whose matter is described by a scalar field with an exponential potential. We construct the state spaces for these models and discuss how their structure changes with respect to the general-relativistic case, in particular, what new criti…
It has very recently been realized that coupling branes to higher dimensional quantum gravity theories and considering the consistency of what lives on the branes, one is able to understand whether such theories can belong either to the swampland or to the landscape. In this regard, in the present work, we study a warm inflation model embedded in the Randall-Sundrum braneworld scenario. It is explicitly shown that this model belongs to the landscape by supporting a strong dissipative regime with an inflaton steep exponential potential. The presence of extra dimension effects from the braneworl…
We study inflation within the framework of non-canonical scalar field. In this scenario, we obtain the inflationary observables such as the scalar spectral index, the tensor-to-scalar ratio, the running of the scalar spectral index as well as the equilateral non-Gaussianity parameter. Then, we apply these results for the exponential and inverse power-law potentials. Our investigation shows that although the predictions of these potentials in the standard canonical inflation are completely ruled out by the Planck 2015 observations, their results in non-canonical scenario can lie inside the allo…
In the present work we study the consequences of considering an inflationary universe model in which the Hubble rate has a quasi-exponential dependence in the inflaton field, given by $H(ϕ)=H_{inf}\exp \left[\frac{\fracϕ{m_p}}{p\left(1+\fracϕ{m_p}\right)}\right]$. We analyze the inflation dynamics under the Hamilton-Jacobi approach, which allows us to consider $H(ϕ)$, rather than $V(ϕ)$, as the fundamental quantity to be specified. By comparing the theoretical predictions of the model together with the allowed contour plots in the $n_s-r$ plane and the amplitude of primordial scalar perturbati…
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 introduce in this paper a new framework for obtaining a period of exponential inflation that is entirely driven by the quadratic kinetic energy of a scalar field. In contrast to recent attempts to realize scalar field inflation without potentials (such as k-inflation or ghost inflation), we find that it is possible to obtain exponential inflation, without invoking any higher derivative actions, or modifying gravity, and that unlike all previous approaches, we do not require a $ρ= -p$ phase in order to realize inflation. The inflaton in our proposed framework is a scalar field with a quadrat…
The Friedmann-Robertson-Walker (FRW) cosmology is analyzed with a general potential $\rm V(ϕ)$ in the scalar field inflation scenario. The Bohmian approach (a WKB-like formalism) was employed in order to constraint a generic form of potential to the most suited to drive inflation, from here a family of potentials emerges; in particular we select an exponential potential as the first non trivial case and remains the object of interest of this work. The solution to the Wheeler-DeWitt (WDW) equation is also obtained for the selected potential in this scheme. Using Hamilton's approach and equation…
We discuss dissipative stochastic wave and diffusion equations resulting from an interaction of the inflaton with an environment in an external expanding metric. We show that a diffusion equation well approximates the wave equation in a strong friction limit. We calculate the long wave power spectrum of the wave equation under the assumption that the perturbations are slowly varying in time and the expansion is almost exponential. Under the assumption that the noise has a form invariant under coordinate transformations we obtain the power spectrum close to the scale invariant one. In the diffu…
The anisotropic Bianchi type I in multi-scalar field cosmology is studied with a particular potential of the form $\rm V= V_0 e^{-\left[λ_1 ϕ_1 + \cdots + λ_n ϕ_n \right]}\,,$ which emerges as a condition between the time derivatives of their corresponding momenta. Using the Hamiltonian formalism for the inflation epoch with a quintessence framework we find the exact solutions for the Einstein-Klein-Gordon (EKG) system with different scenarios specified by the parameter $\rm λ^2= \sum_{i=1}^n λ_i^2$. For the quantum scheme of this model, the corresponding Wheeler-DeWitt (WDW) equation is solve…
A generalization of the canonical and non-canonical theory of inflation is introduced in which the kinetic energy term in action is written as non-local term. The inflationary universe within the framework of considering this non-locality will be studied. To investigate the effects of non-locality on the inflationary parameters we consider two well known models of inflationary scenario includes of chaotic and exponential inflation proposals. For such scenarios some important parameters include slow roll parameters, scalar and tensor power spectra, spectral indices, the tensor-to-scalar ratio a…
A study of the slow-roll inflation for an exponential potential in the frame of the scalar-tensor theory is performed, where non-minimal kinetic coupling to curvature and non-minimal coupling of the scalar field to the Gauss-Bonnet invariant are considered. Different models were considered with couplings given by exponential functions of the scalar field, that lead to graceful exit from inflation and give values of the scalar spectral index and the tensor-to-scalar ratio in the region bounded by the current observational data. Special cases were found, where the coupling functions are inverse …
Global curvature control in a regular black hole with Minkowski core and inner-extremal horizon
School of Physics and Astronomy, China West Normal University（西华师范大学物理与天体学院）；Institute of High Energy Physics, Chinese Academy of Sciences（中国科学院高能物理研究所）；School of Physics, University of Chinese Academy of Sciences（中国科学院大学物理学院）
We study the quantization of the Einstein-Hilbert action for a small true vacuum bubble without matter or scalar field. The quantization of action induces an extra term of potential called quantum potential in Hamilton-Jacobi equation, which gives expanding solutions including the exponential expansion solutions of the scalar factor $a$ for the bubble. We show that exponential expansion of the bubble continues with a short period (about a Planck time $t_p$), no matter whether the bubble is closed, flat or open. The exponential expansion ends spontaneously when the bubble becomes large, i.e., t…
Inflation is studied in the context of asymptotically safe theories of gravitation. Conditions are explored under which it is possible to have a long period of nearly exponential expansion that eventually comes to an end.
