The effective inflationary Lagrangian is a prominent challenge for theoretical cosmologists, since it may contain imprints of the quantum epoch. In view of the fact that higher order curvature terms might be present in the effective inflationary Lagrangian, in this work we introduce the theoretical framework of power-law $f(R)$ gravity corrected canonical scalar field inflation, aiming to study the inflationary dynamics of this new framework. The main characteristic of this new theoretical framework is the dominance of a power-law $f(R)$ gravity term $\sim R^n$, with $1<n<2$, compared to the Einstein-Hilbert term $\sim R$. In effect, the field equations are controlled by the $R^n$ term in contrast to the Einstein-Hilbert canonical scalar theory. We extract the slow-roll field equations and we calculate the slow-roll indices of the resulting theory which acquire quite elegant final form, when the slow-roll conditions hold true. Accordingly, we examine quantitatively the inflationary phenomenological implications of the theoretical framework we introduced, by choosing simple hybrid-like scalar field potentials. As we evince the resulting theory is in good agreement with the latest Planck data for a wide range of the free parameters of the model. Thus our theoretical framework makes possible to obtain viable inflationary theories, which otherwise would be non-viable, such as the simple power-law $f(R)$ gravity model or the simple power-law scalar model.
String theory enjoys an elevated role among quantum gravity theories, since it seems to be the most consistent UV completion of general relativity and the Standard Model. However, it is hard to verify the existence of this underlying theory on terrestrial accelerators. One way to probe string theory is to study its imprints on the low-energy effective inflationary Lagrangian, which are quantified in terms of high energy correction terms. It is highly likely, thus, to find higher order curvature terms combined with string moduli, that is scalar fields, since both these types of interactions and…
We employ a fully renormalized computation of the one loop contribution to the self-mass-squared of the conformally coupled (CC) scalar interacting with gravitons during inflation to study how inflationary produced gravitons affect the CC scalar evolution equation. The quantum corrected scalar mode functions turn out to get a secular growth effect, proportional to a logarithm of the scale factor at late times.
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, in the first part, contemplate a massless minimally coupled scalar which is Yukawa-coupled to a massless Dirac fermion in a locally de Sitter background of an inflating spacetime. We compute the scalar's quantum corrected mode function, power spectrum, spectral index and the running of the spectral index at one-loop order. We find that the spectrum is slightly blue-tilted; hence, the amplitudes of fluctuations grow slightly toward the smaller scales. Then, in the second part, we apply the computation method used in the first part to a massless minimally coupled scalar with a quartic self-i…
The cosmological primordial power spectrum is known to be one of the most promising observable to probe quantum gravity effects. In this article, we investigate how the tensor power spectrum is modified by Loop Quantum Gravity corrections. The two most important quantum terms, holonomy and inverse volume, are explicitly taken into account in a unified framework. The equation of propagation of gravitational waves is derived and solved for one set of parameters.
In this paper we shall study the inflationary aspects of a logarithmic corrected $R^2$ Starobinsky inflation model, in the presence of a Kalb-Ramond field in the gravitational action of $F(R)$ gravity. Our main interest is to pin down the effect of this rank two antisymmetric tensor field on the inflationary phenomenology of the $F(R)$ gravity theory at hand. The effects of the Kalb-Ramond field are expected to be strong during the inflationary era, however as the Universe expands, the energy density of the Kalb-Ramond field scales as $\sim a^{-6}$ so dark matter and radiation dominate over th…
We study the intermediate inflation in a non-canonical scalar field framework with a power-like Lagrangian. We show that in contrast with the standard canonical intermediate inflation, our non-canonical model is compatible with the observational results of Planck 2015. Also, we estimate the equilateral non-Gaussianity parameter which is in well agreement with the prediction of Planck 2015. Then, we obtain an approximation for the energy scale at the initial time of inflation and show that it can be of order of the Planck energy scale, i.e. ${M_P} \sim {10^{18}}\,{\rm{GeV}}$. We will see that a…
In the present paper, we study the inflationary phenomenology of a $k$-inflation corrected Einstein-Gauss-Bonnet theory. Non-canonical kinetic terms are known for producing Jean instabilities or superluminal sound wave velocities in the aforementioned era, but we demonstrate in this work that by adding Gauss-Bonnet string corrections and assuming that the non-canonical kinetic term $ωX^γ$ is in quadratic, one can obtain a ghost free description. Demanding compatibility with the recent GW170817 event forces one to accept that the relation $\ddotξ=H\dotξ$ for the scalar coupling function $ξ(ϕ)$.…
Motivated by issues on inflation, a generalized modified gravity model is investigated, where the model Lagrangian is described by a smooth function $f(R, K, ϕ)$ of the Ricci scalar $R$, the kinetic term $K$ of a scalar field $ϕ$. In particular, the one-loop effective action in the de Sitter background is examined on-shell as well as off-shell in the Landau gauge. In addition, the on-shell quantum equivalence of $f(R)$ gravity in the Jordan and Einstein frames is explicitly demonstrated. Furthermore, we present applications related to the stability of the de Sitter solutions and the one-loop q…
In non-canonical two-field inflation models, deviations from the canonical model can be captured by a parameter $ξ$. We show this parameter is usually one half of the slow-roll order and analytically calculate the primordial power spectra accurate to order $ξ^2$. The super-horizon perturbations are studied with an improved method, which gives a correction of order $ξ^2$. Three typical examples demonstrate that our analytical formulae of power spectra fit well with numerical simulation.
We study the inflation via logarithmic entropy-corrected holographic dark energy LECHDE model with future event horizon, particle horizon and Hubble horizon cut-offs, and compare the results with those of obtained in the study of inflation by holographic dark energy HDE model. In comparison, the spectrum of primordial scalar power spectrum in the LECHDE model becomes redder than the spectrum in HDE model. Moreover, the consistency with the observational data in LECHDE model of inflation, constrains the reheating temperature and Hubble parameter by one parameter of holographic dark energy and t…
$R^2$-corrected dark energy (DE) models in $F(R)$ gravity have been widely investigated in recent years, which not only removes the weak singularity potentially present in DE models but also provide us with a unified picture of the cosmic history, including the inflationary and DE epochs. Towards the unified interpretation of dynamical DE all over the cosmic history in the class of $R^2$-corrected DE models, we explore the universal features of the scalaron dynamics in the radiation-dominated epoch, along with the chameleon mechanism, by keeping our eyes on the inflationary and DE epochs. We s…
We compute corrections to the inflationary potential due to conformally coupled non-relativistic matter. We find that under certain conditions of the matter coupling, inflation may be interrupted abruptly. We display this in the superconformal Starobinsky model, where matter is conformally coupled to the Einstein frame metric. These corrections may easily stop inflation provided that there is an initial density of non-relativistic matter. Since these additional heavy degrees of freedom generically occur in higher dimension theories, for example as Kaluza-Klein modes, this effect can arise in m…
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 …
We revisit inflation with non-canonical scalar fields by applying deformed-steepness exponential potentials. We show that the resulting scenario can lead to inflationary observables, and in particular to scalar spectral index and tensor-to-scalar ratio, in remarkable agreement with observations. Additionally, a significant advantage of the scenario is that the required parameter values, such as the non-canonicality exponent and scale, as well as the potential exponent and scale, do not need to acquire unnatural values and hence can accept a theoretical justification. Hence, we obtain a signifi…
Primordial black holes (PBHs) can generically form in inflationary setups through the collapse of enhanced cosmological perturbations, providing us access to the early Universe through their associated observational signatures. In the current work we propose a new mechanism of PBH production within non-canonical inflation, using a class of steep-deformed inflationary potentials compatible with natural values for the non-canonical exponents. In particular, by requiring significant PBH production we extract constraints on the non-canonical exponents. Additionally, we find that our scenario can l…
We compute the one- and two-loop corrected mode function of a massless minimally coupled scalar endowed with a quartic self-interaction in the locally de Sitter background of an inflating universe for a state which is released in Bunch-Davies vacuum at time $t=0$. We then employ it to correct the scalar's tree-order scale invariant power spectrum $Δ^2_φ$. The corrections are secular, and have scale dependent part that can be expanded in even powers of $k/(Ha)$, where $k$ is the comoving wave number, $H$ is the expansion rate and $a$ is the cosmic scale factor. At one-loop, the scale invariant …
In this paper, we consider an inflationary model of $f(R)$ gravity with polynomial form plus logarithmic term. We calculate some cosmological parameters and compare our results with the Plank 2015 data. We find that presence of both logarithmic and polynomial corrections are necessary to yield slow-roll condition. Also, we study critical points and stability of the model to find that it is a viable model.
In this work, we investigate the non-minimally coupled scenario in the context of warm inflation with quantum-corrected self-interacting potential. We transform the potential in the Jordan frame to the Einstein frame and consider a dissipation parameter of the form $Γ= C_{T}T$ with $C_T$ being a coupling parameter. We focus on the strong regime of which the interaction between inflaton and radiation fluid has been taken into account. We compute inflationary observables and constrain the parameters of our model using current Planck 2018 data. With the sizeable number of {\it e}-folds and proper…
In this paper we investigate the inflationary phenomenology of an Einstein-Gauss-Bonnet theory with the extension of a logarithmic modified $f(R)$ gravity, compatible with the GW170817 event. The main idea of our work is to study different results for an almost linear Ricci scalar through logarithmic corrections and examine whether such model is viable. First of all, the theoretical framework under slow-roll evolution of the scalar field is presented and also developed the formalism of the constant-roll evolution making predictions for the non- Gaussianities of the models is developed , since …
The evolution of the non-adiabatic pressure perturbation during inflation driven by two scalar fields is studied numerically for three different types of models. In the first model, the fields have standard kinetic terms. The other two models considered feature non-canonical kinetic terms; the first containing two fields which are coupled via their kinetic terms, and the second where one field has the standard kinetic term with the other field being a DBI field. We find that the evolution and the final amplitude of the non-adiabatic pressure perturbation depends strongly on the kinetic terms.
Under the main assumption that the axion scalar field mainly composes the dark matter in the Universe, in this paper we shall extend the formalism of kinetic axion $R^2$ gravity to include Gauss-Bonnet terms non-minimally coupled to the axion field. As we demonstrate, this non-trivial Gauss-Bonnet term has dramatic effects on the inflationary phenomenology and on the kinetic axion scenario. Specifically, in the context of our formalism, the kinetic axion ceases to be kinetically dominated at the end of the inflationary era, since the condition $\dotϕ\simeq 0$ naturally emerges in the theory. T…
It is quite well known for some time that string inspired axionic terms of the form $ν(ϕ)\tilde{R}R$, known also as Chern-Simons terms, do not affect the scalar perturbations and the background evolution for a flat Friedman-Robertson-Walker Universe. In this paper we study and quantify the implications of the presence of the above term in the context of vacuum $f(R)$. Particularly, we assume that axionic dark matter is present during inflation, and we examine in a quantitative way the effects of axionic Chern-Simons terms on the tensor perturbations. The axion field is quantified in terms of a…
In this work we investigate which Loop Quantum Cosmology corrected Gauss-Bonnet $F(\mathcal{G})$ gravity can realize two singular cosmological scenarios, the intermediate inflation and the singular bounce scenarios. The intermediate inflation scenario has a Type III sudden singularity at $t=0$, while the singular bounce has a soft Type IV singularity. By using perturbative techniques, we find the holonomy corrected $F(\mathcal{G})$ gravities that generate at leading order the aforementioned cosmologies and we also argue that the effect of the holonomy corrections is minor to the power spectrum…
This paper focuses on the realization of an inflationary model from a canonical scalar field theory with a Woods-Saxon potential, in the slow-roll approximation. Our analysis indicates that the observable quantities derived theoretically from our model, namely the spectral index of the primordial scalar curvature perturbations and the tensor-to-scalar ratio, are compatible with the latest Planck collaboration data. We also discuss the qualitative features of the potential, and we show that the value of the scalar field for which the graceful exit occurs, coincides with the inflection point of …
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…
This paper revisits the Inflationary scenario within the framework of scalar field models possessing a non-canonical kinetic term. We obtain closed form solutions for all essential quantities associated with chaotic inflation including slow roll parameters, scalar and tensor power spectra, spectral indices, the tensor-to-scalar ratio, etc. We also examine the Hamilton-Jacobi equation and demonstrate the existence of an inflationary attractor. Our results highlight the fact that non-canonical scalars can significantly improve the viability of inflationary models. They accomplish this by decreas…
We consider higher-derivative quantum gravity where renormalization group improved effective action beyond one-loop approximation is derived. Using this effective action, the quantum-corrected FRW equations are analyzed. De Sitter universe solution is found. It is demonstrated that such de Sitter inflationary universe is instable. The slow-roll inflationary parameters are calculated. The contribution of renormalization group improved Gauss-Bonnet term to quantum-corrected FRW equations as well as to instability of de Sitter universe is estimated. It is demonstrated that in this case the spectr…
After the recent GW170817 event of the two neutron stars merging, many string corrected cosmological theories confronted the non-viability peril. This was due to the fact that most of these theories produce massive gravitons primordially. Among these theories were the ones containing a non-minimal kinetic coupling correction term in the Lagrangian, which belong to a subclass of Horndeski theories. In this work we demonstrate how these theories may be revived and we show how these theories can produce primordial gravitational waves with speed $c_T^2=1$ in natural units, thus complying with the …
We construct phase-space structure of a typical higher-order theory of gravity, in the background of anisotropic Bianchi-1 mini-superspace, following `Modified Horowitz Formalism' as well as applying `Dirac Algorithm' (after taking care of the divergent terms), and establish equivalence. Canonical quantization, and semiclassical approximation are performed to expatiate the fact that such a quantum theory transits successfully to a classical de-Sitter universe. Inflation has thereafter been studied. The numerical values of the inflationary parameters show excellent agreement with the latest rel…
We investigate in which cases a singular evolution with a singularity of Type IV, can be consistently incorporated in deformations of the $R^2$ inflationary potential. After demonstrating the difficulties that the single scalar field description is confronted with, we use a general two scalar fields model without other matter fluids, to describe the Type IV singular evolution, with one of the two scalar fields being canonical. By appropriately choosing the non-canonical scalar field, we show that the canonical scalar field corresponds to a potential that is nearly the $R^2$ inflation potential…
We study a mechanism for the amplification of the inflationary scalar perturbation when the inflaton field action is non-canonical, i.e. the inflaton kinetic term has a non-standard form. For such a case the speed of sound of the perturbations generated during inflation is less than one and in general changes with time. Furthermore in such models, even when the scalar field potential is negligible, diverse inflationary attractors may exist. The possible effects of a speed of sound approaching zero during some stage of inflation may lead to a large amplification for the amplitude of the scalar …
In this paper we study slow-roll inflation with holonomy corrections from loop quantum cosmology. Both tensor and scalar power spectra of primordial perturbations are computed up to the first order in slow-roll parameters and $V/ρ_{c}$, where $V$ is a potential of the scalar field and $ρ_{c}$ is a critical energy density (expected to be of the order of the Planck energy density). Possible normalizations of modes at short scales are discussed. In case the normalization is performed with use of the Wronskian condition applied to adiabatic vacuum, the tensor and scalar spectral indices are not qu…
It is well known that a canonical scalar field with an exponential potential can drive power law inflation (PLI). However, the tensor-to-scalar ratio in such models turns out to be larger than the stringent limit set by recent Planck results. We propose a new model of power law inflation for which the scalar spectra index, the tensor-to-scalar ratio and the non-gaussianity parameter $f_{_{\mathbf{NL}}}^{\mathrm{equil}}$ are in excellent agreement with Planck results. Inflation, in this model, is driven by a non-canonical scalar field with an inverse power law potential. The Lagrangian for our …
The reheating dynamics after the inflation induced by $R^2$-corrected $f(R)$ model is considered. To avoid the complexity of solving the fourth order equations, we analyze the inflationary and reheating dynamics in the Einstein frame and its analytical solutions are derived. We also perform numerical calculation including the backreaction from the particle creation and compare the results with the analytical solutions. Based on the results, observational constraints on the model are discussed.
We show explicitly how the T-model, E-model, and Hilltop inflations are obtained from the inflation models with a non-canonical kinetic term and an arbitrary potential. By this method, any attractor of observables $n_s$ and $r$ is possible. The presence of attractors poses a challenge to differentiate inflation models.
Primordial black holes (PBHs) cannot be produced abundantly enough to be the dark matter in canonical single-field inflation under slow roll. This conclusion is robust to local non-Gaussian correlations between long- and short-wavelength curvature modes, which we show have no effect in slow roll on local primordial black hole abundances. For the prototypical model which evades this no go, ultra-slow roll (USR), these squeezed non-Gaussian correlations have at most an order unity effect on the variance of PBH-producing curvature fluctuations for models that would otherwise fail to form sufficie…
We consider inflation using a class of non-canonical Lagrangians for which the modification to the kinetic term depends on the field, but not its derivatives. We generalize the standard Hubble slow roll expansion to the non-canonical case and derive expressions for observables in terms of the generalized slow roll parameters. We apply the general results to the illustrative case of ``Slinky'' inflation, which has a simple, exactly solvable, non-canonical representation. However, when transformed into a canonical basis, Slinky inflation consists of a field oscillating on a multi-valued potentia…
We study a unification model for dark energy, dark matter, and inflation with a single scalar field with non canonical kinetic term. In this model the kinetic term of the Lagrangian accounts for the dark matter and dark energy, and at early epochs a quadratic potential accounts for slow roll inflation. The present work is an extension to the work by Bose and Majumdar [1] with a more general kinetic term that was proposed by Chimento in [2]. We demonstrate that the model is viable at the background and linear perturbation levels.
We solve the one loop effective scalar field equations for spatial plane waves in massless, minimally coupled scalar quantum electrodynamics on a locally de Sitter background. The computation is done in two different gauges: a non-de Sitter invariant analogue of Feynman gauge, and in the de Sitter invariant, Lorentz gauge. In each case our result is that the finite part of the conformal counterterm can be chosen so that the mode functions experience no significant one loop corrections at late times. This is in perfect agreement with a recent, all orders stochastic prediction.
Effect of non-canonical scalar fields on the CMB imprints of the anisotropic inflation will be discussed in details in this paper. In particular, we are able to obtain the general formalism of the angular power spectra in the scalar perturbations, tensor perturbations, cross-correlations, and linear polarization in the context of the anisotropic inflation model involving non-canonical scalar fields. Furthermore, some significant numerical spectra will be plotted using the most recent data of Planck as well as the BICEP2 and Keck array. As a result, we find a very interesting point that the $TT…
Assuming that a scalar field controls the inflationary era, we examine the combined effects of string and $f(R)$ gravity corrections on the inflationary dynamics of canonical scalar field inflation, imposing the constraint that the speed of the primordial gravitational waves is equal to that of light's. Particularly, we study the inflationary dynamics of an Einstein-Gauss-Bonnet gravity in the presence of $αR^2$ corrections, where $α$ is a free coupling parameter. As it was the case in the pure Einstein-Gauss-Bonnet gravity, the realization that the gravitational waves propagate through spacet…
In this work, we have considered a non-canonical scalar field dark energy model in the framework of flat FRW background. It has also been assumed that the dark matter sector interacts with the non-canonical dark energy sector through some interaction term. Using the solutions for this interacting non-canonical scalar field dark energy model, we have investigated the validity of generalized second law (GSL) of thermodynamics in various scenarios using first law and area law of thermodynamics. For this purpose, we have assumed two types of horizons viz apparent horizon and event horizon for the …
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…
We apply Starobinsky's formalism of stochastic inflation to the case of a minimally coupled scalar field with linear self-interaction potential. We solve the corresponding Fokker-Planck equation exactly, and obtain analytical expressions for the stochastic expectation values.
There exists some evidence of a suppression in power in the CMB multipoles around $l \sim 20-30$. If taken seriously, this is in tension with the simplest inflationary models driven by a single scalar field with a standard type of slowly varying potential function $V(ϕ)$. Such potential functions generate a nearly scale invariant spectrum and so they do not possess the requisite suppression in power. In this paper we explore if canonical two-derivative inflation models, with a step-like feature in the potential, can improve agreement with data. We find that improvement can be made when one uti…
We generalize former findings regarding quantum-gravitational corrections arising from a canonical quantization of a perturbed FLRW universe during inflation by considering an initial state for the scalar and tensor perturbations that generalizes the adiabatic vacuum state and allows us to consider the scenario that the perturbation modes start their evolution in an excited state. Our result shows that the quantum-gravitationally corrected power spectra get modified by pre-factors including the excitation numbers.
