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 matter fields appear in string theory. In this work we aim to stress the probability that the inflationary dynamics are controlled by the synergy of scalar fields and higher order curvature terms. Specifically, we shall consider a well motivated quantum corrected canonical scalar field theory, with the quantum corrections being of the $\mathcal{R}^2$ type. The reason for choosing minimally coupled scalar theory is basically because if scalar fields are evaluated in their vacuum configuration, they will either be minimally coupled or conformally coupled. Here we choose the former case, and the whole study shall be performed in the string frame (Jordan frame), in contrast to similar studies in the literature where the Einstein frame two scalar theory is considered. We derive the field equations of the quantum-corrected theory at leading order and we present the form the slow-roll indices obtain for the quantum corrected theory. We exemplify our theoretical framework by using the quadratic inflation model, and as we show, the $\mathcal{R}^2$ quantum corrected quadratic inflation model produces a viable inflationary phenomenology, in contrast with the simple quadratic inflation model.
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.
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 E…
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…
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…
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 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 …
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…
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 …
Cosmological inflation is discussed in the framework of $F(R,{\cal G})$ gravity where $F$ is a generic function of the curvature scalar $R$ and the Gauss-Bonnet topological invariant $\cal G$. The main feature that emerges in this analysis is the fact that this kind of theory can exhaust all the curvature budget related to curvature invariants without considering derivatives of $R,$ $R_{μν}$, $R^λ_{σμν}$ etc. in the action. Cosmological dynamics results driven by two effective masses (lenghts) related to the $R$ scalaron and the $\cal G$ scalaron working respectively at early and very early ep…
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…
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.
In this work we study certain classes of $F(R,{\cal G})$ gravity which have appealing phenomenological features, with respect to the successful realization of the dark energy and of the inflationary era. Particularly, we discuss the general formalism and we demonstrate how several inflationary and dark energy evolutions can be described in the context of $F(R,{\cal G})$ gravity. Also we propose a unified model, in the context of which the early and late-time dynamics are controlled by the $F(R,{\cal G})$ gravity, thus producing inflation and the dark energy era, while the intermediate era is a…
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.
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.
We compute the leading order connected four-point function of the primordial curvature perturbation coming from the four-point function of the fields in multi-field DBI inflation models. We confirm that the consistency relations in the squeezed limit and in the counter-collinear limit hold as in single field models thanks to special properties of the DBI action. We also study the momentum dependence of the trispectra coming from the adiabatic, mixed and purely entropic contributions separately and we find that they have different momentum dependence. This means that if the amount of the transf…
There are many single field inflationary models that are consistent with the recent Planck 2018 measurements of the spectral index $n_s$ and tensor-to-scalar ratio $r$. Despite good agreement with observational data some of these models suffer from having unregularized potentials which would produce a collapsing universe shortly after the end of inflation. In this paper we show that how one chooses to correct the behaviour potential towards the end of inflation can have a significant effect on the inflationary predictions of the model, specifically in the case of quartic hilltop and radiativel…
In this work we re-investigate pros and cons of mutated hilltop inflation. Applying Hamilton-Jacobi formalism we solve inflationary dynamics and find that inflation goes on along the ${\cal W}_{-1}$ branch of the Lambert function. Depending on the model parameter mutated hilltop model renders two types of inflationary solutions: one corresponds to small inflaton excursion during observable inflation and the other describes large field inflation. The inflationary observables from curvature perturbation are in tune with the current data for a wide range of the model parameter. The small field br…
We study if eternal inflation is realized while satisfying the recently proposed string Swampland criteria concerning the range of scalar field excursion, $|Δϕ| < \mathcal{D} \cdot M_{\rm P}$, and the potential gradient, $|\nabla V| > c \cdot V/M_{\rm P}$, where $\mathcal{D}$ and $c$ are constants of order unity, and $M_{\rm P}$ is the reduced Planck mass. We find that only the eternal inflation of chaotic type is possible for $c \sim {\cal O}(0.01)$ and $1/\mathcal{D} \sim {\cal O}(0.01)$, and that the Hubble parameter during the eternal inflation is parametrically close to the Planck scale, …
In this paper we shall analyze the $f(\mathcal{G})$ gravity phase space, in the case that the corresponding dynamical system is autonomous. In order to make the dynamical system autonomous, we shall appropriately choose the independent variables, and we shall analyze the evolution of the variables numerically, emphasizing on the inflationary attractors. As we demonstrate, the dynamical system has only one de Sitter fixed point, which is unstable, with the instability being traced in one of the independent variables. This result holds true both in the presence and in the absence of matter and r…
We develop a Gauss-Bonnet extension of Loop Quantum Cosmology, by introducing holonomy corrections in modified $F(\mathcal{G})$ theories of gravity. Within the context of our formalism, we provide a perturbative expansion in the critical density, a parameter characteristic of Loop Quantum Gravity theories, and we result in having leading order corrections to the classical $F(\mathcal{G})$ theories of gravity. After extensively discussing the formalism, we present a reconstruction method that makes possible to find the Loop Quantum Cosmology corrected $F(\mathcal{G})$ theory that can realize va…
In this work, we study the effects on the relevant observational parameters of an inflationary universe from a chaotic potential with a step. We numerically evolve the perturbation equations within both cold inflation and warm inflation. On the one hand, in a cold inflation scenario we analyse the scalar power spectrum $P_{\mathcal{R}}$ in terms of the number of e-folds $N_{e}$, and in terms of the ratio $k/k_{0}$, where $k_{0}$ is our pivot scale. We show how $P_{\mathcal{R}}$ oscillates around $0.2< k/k_{0} < 20$. Additionally, we present the evolution of two relevant parameters: the scalar …
The aim of this paper is to explore warm inflation in the background of $f(\mathcal{G})$ theory of gravity using scalar fields for the FRW universe model. We construct the field equations under slow-roll approximations and evaluate the slow-roll parameters, scalar and tensor power spectra and their corresponding spectral indices using viable power-law model. These parameters are evaluated for a constant as well as variable dissipation factor during intermediate and logamediate inflationary epochs. We also find the number of e-folds and tensor-scalar ratio for each case. The graphical behavior …
In this paper, we investigate the no-boundary wave function and the complex-valued instantons for two-field inflation models that have different masses. If there is a relatively massive direction, to classicalize the massive field, the solution should start from the slow direction with relatively larger vacuum energy. Therefore, the existence of the massive direction implies the increase of expected $e$-foldings. The most probable $e$-foldings are approximately $\mathcal{N} \simeq (m_{2}/m_{1})^{2} \times \mathcal{O}(1)$ in the $m_{1} \ll m_{2}$ limit. Therefore, as long as there is a sufficie…
The dilaton is a possible inflaton candidate following recent CMB data allowing a non-minimal coupling to the Ricci curvature scalar in the early Universe. In this paper, we introduce an approach that has seldom been used in the literature, namely dilaton inflation with non-local features. More concretely, employing non-local features expressed in J. High Energy Phys. 04 (2007) 029, we study quadratic variations around a de Sitter geometry of an effective action with a non-local dilaton. The non-locality refers to an infinite derivative kinetic term involving the operator $\mathcal{F}\left(\Bo…
We show that in single field inflationary models the super-horizon evolution of curvature perturbations on comoving slices $\mathcal{R}$, which can cause the production of primordial black holes (PBH), is not due to entropy perturbations, but to the background evolution effect on the conversion between entropy and curvature perturbations. We derive a general relation between the time derivative of comoving curvature perturbations and entropy perturbations, in terms of a conversion factor depending on the background evolution. Contrary to previous results derived in the uniform density gauge as…
We propose a novel enhancement mechanism of the curvature perturbations in the nonminimal derivative coupling inflation model with a coupling parameter related to the inflaton field. By considering a special form of the coupling parameter as a function of the inflaton, a period of ultra-slow-roll inflation can be realized due to the gravitationally enhanced friction, and the resulting power spectrum of the curvature perturbations has a sharp peak, which is large enough to produce the primordial black holes. Under this mechanism, we can easily obtain a sharp mass spectrum of primordial black ho…
Cosmology of f(Q,L_m) gravity with Holographic Ricci Dark Energy: Early-Time Inflation and Late-Time Acceleration and RGUP Corrected Observables
Amity University Kolkata（阿米提大学加尔各答分校）；Ahram Canadian University, Faculty of Engineering, Basic Science Department（艾哈兰加拿大大学工程学院基础科学系）；The Egyptian Center for Theoretical Physics (ECTP)（埃及理论物理中心）
