In this work we shall study Einstein Gauss-Bonnet theories and we investigate when these can have their gravitational wave speed equal to the speed of light, which is unity in natural units, thus becoming compatible with the striking event GW170817. We demonstrate how this is possible and we show that if the scalar coupling to the Gauss-Bonnet invariant is constrained to satisfy a differential equation, the gravitational wave speed becomes equal to one. Accordingly, we investigate the inflationary phenomenology of the resulting restricted Einstein Gauss-Bonnet model, by assuming that the slow-roll conditions hold true. As we demonstrate, the compatibility with the observational data coming from the Planck 2018 collaboration, can be achieved, even for a power-law potential. We restricted ourselves to the study of the power-law potential, due to the lack of analyticity, however more realistic potentials can be used, in this case though the calculations are not easy to be performed analytically. We also pointed out that a string-corrected extension of the Einstein Gauss-Bonnet model we studied, containing terms of the form $\sim ξ(ϕ) G^{ab}\partial_aϕ\partial_b ϕ$ can also provide a theory with gravity waves speed $c_T^2=1$ in natural units, if the function $ξ(ϕ)$ is appropriately constrained, however in the absence of the Gauss-Bonnet term $\sim ξ(ϕ) \mathcal{G}$ the gravity waves speed can never be $c_T^2=1$. Finally, we discuss which extensions of the above models can provide interesting cosmologies, since any combination of $f(R,X,ϕ)$ gravities with the above string-corrected Einstein Gauss-Bonnet models can yield $c_T^2=1$, with $X=\frac{1}{2}\partial_μϕ\partial^μϕ$.
We study inflationary models with a Gauss-Bonnet term to reconstruct the scalar field potentials and the Gauss-Bonnet coupling functions from the observable quantities. Using the observationally favored relations for both $n_s$ and $r$, we derive the expressions for both the scalar field potentials and the coupling functions. The implication of the blue-tilted spectrum, $n_t>0$, of the primordial tensor fluctuations is discussed for the reconstructed configurations of the scalar field potential and the Gauss-Bonnet coupling.
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…
In this article, we study a type of one-field approach for open inflationary universe scenario in the context of braneworld models with a Gauss-Bonnet correction term. For a one-bubble universe model, we determine and characterize the existence of the Coleman-De Lucia instanton together with the period of inflation after tunneling has occurred. Our results are compared those analogous obtained when the usual Einstein Theory of Gravitation is used.
Inflationary models with a scalar field nonminimally coupled both with the Ricci scalar and with the Gauss-Bonnet term are studied. We propose the way of generalization of inflationary scenarios with the Gauss-Bonnet term and a scalar field minimally coupled with the Ricci scalar to the corresponding scenarios with a scalar field nonminimally coupled with the Ricci scalar. Using the effective potential, we construct a set of models with the same values of the scalar spectral index $n_s$ and the amplitude of the scalar perturbations $A_s$ and different values of the tensor-to-scalar ratio $r$.
We provide a refined and much more simplified Einstein-Gauss-Bonnet inflationary theoretical framework, which is compatible with the GW170817 observational constraints on the gravitational wave speed. As in previous works, the constraint that the gravitational wave speed is $c_T^2=1$ in natural units, results to a constraint differential equation that relates the coupling function of the scalar field to the Gauss-Bonnet invariant $ξ(ϕ)$ and the scalar potential $V(ϕ)$. Adopting the slow-roll conditions for the scalar field and the Hubble rate, and in contrast to previous works, by further assu…
In this work we investigate the inflationary phenomenological implications of a recently developed ghost-free Gauss-Bonnet theory of gravity. The resulting theory can be viewed as a scalar Einstein-Gauss-Bonnet theory of gravity, so by employing the formalism for cosmological perturbations for the latter theory, we calculate the slow-roll indices and the observational indices, and we compare these with the latest observational data. Due to the presence of a freely chosen function in the model, in principle any cosmological evolution can be realized, so we specify the Hubble rate and the freely…
Recent analyses combining Atacama Cosmology Telescope (ACT) data with other cosmological datasets report a higher scalar spectral index $n_s$, creating tension with a wide range of inflationary models. Since a Gauss-Bonnet term with a coupling function $ξ(ϕ) = 3λ/[4V(ϕ)]$ leaves $n_s$ nearly unchanged (up to a field rescaling) while reducing the tensor-to-scalar ratio $r$ by a factor $(1-λ)$, so choosing $(1-λ)$ sufficiently small effectively removes $r$ as a limiting observable, making it easier for inflationary models to satisfy the latest observational constraints and alleviating this tensi…
In this paper we study a class of quintessential Einstein Gauss-Bonnet models, focusing on their early and late-time phenomenology. With regard to the early-time phenomenology, we formalize the slow-roll evolution of these models and we calculate in detail the spectral index of the primordial curvature perturbations and the tensor-to-scalar ratio. As we demonstrate, the resulting observational indices can be compatible with both the Planck and the BICEP2/Keck-Array observational constraints on inflation. With regard to the late-time behavior, by performing a numerical analysis we demonstrate t…
We study the slow-roll single field inflation in the context of the consistent $D\to4$ Einstein-Gauss-Bonnet gravity that was recently proposed in \cite{Aoki:2020lig}. In addition to the standard attractor regime, we find a new attractor regime which we call the Gauss-Bonnet attractor as the dominant contribution comes from the Gauss-Bonnet term. Around this attractor solution, we find power spectra and spectral tilts for the curvature perturbations and gravitational waves (GWs) and also a model-independent consistency relation among observable quantities. The Gauss-Bonnet term provides a nonl…
Recently, an interesting inflationary scenario, named Gauss-Bonnet inflation, is proposed by Kanti et al.~\cite{Kanti:2015pda,Kanti:2015dra}. In the model, there is no inflaton potential but the inflaton couples to the Guass-Bonnet term. In the case of quadratic coupling, they find inflation occurs with graceful exit. The scenario is attractive because of the natural set-up. However, we show there exists the gradient instability in the tensor perturbations in this inflationary model. We further prove the no-go theorem for the Gauss-Bonnet inflation without an inflaton potential.
In this work we shall calculate in detail the effect of an GW170817-compatible Einstein-Gauss-Bonnet theory on the energy spectrum of the primordial gravitational waves. The spectrum is affected by two characteristics, the overall amplification/damping factor caused by the GW170817-compatible Einstein-Gauss-Bonnet theory and by the tensor spectral index and the tensor-to-scalar ratio. We shall present the formalism for studying the inflationary dynamics and post-inflationary dynamics of GW170817-compatible Einstein-Gauss-Bonnet theories for all redshifts starting from the radiation era up to t…
We study the inflationary phenomenology of a non-minimally coupled Einstein Gauss-Bonnet gravity theory, in the presence of a scalar potential, under the condition that the gravitational wave speed of the primordial gravitational waves is equal to unity, that is $c_T^2=1$, in natural units. The equations of motion, which are derived directly from the gravitational action, form a system of differential equations with respect to Hubble's parameter and the inflaton field which are very complicated and cannot be solved analytically, even in the minimal coupling case. In this paper, we present a va…
In this paper the focus is on inflationary dynamics in the context of Einstein Gauss-Bonnet gravitational theories. We investigate the implications of the slow-roll condition on the slow-roll indices and we investigate how the inflationary dynamical evolution is affected by the presence of the Gauss-Bonnet coupling to the scalar field. For exemplification of our analysis we investigate how the dynamics of inflationary cubic, quartic order and also exponential scalar potentials are affected by the non-trivial Gauss-Bonnet coupling to the scalar field. As we demonstrate it is possible to obtain …
In this article we study an intermediate inflationary universe models using the Gauss-Bonnet brane. General conditions required for these models to be realizable are derived and discussed. We use recent astronomical observations to constraint the parameters appearing in the model.
Inflationary era of our Universe can be characterized as semi-classical because it can be described in the context of four-dimensional Einsteins's gravity involving quantum corrections. These string motivated corrections originate from quantum theories of gravity such as superstring theories and include higher gravitational terms as, Gauss-Bonnet and Chern-Simons terms. In this paper we investigated inflationary phenomenology coming from a scalar field, with quadratic curvature terms in the view of GW170817. Firstly, we derived the equations of motion, directly from the gravitational action. A…
Einstein--Gauss--Bonnet Inflationary Cosmology in Phase-$θ$ Formalism
Bauman Moscow State Technical University（鲍曼莫斯科国立技术大学）；Sternberg Astronomical Institute, Moscow State University（莫斯科大学斯特恩伯格天文研究所）；Birla Institute of Technology and Science-Pilani（比拉科学技术学院-皮拉尼校区）
We construct models with the Gauss-Bonnet term multiplied to a function of the scalar field leading to inflationary scenario. The consideration is related with the slow-roll approximation. The cosmological attractor approach gives the spectral index of scalar perturbations which is in a good agreement with modern observation and allows variability for tensor-to-scalar ratio. We reconstruct models with variability of parameters which allow to reproduce cosmological attractor predictions for inflationary parameters in the leading order of $1/N$ approximation in the Einstein-Gauss-Bonnet gravity.
We have explicitly demonstrated that scalar coupled Gauss-Bonnet gravity in four dimension can have non-trivial effects on the early inflationary stage of our universe. In particular, we have shown that the scalar coupled Gauss-Bonnet term alone is capable of driving the inflationary stages of the universe without incorporating slow roll approximation, while remaining compatible with the current observations. Subsequently, to avoid the instability of the tensor perturbation modes we have introduced a self-interacting potential for the inflaton field and have shown that in this context as well …
In this paper we investigate the inflationary phenomenology of an Einstein-Gauss-Bonnet theory compatible with the GW170817 event, by imposing the constant-roll evolution on the scalar field. We develop the constant-roll GW170817-compatible Einstein-Gauss-Bonnet formalism, and we calculate the slow-roll indices and the observational indices of inflation, for several models of interest. As we demonstrate, the phenomenological viability of the models we study is achieved for a wide range of the free parameters. In addition, for the same values of the free parameters that guarantee the inflationa…
The newly released Planck CMB data place tight constraints on slow-roll inflationary models. Some of commonly discussed inflationary potentials are disfavored due mainly to the large tensor-to-scalar ratio. In this paper we show that these potentials may be in good agreement with the Planck data when the inflaton has a non-minimal coupling to the Gauss-Bonnet term. Moreover, such a coupling violates the consistency relation between the tensor spectral index and tensor-to-scalar ratio. If the tensor spectral index is allowed to vary freely, the Planck constraints on the tensor-to-scalar ratio a…
We revisit the inflationary dynamics in detail for theories with Gauss-Bonnet gravity coupled to scalar functions, in light of the Planck data. Considering the chaotic inflationary scenario, we constrain the parameters of two models involving inflaton-Gauss-Bonnet coupling by current Planck data. For non zero inflaton-Gauss-Bonnet coupling $β$, an inflationary analysis provides us a big cosmologically viable region in the space of $(m,β)$, where $m$ is the mass of inflaton. However, we study further on constraining $β$ arising from reheating considerations and unitarity of tree-level amplitude…
In this short note we present the dynamics of a general scalar-tensor model, and in particular a scalar Einstein-Gauss-Bonnet model with a non-minimal coupling between gravity and the kinetic term of the scalar field. For the sake of simplicity two $f(R)$ models are studied separately, an exponential and a power-law, accompanied by either an exponential or quartic scalar potential and a strictly exponential Gauss-Bonnet scalar coupling function known for being a suitable candidate for describing both the early and the late time. By introducing the general framework of a late-time study for an …
In this work we shall use a bottom-up approach for obtaining viable inflationary Einstein-Gauss-Bonnet models which are also compatible with the GW170817 event. Specifically, we shall use a recently developed theoretical framework in which we shall specify only the tensor-to-scalar ratio, in terms of the $e$-foldings number. Starting from the tensor-to-scalar ratio, we shall reconstruct from it the Einstein-Gauss-Bonnet theory which can yield such a tensor-to-scalar ratio, finding the scalar potential and the Gauss-Bonnet coupling scalar function as functions of the $e$-foldings number. Accord…
The influence of non-minimal coupling of a scalar field and the Gauss-Bonnet term on the inflationary stage of evolution of the universe is investigated in this paper. The main cosmological effects of such a coupling were considered. The deviations between Einstein-Gauss-Bonnet inflation and standard one based on Einstein gravity were determined. The corrections of a weak GB coupling preserving the type of the scalar field potential to standard inflationary models is considered as well.
A scalar-tensor model with Gauss-Bonnet and non-minimal kinetic couplings is considered, in which ghost modes are eliminated via a Lagrange multiplier constraint. A reconstruction procedure is deviced for the scalar potential and Lagrange multiplier, valid for any given cosmological scenario. In particular, inflationary and dark energy cosmologies of different types (power-law, Little-Rip, de Sitter, quasi de Sitter) are reconstructed in such models. It is shown that, for various choices of the kinetic coupling terms, it is possible to obtain a viable inflationary phenomenology compatible with…
We study the effects of the Gauss-Bonnet term on the energy spectrum of inflationary gravitational waves. The models of inflation are classified into two types based on their predictions for the tensor power spectrum: red-tilted ($n_T<0$) and blue-tilted spectra ($n_T>0$), respectively, and then the energy spectra of the gravitational waves are calculated for each type of model. We find that the gravitational wave spectra are enhanced depending on the model parameter if the predicted inflationary tensor spectra have a blue tilt, whereas they are suppressed for the spectra that have a red tilt.…
The striking GW170817 event indicated that the graviton is nearly massless, since the gamma rays emitted from the two neutron stars merging arrived almost simultaneously with the gravitational waves. Thus, the graviton must also be massless during the inflationary and post-inflationary era, since there is no obvious reason to believe otherwise. In this letter we shall investigate the theoretical implications of the constraint that the graviton is massless to an Einstein-Gauss-Bonnet theory with linear coupling of the scalar field to the four dimensional Gauss-Bonnet invariant. As we show, the …
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 investigate the inflationary era in the presence of a canonical scalar field and Chern-Simons parity violating corrections. It was also assumed that a non minimal coupling between curvature and the scalar field is present. For the shake of completeness, the slow-roll and the constant-roll scenarios were examined separately. In the context of this scalar-tensor theory, inflation can be viable for both scenarios since the observational indices take acceptable values according to the most recent Planck data. Furthermore, the involvement of the Chern-Simons term has no effect on th…
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…
In the present article we showcase how the reheating era can be described properly in the context of Einstein-Gauss-Bonnet gravity assuming that the primordial gravitational waves propagate with the velocity of light. The equations of the duration of reheating along with the reheating temperature are derived and as demonstrated, their expressions are quite similar to the case of a canonical scalar field where now the second derivative of the Gauss-Bonnet scalar coupling function appears and effectively alters the numerical value of the scalar potential. The appearance of such term is reminisci…
We consider Einstein-Gauss-Bonnet (EGB) inflationary models using the effective potential approach. We present evolution equations in the slow-roll regime using the effective potential and the tensor-to-scalar ratio. The choice of the effective potential is related to an expression of the spectral index in terms of e-folding number $N_e$. The satisfaction of the slow-roll regime is mostly related to the form of the tensor-to-scalar ratio $r$. The case of $r\sim1/N^2_e$ leads to a generalization of $α$-attractors inflationary parameters to Einstein-Gauss-Bonnet gravity with exponential effectiv…
In this work we shall study the implications of a subclass of $E$-models cosmological attractors, namely of $a$-attractors, on hydrodynamically stable slowly rotating neutron stars. Specifically, we shall present the Jordan frame theory of the $a$-attractors, and by using a conformal transformation we shall derive the Einstein frame theory. We discuss the inflationary context of $a$-attractors in order to specify the allowed range of values for the free parameters of the model based on the latest cosmic-microwave-background-based Planck 2018 data. Accordingly, using the notation and physical u…
We propose a novel {\it k}-Gauss-Bonnet inflationary model, in which a kinetic term of scalar field is allowed to non-minimally couple to the Gauss-Bonnet topological invariant in the absence of a potential of scalar field. As a result, this model is shown to admit an isotropic power-law inflation provided that the scalar field is phantom. Furthermore, stability analysis based on the dynamical system method is performed to indicate that this inflation solution is indeed stable and attractive. More interestingly, a gradient instability in tensor perturbations is shown to disappear in this model…
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 $ξ(ϕ)$.…
We will examine whether anisotropic hairs exist in a string-inspired scalar-Gauss-Bonnet gravity model with the absence of potential of scalar field during the inflationary phase. As a result, we are able to obtain the Bianchi type I power-law solution to this model under the assumption that the scalar field acts as the phantom field, whose kinetic is negative definite. However, the obtained anisotropic hair of this model turns out to be large, which is inconsistent with the observational data. We will therefore introduce a nontrivial coupling between scalar and vector fields such as $f^2(ϕ)F_…
We consider an Einstein-Scalar-Gauss-Bonnet gravitational theory, and argue that at early times the Ricci scalar can be safely ignored. We then demonstrate that the pure scalar-Gauss-Bonnet theory, with a quadratic coupling function, naturally supports inflationary -- de Sitter -- solutions. During inflation, the scalar field decays exponentially and its effective potential remains always bounded. The theory contains also solutions where these de Sitter phases possess a natural exit mechanism and are replaced by linearly expanding -- Milne -- phases.
A Gauss-Bonnet term naturally appears in the action for gravity when one considers the existence of space time with dimensions more than 1+3. A variety of inflationary models can be obtained within such a framework, once the scale factor for the hidden dimension(s) is not constrained to be the same as that of the visible ones. In particular, the need for an adhoc inflaton field is eliminated. The phase space has a rich structure with different types of solutions, both stable and unstable. For a large class of solutions, the scale factors rapidly approach an asymptotic exponential form. Further…
We investigate inflationary dynamics in the framework of the Einstein-Gauss-Bonnet gravity. In the model under consideration, the inflaton field is non-minimally coupled to the Gauss-Bonnet curvature invariant, so that the latter appears to be dynamically important. We consider a quartic potential for the inflaton field, in particular the one asymptotically connected to the Higgs inflation, and a wider class of coupling functions not considered in the earlier work. Keeping in mind the observational bounds on the parameters - the amplitude of scalar perturbations $A_s$, spectral index $n_s$ and…
We study cosmological inflation in the Einstein gravity model, where additionally the Gauss-Bonnet term non-minimally coupled to a scalar field is included. We prove that inflationary solutions of exponential and power-law types are allowable and we found few examples of them. We also proposed the method of the exact inflationary solutions construction for a single scalar field with given scale factor and Gauss-Bonnet coupling term in the spatially flat Friedmann-Robertson-Walker Universe on the basis of connection with standard inflation and using special anzatses. With one special anzats we …
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 consider a gravitational theory that contains the Einstein term, a scalar field and the quadratic Gauss-Bonnet term. We focus on the early-universe dynamics, and demonstrate that the Ricci scalar does not affect the cosmological solutions at early times, when the curvature is strong. We then consider a pure scalar-GB theory with a quadratic coupling function: for a negative coupling parameter, we obtain solutions that contain always an inflationary, de Sitter phase, while for a positive coupling function, we find instead expanding singularity-free solutions.
We study slow-roll inflation with a Gauss-Bonnet term that is coupled to an inflaton field nonminimally. We investigate the inflationary solutions for a specific type of the nonminimal coupling to the Gauss-Bonnet term and inflaton potential both analytically and numerically. We also calculate the observable quantities such as the power spectra of the scalar and tensor modes, the spectral indices, the tensor-to-scalar ratio and the running spectral indices. Finally, we constrain our result with the observational data by Planck and BICEP2 experiment.
We study a nonminimal derivative inflationary model in the presence of the Gauss-Bonnet term. To have a complete treatment of the model, we consider a general form of the nonminimal derivative function and also the Gauss-Bonnet coupling term. By following the ADM formalism, expanding the action up to the third order in the perturbations and using the correlation functions, we study the perturbation and its non-Gaussian feature in details. We also study the consistency relation that gets modified in the presence of the Gauss-Bonnet term in the action. We compare the results of our consideration…
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 theory of General Relativity was established on a spacetime manifold equipped with a metric tensor, $(\mathcal{M}_4,\text{g})$, and the connection on $\mathcal{M}_4$ identified with the Levi-Civita one. Even though there are valid reasons to assume a torsionless manifold that preserves the metric, it was shown that dealing away with these assumptions the Levi-Civita condition can be reproduced at the level of equations of motion of GR. It was not long before the equivalence of General Relativity between the two descriptions, known as the Palatini or first-order formalism in which the conne…
De Sitter solutions play an important role in cosmology because the knowledge of unstable de Sitter solutions can be useful to describe inflation, whereas stable de Sitter solutions are often used in models of late-time acceleration of the Universe. The Einstein-Gauss-Bonnet gravity cosmological models are actively used both as inflationary models and as dark energy models. To modify the Einstein equations one can add a nonlinear function of the Gauss-Bonnet term or a function of the scalar field multiplied on the Gauss-Bonnet term. The effective potential method essentially simplifies the sea…
In this work we shall introduce a theoretical framework comprised by a non-minimal coupled canonical scalar field, a non-minimal coupling to the Gauss-Bonnet invariant and a non-minimal kinetic coupling. This theoretical framework is basically a non-minimally coupled Einstein-Gauss-Bonnet theory with extra corrections of the form of a non-minimal kinetic coupling. In order to comply with the GW170817 event, we shall impose a constraint on the propagation speed of the primordial tensor perturbations that it is equal to that of light's in vacuum, and this constraint basically specifies the way t…
