We study the primordial perturbations and reheating process in the models where the Gauss-Bonnet term is non-minimally coupled to the canonical and non-canonical (DBI and tachyon) scalar fields. We consider several potentials and Gauss-Bonnet coupling terms as power-law, dilaton-like, $\cosh$-type, E-model and T-model. To seek the observational viability of these models, we study the scalar perturbations numerically and compare the results with the Planck2018 TT, TE, EE+lowE+lensing+BK14+BAO joint data at $68\%$ CL and $95\%$ CL. We also study the tensor perturbations in confrontation with the Planck2018 TT, TE, EE+lowE+lensing+BK14+BAO+ LIGO$\&$Virgo2016 joint data at $68\%$ CL and $95\%$ CL. In this regard, we obtain some constraints on the Gauss-Bonnet coupling parameter $β$. Another important process in the early universe is the reheating phase after inflation which is necessary to reheat the universe for subsequent evolution. In this regard, we study the reheating process in these models and find some expressions for the e-folds number and temperature during that era. Considering that from Planck TT,TE,EE+lowEB+lensing data and BICEP2/Keck Array 2014, based on the $Λ$CDM$+r+\frac{dn_{s}}{d\ln k}$ model, we have $n_{s}=0.9658\pm 0.0038$ and $r<0.072$, we obtain some constraints on the e-folds number and temperature. From the values of the e-folds number and the effective equation of state and also the observationally viable value of the scalar spectral index, we explore the capability of the models in explaining the reheating phase.
We consider an extension of Higgs inflation in which the Higgs field is coupled to the Gauss-Bonnet term. Working solely in the Jordan frame, we firstly recover the standard predictions of Higgs inflation without a Gauss-Bonnet term. We then calculate the power spectra for scalar and tensor perturbations in the presence of a coupling to a Gauss-Bonnet term. We show that generically the predictions of Higgs inflation are robust and the contributions to the power spectra coming from the Gauss-Bonnet term are negligible. We find, however, that the end of inflation can be strongly modified and tha…
We study slow-roll inflation with the Gauss-Bonnet and Chern-Simons corrections. We obtain general formulas for the observables: spectral indices, tensor-to-scalar ratio and circular polarization of gravitational waves. The Gauss-Bonnet term violates the consistency relation r = -8n_T. Particularly, blue spectrum n_T > 0 and scale invariant spectrum |8n_T|/r << 1 of tensor modes are possible. These cases require the Gauss-Bonnet coupling function of ξ_{,ϕ} \sim 10^8/M_{Pl}. We use examples to show new-inflation-type potential with 10M_{Pl} symmetry breaking scale and potential with flat region…
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.
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 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.
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…
The two swampland criteria are generically in tension with the single field slow-roll inflation because the first swampland criterion requires small tensor to scalar ratio while the second swampland criterion requires large tensor to scalar ratio. The challenge to the single field slow-roll inflation imposed by the swampland criteria can be avoided by modifying the relationship between the tensor to scalar ratio and the slow-roll parameter. We show that the Gauss-Bonnet inflation with the coupling function inversely proportional to the potential overcomes the challenge by adding a constant fac…
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…
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 $r$.
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…
We investigate the feasibility of models of inflation with a large Gauss-Bonnet coupling at late times, which have been shown to modify and prevent the end of inflation. Despite the potential of Gauss-Bonnet models in predicting favourable power spectra, capable of greatly lowering the tensor-to-scalar-ratio compared to now-disfavoured models of standard chaotic inflation, it is important to also understand in what context it is possible for post-inflationary (p)reheating to proceed and hence recover an acceptable late-time cosmology. We argue that in the previously-studied inverse power law c…
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.
The measured masses of the Higgs boson and top quark indicate that the effective potential of the standard model either develops an unstable electroweak vacuum or stands stable all the way up to the Planck scale. In the latter case in which the top quark mass is about $2σ$ below its present central value, the Higgs boson can be the inflaton with the help of a large nonminimal coupling to curvature in four dimensions. We propose a scenario in which the Higgs boson can be the inflaton in a five-dimensional Gauss-Bonnet braneworld model to solve both the unitarity and stability problems which usu…
We study the inflation in a model with a Gauss-Bonnet term which is non-minimally coupled to a DBI field. We study the spectrum of the primordial perturbations in detail. The non-Gaussianity of this model is considered and the amplitude of the non-Gaussianity is studied in both the equilateral and orthogonal configurations. By taking various functions of the DBI field, inflaton potential and the Gauss-Bonnet coupling term, we test the model with observational data and find some constraints on the Gauss-Bonnet coupling parameter.
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 light of the recent Planck 2015 results for the measurement of the CMB anisotropy, we study simple inflationary models in the context of the Gauss-Bonnet brane-world cosmology. The brane-world cosmological effect modifies the power spectra of scalar and tensor perturbations generated by inflation and causes a dramatic change for the inflationary predictions of the spectral index ($n_s$) and the tensor-to-scalar ratio ($r$) from those obtained in the standard cosmology. In particular, the power spectrum of tensor perturbation is suppressed due to the Gauss-Bonnet brane-world cosmological eff…
Recent LHC data provides precise values of coupling constants of the Higgs field, however, these measurements do not determine its coupling with gravity. We explore this freedom to see whether Higgs field non-minimally coupled to Gauss-Bonnet term in 4-dimensions can lead to inflation generating the observed density fluctuations. We obtain analytical solution for this model and that the exit of inflation (with a finite number of e-folding) demands that the energy scale of inflation is close to Electro-weak scale. We compare the scalar and tensor power spectrum of our model with PLANCK data and…
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 …
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 slow-roll inflation for a single scalar field with an arbitrary potential and an arbitrary nonminimal coupling to the Gauss-Bonnet term. By introducing a combined hierarchy of Hubble and Gauss-Bonnet flow functions, we analytically derive the power spectra of scalar and tensor perturbations. The standard consistency relation between the tensor-to-scalar ratio and the spectral index of tensor perturbations is broken. We apply this formalism to a specific model with a monomial potential and an inverse monomial Gauss-Bonnet coupling and constrain it by the 7-year Wilkinson Microwave A…
We study two of the most theoretically promising models of inflation, namely the Natural inflation and the Mutated Hilltop inflation, in the Einstein-Gauss Bonnet(EGB) gravity framework. In this work, we try to explore these models in EGB framework, keeping the observations from $GW170817$ on the speed of gravitational wave to be equal to the speed of light. This has direct implication on the non-minimal coupling to the Gauss-Bonnet invariant in the action. Thus, the effective potential gets new features. We have not only analysed the inflationary dynamics, but also the reheating dynamics and …
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…
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…
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…
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 …
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.…
Motivated by the idea that quantum gravity corrections usually suppress the power of the scalar primordial spectrum (E-mode) more than the power of the tensor primordial spectrum (B-mode), in this paper we construct a concrete gravitational theory in five-dimensions for which $V(ϕ)\propto ϕ^n$-type inflation ($n\ge 1$) generates an appropriate tensor-to-scalar ratio that may be compatible with the BICEP2 and Planck data together. The true nature of gravity is five-dimensional and described by the action $S = \int d^5{x} \sqrt{|g|} M^3 (- 6λM^2 + R + αM^{-2} {\cal R}^2)$ where $M$ is the five-d…
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.
(Lovelock)$^2$ inflation: explaining the ACT data and equivalence to Higgs-Gauss-Bonnet inflation
Anqing Normal University（安庆师范大学）；University of Science and Technology of China（中国科学技术大学）；INFN（意大利国家核物理研究所）；Fudan University（复旦大学）；Al-Farabi Kazakh National University（阿尔法拉比哈萨克国立大学）
基于ACT数据重新审视暴胀的斯塔罗宾斯基模型，用二次\(f(L)\)引力\(\sim L + L^2\)解决数据矛盾，其标量 - 张量形式改变暴胀慢滚动力学，还发现与希格斯 - 高斯 - 博内特暴胀等效，改进了对宇宙学数据的拟合。
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…
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 …
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…
Primordial black holes (PBHs) can be the source for all or a part of today's dark matter density. Inflation provides a mechanism for generating the seeds of PBHs in the presence of a temporal period where the velocity of an inflaton field $ϕ$ rapidly decreases toward 0. We compute the primordial power spectra of curvature perturbations generated during Gauss-Bonnet (GB) corrected Higgs inflation in which the inflaton field has not only a nonminimal coupling to gravity but also a GB coupling. For a scalar-GB coupling exhibiting a rapid change during inflation, we show that curvature perturbatio…
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…
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 slow-roll inflation for a single scalar field that couples to the Gauss-Bonnet (GB) term represents an important higher-order curvature correction inspired by string theory. With the arrival of the era of precision cosmology, it is expected that the high-order corrections become more and more important. In this paper we study the observational predictions of the slow-roll inflation with the GB term by using the third-order uniform asymptotic approximation method. We calculate explicitly the primordial power spectra, spectral indices, running of the spectral indices for both scalar and tens…
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 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 $ξ(ϕ)$.…
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…
Primordial blackholes formed in the early Universe via gravitational collapse of over-dense regions may contribute a significant amount to the present dark matter relic density. Inflation provides a natural framework for the production mechanism of primordial blackholes. For example, single field inflation models with a fine-tuned scalar potential may exhibit a period of ultra-slow roll, during which the curvature perturbation may be enhanced to become seeds of the primordial blackholes formed as the corresponding scales reenter the horizon. In this work, we propose an alternative mechanism fo…
Realizing the inflationary epoch driven by a pseudo-Nambu Goldstone boson (pNGB) could ensure the coveted flatness, and the sub-Planckian scales related to the dynamics of the paradigm. In this work, we have taken the most general form of such a scenario: Goldstone inflation proposed in \cite{croon}, and studied the model in Einstein-Gauss-Bonnet gravity. Natural inflation is a limiting case of this model, is also studied here. The specific form of the EGB coupling gives ample opportunity to study the rich phenomenology associated with inflation as well as the reheating epoch. Predicted values…
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…
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 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…
