Non-minimal Derivative Coupling Research Articles

Intermediate inflation in a generalized non-minimal derivative coupling model

In this work, we consider intermediate inflation in the context of the generalized non-minimal derivative coupling (GNMDC) model. In the GNMDC model, inflation is driven by a canonical scalar field that is coupled not only to gravity but also to the derivative of the scalar field. The model introduces new dynamics and features during the inflationary epoch. We find inflationary solutions with a power law scalar field for the power law coupling function. Additionally, we determine the inflaton potential that generates intermediate expansion of the scale factor. We also discuss the background equations in the high friction limit and derive constraints on the parameters of our model. Furthermore, we investigate the cosmological perturbations in the slow roll approximation within the GNMDC model, and we calculate the scalar and tensor spectral index and the tensor-to-scalar ratio during intermediate inflation. We compare the results of this model with observational data that can be used to test the model using cosmic microwave background radiation data. Overall, we establish conditions for the inflaton potential that ensure the continuation of accelerated expansion during slow roll inflation. We numerically analyze the power spectrum and spectral index for scalar and tensor modes in intermediate inflation in the high friction limit, and we use Planck 2018 data to obtain constraints on the parameters of the model. We demonstrate that intermediate inflation in the GNMDC model is successful in evaluation and explanation of background and perturbation quantities using observational data.

Towards testing the general bounce cosmology with the CMB B-mode auto-bispectrum

It has been shown that a three-point correlation function of tensor perturbations from a bounce model in general relativity with a minimally-coupled scalar field is highly suppressed, and the resultant three-point function of cosmic microwave background (CMB) B-mode polarizations is too small to be detected by CMB experiments. On the other hand, bounce models in a more general class with a non-minimal derivative coupling between a scalar field and gravity can predict the three-point correlation function of the tensor perturbations without any suppression, the amplitude of which is allowed to be much larger than that in general relativity. In this paper, we evaluate the three-point function of the B-mode polarizations from the general bounce cosmology with the non-minimal coupling and show that a signal-to-noise ratio of the B-mode auto-bispectrum in the general class can reach unity for ℓ max=100 in the full-sky case, with and without the lensing B-mode added to cosmic variance. Considering additionally the LiteBIRD experimental noise, we obtain a SNR smaller than unity.

Healthy Horndeski cosmologies with torsion

We show that the full Horndeski theory with both curvature and torsion can support nonsingular, stable and subluminal cosmological solutions at all times. Thus, with torsion, the usual No-Go theorem that holds in a curved spacetime is avoided. In particular, it is essential to include the nonminimal derivative couplings of the ℒ5 part of the Horndeski action (Gμν ∇ μ ∇ νϕ, and (∇2 ϕ)3). Without the latter a No-Go already impedes the eternal subluminality of nonsingular, stable cosmologies.

Localization of scalar matter with nonminimal derivative coupling on braneworlds

The localization of scalar matter with nonminimal derivative coupling (NMDC) in the braneworld model is studied. Two types of brane models are considered: a thin brane (the Modified Randall-Sundrum) and a thick brane generated by the bulk scalar field. The 5-dimensional theory of scalar field with NMDC is reduced to the effective 4-dimensional theory by imposing the fulfillment of localization conditions. In this article, the localization properties of field with NMDC are examined in both models. We found that the massless and massive scalar field with NMDC can be localized on the MRS thin brane. In the thick brane, the massless scalar field is localized.

Non-minimal derivative coupling theories compatible with GW170817

In this work we aim to revive the interest for non-minimal derivative coupling theories of gravity, in light of the GW170817 event. These theories include a string motivated non-minimal kinetic term for the scalar field of the form ∼ξ(ϕ)Gμν∂μϕ∂νϕ and predict that the primordial tensor perturbations have a speed that it is distinct from the speed of light. Due to the fact that the Universe is classical during and in the post-inflationary epoch, there is no fundamental reason for the graviton to change its mass, the GW170817 event severely constrained these theories. We analyze and formalize the inflationary phenomenology of these theories, using both the latest Planck data and the GW170817 event data to constrain these theories. Due to the fact that there is no constraint in the choice of the scalar potential and the non-minimal coupling function, we provide several classes of viable models, using convenient forms of the minimal coupling function in terms of the scalar potential, aiming for analyticity, and we discuss the advantages and disadvantages of each viable model.

A preliminary study on linear perturbation for a non-minimal derivative coupling scalar-tensor theory

The Cisterna-Delsate-Rinaldi (CDR) model is a variant of scalar-tensor theory that modify gravity by including a term of non-minimal derivative coupling. This model gives interesting aspects in the properties of compact objects, specifically neutron stars. By adjusting one of its parameters, the maximum possible mass of neutron stars can be increased. The authors of the model had also did a perturbation analysis using odd-parity perturbation and following that they also did analysis on the slowly-rotating neutron stars. In this paper, we report our ongoing research on the linear perturbation for the Cisterna model to see its dynamical properties. More precisely, we work on the polar perturbation that affected both the metric and the scalar field, which is different from the axial perturbation used in the slow rotation case. We use higher-dimensional spacetimes to see if the obtained equations will be dimensionally dependent. To simplify calculations for this metric form, we use tetrad method. Currently, we have not succeeded in obtaining the equations of motions in the form of Regge-Wheeler-Zerilli wave equation. The reason is the metric functions cannot be easily decoupled and we find no second derivatives with respect to both time t and radius r in the equations of motion. Only the scalar field can give a wave equation. Further investigation is undergoing.

Gravitational baryogenesis in non-minimal kinetic coupling model

In this work, we consider the gravitational baryogenesis in the framework of non-minimal derivative coupling model. A mechanism to generate the baryon asymmetry based on the coupling between the derivative of the Ricci scalar curvature and the baryon current in context of non-minimal derivative coupling model is investigated. We show that, in this model, the temperature increases during the reheating periods to the end of reheating period or beginning of radiation dominated era. Therefore the reheating temperature is larger then decoupling temperature. It can be demonstrated that, the evaluation of baryon asymmetry is not depends on coupling constant. In this model we can generate baryon asymmetry at low and high reheating temperature, by considering the high friction constraint.

Inflationary cross-correlations of a non-minimal spectator and their soft limits

Light spectator fields may not be dynamically relevant for the inflationary phase of the early universe, but they can still induce interesting imprints on cosmological observables. In this paper, we compute the cross-correlations of the inflationary perturbations, both scalar and tensor, with the fluctuations of a non-minimally interacting spectator field using the in-in formalism and investigate the consistency relations associated with such cross-correlations. In particular, the scalar consistency relation is derived semi-classically by generalizing the consistency relation obtained earlier for cosmic magnetic fields. Notably, we find that the direct coupling between the inflaton and the spectator solely determines the local non-linearity parameter associated with the scalar cross-correlation during slow-roll inflation, regardless of the specific form of the Lagrangian for the spectator field. Further, we calculate the tensor correlation with spectator fluctuations, explore the associated soft limits, and demonstrate the violation of the conventional tensor consistency relation with a non-minimal derivative coupling. Our analysis stresses that the violation of tensor consistency relations does not necessarily imply the superhorizon evolution of tensor modes. Instead, such violations can arise due to the non-minimal derivative coupling of the spectator field to gravity. Finally, we discuss the wider implications of our results in the context of cosmological soft theorems.

Cosmological models with arbitrary spatial curvature in the theory of gravity with nonminimal derivative coupling

Cosmological models with arbitrary spatial curvature in the theory of gravity with nonminimal derivative coupling

Cosmology in holographic non-minimal derivative coupling theory: Constraints from inflation and variation of gravitational constant

We consider a cosmological model of non-minimal derivative coupling (NMDC) to gravity with holographic effect from Bekenstein–Hawking entropy using Hubble horizon IR cutoff. Holographic parameter c is considered constant with value in a range, 0≤c<1. The NMDC effect is considered either as modification in kinetic scalar field or in gravitational constant. The NMDC effect allows gravitational constant to be time-varying. Since the NMDC effect is cosmological, definition of holographic density should include time-varying part of the gravitational constant. The NMDC part reduces strength of gravitational constant for κ>0 and opposite for κ<0. The holographic part enhances gravitational strength. Slow-roll parameters are derived. We use spectral index and tensor-to-scalar ratio to test the model against CMB constraint. Number of e-folding is chosen to be N≥60. Power-law scalar potentials, V=V0ϕn with n=2,4, and exponential potential, V=V0exp(−βϕ) are considered. Combined parametric plots of κ and ϕ show that the allowed regions of the power spectrum index and of the tensor-to-scalar ratio are not overlapping. NMDC inflation is ruled out and the holographic NMDC inflation is also ruled out for 0<c<1. NMDC significantly changes major anatomy of the dynamics, i.e. it gives new late-time attractor trajectories in acceleration regions. The holographic part clearly affects pattern of trajectories. However, for the holographic part to affect shape of the acceleration region, the NMDC field must be in presence. To constrain the model at late time, variation of gravitational constant is considered. Gravitational-wave standard sirens and supernovae data give a constraint, Ġ/G|t0≲3×10−12year−1 (Zhao et al., 2018) which, for this model, results in 10−12year−1≳−κϕ̇ϕ̈/MP2. Positive κ is favored and greater c2 results in lifting up lower bound of κ.

Implications of Palatini gravity for inflation and beyond

In this paper, we present an introduction to cosmic inflation in the framework of Palatini gravity, which provides an intriguing alternative to the conventional metric formulation of gravity. In the latter, only the metric specifies the spacetime geometry, whereas in the former, the metric and the spacetime connection are independent variables—an option that can result in a gravity theory distinct from the metric one. In scenarios where the field(s) responsible for cosmic inflation are non-minimally coupled to gravity or the gravitational sector is extended, assumptions about the underlying gravitational degrees of freedom can have substantial implications for the observational effects of inflation. We examine this explicitly by discussing various compelling scenarios, such as Higgs inflation with a non-minimal coupling to gravity, Higgs inflation with a non-minimal derivative coupling, [Formula: see text] inflation, and beyond. We also comment on reheating in these models. Finally, as an application of the general results of Palatini [Formula: see text] inflation, we review a model of successful quintessential inflation, where a single scalar field acts initially as the inflaton and then becomes dynamical dark energy, in agreement will all experimental constraints.

Nonminimal derivative coupling cosmology and the speed of gravitational waves

The so-called Nonminimal Derivative Coupling (NDC) is an alternative to General Relativity, which produces an asymptotic inflationary mechanism when applied to cosmology. The detection of gravitational waves in the last decade has imposed very stringent constraints over gravitational theories, which gave rise to a massive revision of those theories, in order to investigate the compatibility between them and that observational data. In this paper, we review NDC and address the question if it is compatible with gravitational waves or not. We show that the very existence of gravitational waves in this theory is restricted to a limited range in phase space and there are no accelerated solutions compatible with the present day data for the speed of such waves. This last result is alleviated by the fact that we did not detect primordial gravitational waves so far. Those conclusions are based on the comparison between the expression for the speed of tensor perturbations and the phase space. Finally, some possible scenarios and solutions are considered.

Understanding large scale CMB anomalies with the generalized nonminimal derivative coupling during inflation

We study the observational implications of a class of inflationary models wherein the inflaton is coupled to the Einstein tensor through a generalized nonminimal derivative coupling (GNMDC). In particular, we explore whether these models can generate suitable features in the primordial spectrum of curvature perturbations as a possible explanation for the large-scale anomalies associated with the angular power spectrum of CMB temperature anisotropies. We derive model-independent constraints on the GNMDC function for such a scenario, considering both the scalar and tensor perturbations. We modify cosmomc to accommodate our GNMDC framework and investigate different classes of inflationary models using a fully consistent numerical approach. We find that the hilltop-quartic model with a specific choice of the GNMDC function provides a considerable improvement over the best-fit reference $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model with a nearly scale-invariant power spectrum. While the large-scale structure observations should be able to provide independent constraints, future CMB experiments, such as CMB-S4 and CMB-Bharat, are expected to constrain further the parameter space of such beyond canonical single-field inflationary models.

Modified gravity and cosmology with nonminimal direct or derivative coupling between matter and the Einstein tensor

We construct new classes of modified theories in which the matter sector couples with the Einstein tensor, namely we consider direct couplings of the latter to the energy-momentum tensor, and to the derivatives of its trace. We extract the general field equations, which do not contain higher-order derivatives, and we apply them in a cosmological framework, obtaining the Friedmann equations, whose extra terms give rise to an effective dark energy sector. At the background level we show that we can successfully describe the usual thermal history of the universe, with the sequence of matter and dark-energy epochs, while the dark-energy equation-of-state parameter can lie in the phantom regime, tending progressively to $-1$ at present and future times. Furthermore, we confront the theory with Cosmic Chronometer data, showing that the agreement is very good. Finally, we perform a detailed investigation of scalar and tensor perturbations, and extracting an approximate evolution equation for the matter overdensity we show that the predicted behavior is in agreement with observations.

Constraints on primordial curvature spectrum from primordial black holes and scalar-induced gravitational waves

The observational data of primordial black holes and scalar-induced gravitational waves can constrain the primordial curvature perturbation at small scales. We parameterize the primordial curvature perturbation by a broken power law form and find that it is consistent with many inflation models that can produce primordial black holes, such as nonminimal derivative coupling inflation, scalar–tensor inflation, Gauss–Bonnet inflation, and K/G inflation. The constraints from primordial black holes on the primordial curvature power spectrum with the broken power law form are obtained, where the fraction of primordial black holes in dark matter is calculated by the peak theory. Both the real-space top-hat and the Gaussian window functions are considered. The constraints on the amplitude of primordial curvature perturbation with Gaussian window function are around three times larger than those with real-space top-hat window function. The constraints on the primordial curvature perturbation from the NANOGrav 12.5 years data sets are displayed, where the NANOGrav signals are assumed as the scalar-induced gravitational waves, and only the first five frequency bins are used.

Anti-de Sitter neutron stars in the theory of gravity with nonminimal derivative coupling

We consider neutron star configurations in the scalar-tensor theory of gravity with the coupling between the kinetic term of a scalar field and the Einstein tensor (such the model is a subclass of Horndeski gravity). Neutron stars in this model were studied earlier for the special case with a vanishing “bare” cosmological constant, Λ0 = 0, and a vanishing standard kinetic term, α = 0. This special case is of interest because it admits so-called stealth configuration, i.e. vacuum configuration with nontrivial scalar field and the Schwarzschild metric. However, generally one has Λ0 ≠ 0 and α ≠ 0 and in this case a vacuum configuration is represented as an asymptotically anti-de Sitter (AdS) black hole solution with the nontrivial scalar field. We construct neutron star configurations in this general case and show that resulting diagrams describing the relation between mass and radius of the star essentially differ from those obtained in GR or the particular model with α = Λ0 = 0. Instead, the mass-radius diagrams are similar to those obtained for so-called bare strange stars when a star radius decreases monotonically with decreasing mass. We show also that neutron stars in the theory of gravity with nonminimal derivative coupling are more compact comparing to those in GR or the particular model with α = Λ0 = 0 and suggest a way to estimate possible values of the parameter of nonminimal coupling ℓ. At last, using the Regge-Wheeler method, we discuss briefly the stability of obtained neutron star configurations.

An An Interacting Dark Energy Model with Nonminimal Derivative Coupling in the Parameterized Post-Friedmannian Framework

We investigation the parameterization of the cosmological model with the nonminimal derivative coupling of a scalar field where gravity is coupled nonminimally with the derivatives of dark energy components in the form of a scalar field. We follow the parameterized post-Friedmannian approach for the interacting dark energy theories. We show how the big number of free functions can be reduced by limiting certain assumptions to a few non-zero coefficients. We only consider the case that the dark sector contains at most second order in time derivatives of the metric and scalar fields. In this paper, we demonstrate their use through an example of the dark sector interactions model and classify them according to the current literature.

Slow-roll inflation in f(R,T) gravity with a RT mixing term

We consider slow-roll inflationary models in a class of modified theories of gravity which contains non-minimal curvature-inflaton couplings, i.e., the $f(R,T)$ gravity, where $R$ is the Ricci scalar and $T$ is the trace of the inflaton energy-momentum tensor. On top of the minimally coupled $T$ that has been widely investigated in the literature, we further include a $RT$ mixing term in the theory. This mixing term introduces non-minimal derivative couplings and plays an important role in inflationary dynamics. Taking chaotic and natural inflation as examples, we find that the predictions for spectral tilt and the tensor-to-scalar ratio are sensitive to the existence of the $RT$ mixing term. In particular, by turning on this mixing term, it is possible to bring chaotic and natural inflation into better agreement with observational data.

GW170817 Implementation on Einstein-Gauss-Bonnet Theory with Non Minimal and Non Minimal Derivative Coupling

The GW170817 event manifests that gravitational wave velocity is close to thespeed of light. As a result, several theories of gravity are no longer applicable, including EinsteinGauss-Bonnet (EGB) inflation. However, a constraint equation could be applied so that thetheory could produce a viable result. In this study, the EGB inflation is being extended byadding a non-minimal coupling (NMC) and a non-minimal derivative coupling (NMDC). Freeparameters values were evaluated to obtained viability with observational indices. We use powerlaw and exponential Gauss-Bonnet coupling functions. Each model provides observational valuesof ns and r that are compatible with the observations and has its characteristic. It specifiesthe free parameter that controls the alteration of ns and r values. The power-law model iscontrolled by the power m of the Gauss-Bonnet coupling function and the potential integrationconstant, V2. While the exponential model is controlled by the potential integration constant cand the power m of the exponential function. Some approximations do not hold true so that themodels need to be rectified. Apparently, the rectified power-law model is violating null energycondition (NEC), so we also provide the non-violating NEC power-law model.

Compatibility of Einstein-Gauss-Bonnet inflation theory with non-minimal derivative coupling in the constant-roll

Inflation is a theory in cosmology that explains that the early universe experienceda very fast expansion in a very short time and is able to explain some cosmological problemsand the presence of gravitational waves generated during the inflation period. Based on theevent GW170817, it was found that c2t = 1, which indicates that the speed of gravitationalwaves is nearly equal to the speed of light. This contradicts several modified theories of gravity,one of which is the Einstein-Gauss-Bonnet theory. This paper examines the compatibility ofEinstein-Gauss-Bonnet inflation theory with the GW170817 phenomenon, with the addition ofthe Non-minimal derivative coupling term and the constant-roll approach and its characteristics.The formulation of observational quantities is carried out using Horndeski theory and EffectiveField Theory with ADM formalism and the calculations are done numerically. The constantvalues are selected in such a way that the spectral index values and tensor-scalar ratios are closeto the 2018 Planck data. The results found that this theory is compatible with GW170817 withthe influence of Gauss-Bonnet term and constant-roll parameter β most dominant.