In the context of massive gravity, bi-gravity and multi-gravity non-minimal matter couplings via a specific composite effective metric were investigated recently. Even if these couplings generically reintroduce the Boulware-Deser ghost, this composite metric is unique in the sense that the ghost reemerges only beyond the decoupling limit and the matter quantum loop corrections do not detune the potential interactions. We consider non-minimal {\it derivative} couplings of the composite metric to matter fields for a specific subclass of Horndeski scalar-tensor interactions. We first explore these couplings in the mini-superspace and investigate in which scenario the ghost remains absent. We further study these non-minimal derivative couplings in the decoupling-limit of the theory and show that the equation of motion for the helicity-0 mode remains second order in derivatives. Finally, we discuss preliminary implications for cosmology.
We investigate models in which the inflaton emerges as a composite field of a four dimensional, strongly interacting and nonsupersymmetric gauge theory featuring purely fermionic matter. We show that it is possible to obtain successful inflation via non-minimal coupling to gravity, and that the underlying dynamics is preferred to be near conformal. We discover that the compositeness scale of inflation is of the order of the grand unified energy scale.
In the N=1 four-dimensional new-minimal supergravity framework, we supersymmetrise the coupling of the scalar kinetic term to the Einstein tensor. This coupling, although introduces a non-minimal derivative interaction of curvature to matter, it does not introduce harmful higher-derivatives. For this construction, we employ off-shell chiral and real linear multiplets. Physical scalars are accommodated in the chiral multiplet whereas curvature resides in a linear one.
Inflation during rapid oscillation of a scalar field in non-minimal derivative coupling model is discussed. Cosmological perturbations originated in this stage are studied and consistency of the results with observational constraints coming from Planck 2013 data are investigated.
A scalar field model with non-minimal derivative coupling to gravity is considered. It is shown that although in the absence of matter and potential the phantom divide line crossing is forbidden, but for the power law potential and in the presence of matter this crossing is, in principle, possible.
We derive the general formulae for the the scalar and tensor spectral tilts to the second order for the inflationary models with non-minimally derivative coupling without taking the high friction limit. The non-minimally kinetic coupling to Einstein tensor brings the energy scale in the inflationary models down to be sub-Planckian. In the high friction limit, the Lyth bound is modified with an extra suppression factor, so that the field excursion of the inflaton is sub-Planckian. The inflationary models with non-minimally derivative coupling are more consistent with observations in the high fr…
We perform a combined perturbation and observational investigation of the scenario of non-minimal derivative coupling between a scalar field and curvature. First we extract the necessary condition that ensures the absence of instabilities, which is fulfilled more sufficiently for smaller coupling values. Then using Type Ia Supernovae (SNIa), Baryon Acoustic Oscillations (BAO), and Cosmic Microwave Background (CMB) observations, we show that, contrary to its significant effects on inflation, the non-minimal derivative coupling term has a negligible effect on the universe acceleration, since it …
We study the quasi-normal modes of asymptotically anti-de Sitter black holes in a class of shift-symmetric Horndeski theories where a gravitational scalar is derivatively coupled to the Einstein tensor. The space-time differs from exact Schwarzschild-anti-de Sitter, resulting in a different effective potential for the quasi-normal modes and a different spectrum. We numerically compute this spectrum for a massless test scalar coupled both minimally to the metric, and non-minimally to the gravitational scalar. We find interesting differences from the Schwarzschild-anti-de Sitter black hole found…
We investigate cosmological scenarios with a non-minimal derivative coupling between the scalar field and the curvature, examining both the quintessence and the phantom cases in zero and constant potentials. In general, we find that the universe transits from one de Sitter solution to another, determined by the coupling parameter. Furthermore, according to the parameter choices and without the need for matter, we can obtain a Big Bang, an expanding universe with no beginning, a cosmological turnaround, an eternally contracting universe, a Big Crunch, a Big Rip avoidance and a cosmological boun…
The magnetic field redefinition in Jain's composite fermion model for the fractional quantum Hall effect is shown to be effectively described by a mean-field approximation of a model containing a Maxwell-Chern-Simons gauge field non-minimally coupled to matter. Also an explicit non-relativistic limit of the non-minimal (2+1)D Dirac equation is derived.
We introduce inflationary models where the inflaton features a field dependent non-minimal derivative coupling to the Einstein tensor, that we name GNMDC. This Horndeski term gives new and distinguishable inflationary predictions in a framework that ameliorates possible problems related with gradient instabilities during the reheating stage. We examine the inflationary phenomenology using power law monomial and exponential potentials. We further elaborate on the implications of the inflaton-modulated GNMDC and construct GNMDC terms that can amplify the power spectrum of primordial perturbation…
We give a brief review of the non-minimal derivative coupling (NMDC) scalar field theory in which there is non-minimal coupling between the scalar field derivative term and the Einstein tensor. We assume that the expansion is of power-law type or super-acceleration type for small redshift. The Lagrangian includes the NMDC term, a free kinetic term, a cosmological constant term and a barotropic matter term. For a value of the coupling constant that is compatible with inflation, we use the combined WMAP9 (WMAP9+eCMB+BAO+ $H_0$) dataset, the PLANCK+WP dataset, and the PLANCK $TT,TE,EE$+lowP+Lensi…
The composite operator T\bar{T}, obtained from the components of the energy-momentum tensor, enjoys a quite general characterization in two-dimensional quantum field theory also away from criticality. We use the form factor bootstrap supplemented by asymptotic conditions to determine its matrix elements in the sinh-Gordon model. The results extend to the breather sector of the sine-Gordon model and to the minimal models M_{2/(2N+3)} perturbed by the operator phi_{1,3}.
We study the gravitational field equations in the presence of a coupling between the derivative of a massless scalar field and the Einstein tensor. This configuration is motivated by Galileon gravity as it preserves shift invariance in the scalar sector. We analytically obtain solutions with static and spherically symmetric geometry, which also include black holes with a single regular horizon. We examine the thermodynamical properties of these solutions, and we reveal the non-perturbative nature of the Galileon coupling constant. We also find a phase transition, similar to the one described b…
The pairing interaction among identical nucleons in a single-particle level is treated in the hamiltonian formalism using even Grassmann variables. A minimal (irreducible) basis having a remarkable symmetry property is set up using composite, commuting variables with a finite index of nilpotency. Eigenvalues and eigenfunctions of given energy, seniority and zero third component of the angular momentum of the pairing hamiltonian are then found. The eigenvectors, which cannot be cast solely in terms of composite bosons with angular momentum zero and two, are expanded in the minimal basis with co…
With the usual definitions for the entropy and the temperature associated with the apparent horizon, we discuss the first law of the thermodynamics on the apparent in the general scalar-tensor theory of gravity with the kinetic term of the scalar field non-minimally coupling to Einstein tensor. We show the equivalence between the first law of thermodynamics on the apparent horizon and Friedmann equation for the general models, by using a mass-like function which is equal to the Misner-Sharp mass on the apparent horizon. The results further support the universal relationship between the first l…
We study the idea of a composite Higgs in the framework of a five-dimensional AdS theory. We present the minimal model of the Higgs as a pseudo-Goldstone boson in which electroweak symmetry is broken dynamically via top loop effects, all flavour problems are solved, and contributions to electroweak precision observables are below experimental bounds. Since the 5D theory is weakly coupled, we are able to fully determine the Higgs potential and other physical quantities. The lightest resonances are expected to have a mass around 2 TeV and should be discovered at the LHC. The top sector is mostly…
In this letter we show that there is a unique non-minimal derivative coupling of the Standard Model Higgs boson to gravity such that: it propagates no more degrees of freedom than General Relativity sourced by a scalar field, reproduces a successful inflating background within the Standard Model Higgs parameters and, finally, does not suffer from dangerous quantum corrections.
We consider the inflaton as a scalar field described by a non-minimal derivative coupling model with a power law potential. We study the slow roll inflation, the rapid oscillation phase, the radiation dominated and the recombination eras respectively, and estimate e-folds numbers during these epochs. Using these results and recent astrophysical data we determine the reheating temperature in terms of the spectral index and the amplitude of the power spectrum of scalar perturbations.
In this article we motivate and review the embedding of the gravitationally enhanced friction mechanism in supergravity. The very interesting feature is that inflationary models which utilize this mechanism drive inflation for a wider range of parameter values and predict lower values for the tensor-to-scalar ratio.
We study the gravitational production of heavy X-particles of mass of the order of the inflaton mass, produced after the end of inflation. We find that, in the presence of a derivative coupling of the inflaton field or of the X-field to the Einstein tensor, the number of gravitationally produced particles is suppressed as the strength of the coupling is increased.
We study a general class of holographic superconductor models via the Stückelberg mechanism in the non-minimal derivative coupling theory in which the charged scalar field is kinetically coupling to Einstein's tensor. We explore the effects of the coupling parameter on the critical temperature, the order of phase transitions and the critical exponents near the second-order phase transition point. Moreover, we compute the electric conductive using the probe approximation and check the ratios $ω_g/T_c$ for the different coupling parameters.
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…
In de Rham-Gabadadze-Tolley (dRGT) massive gravity and bigravity, a non-minimal matter coupling involving both metrics generically re-introduces the Boulware--Deser (BD) ghost. A non-minimal matter coupling via a simple, yet specific composite metric has been proposed, which eliminates the BD ghost below the strong coupling scale. Working explicitly in the metric formulation and for arbitrary spacetime dimensions, we show that this composite metric is the unique consistent non-minimal matter coupling below the strong coupling scale, which emerges out of two diagnostics, namely, absence of Ostr…
In this work, we study constant-roll inflation driven by a scalar field with non-minimal derivative coupling to gravity, via the Einstein tensor. This model contains a free parameter, $η$, which quantifies the non-minimal derivative coupling and a parameter $α$ which characterize the constant-roll condition. In this scenario, using the Hamilton-Jacobi-like formalism, an ansatz for the Hubble parameter (as a function of the scalar field) and some restrictions on the model parameters, we found new exact solutions for the inflaton potential which include power-law, de Sitter, quadratic hilltop an…
The bouncing cosmology provides a successful solution of the cosmological singularity problem. In this paper, we study the bouncing behavior of a single scalar field model with tachyon field non-minimally coupled to itself, its derivative and to the curvature. By utilizing the numerical calculations we will show that the bouncing solution can appear in the universe dominated by such a quintom matter with equation of state crossing the phantom divide line. We also investigate the classical stability of our model using the phase velocity of the homogeneous perturbations of the tachyon scalar fie…
We construct higher-derivative gravities with a non-minimally coupled Maxwell field. The Lagrangian consists of polynomial invariants built from the Riemann tensor and the Maxwell field strength in such a way that the equations of motion are second order for both the metric and the Maxwell potential. We also generalize the construction to involve a generic non-minimally coupled $p$-form field strength. We then focus on one low-lying example in four dimensions and construct the exact magnetically-charged black holes. We also construct exact electrically-charged $z=2$ Lifshitz black holes. We ob…
We study four-derivative corrections to pure $\mathcal{N}=2$, $D=5$ gauged supergravity. In particular, we find that, up to field redefinitions, there is a single four-derivative superinvariant that one can add to the action, up to factors of the two-derivative action. Consequently, this selects out a unique set of coefficients for the four-derivative corrections. We confirm these coefficients (in the ungauged limit) on the BMPV solution.
We study asymptotic safety of models of the higher derivative quantum gravity with and without matter. The beta functions are derived by utilizing the functional renormalization group, and non-trivial fixed points are found. It turns out that all couplings in gravity sector, namely the cosmological constant, the Newton constant, and the $R^2$ and $R_{μν}^2$ coupling constants, are relevant in case of higher derivative pure gravity. For the Higgs-Yukawa model non-minimal coupled with higher derivative gravity, we find a stable fixed point at which the scalar-quartic and the Yukawa coupling cons…
We study the greybody factor and Hawking radiation with a non-minimal derivative coupling between the scalar field and the curvature in the background of the slowly rotating Kerr-Newman black hole. Our results show that both the absorption probability and luminosity of Hawking radiation of the scalar field increase with the coupling. Moreover, we also find that for the weak coupling $η<η_c$, the absorption probability and luminosity of Hawking radiation decrease when the black hole's Hawking temperature decreases; while for stronger coupling $η>η_c$, the absorption probability and luminosity o…
In the minimal composite Higgs model (MCHM), the size of the Higgs mass and vacuum expectation value is determined, via the Higgs potential, by the size of operators that violate the global SO(5) symmetry. In 5D holographic realisations of this model, this translates into the inclusion of brane localised operators. However, the inclusion of all such operators results in a large and under-constrained parameter space. In this paper we study the level of fine-tuning involved in such a parameter space, focusing on the MCHM${}_5$. It is demonstrated that the gauge contribution to the Higgs potentia…
In inflation with nonminimal derivative coupling there is not a conformal transformation to the Einstein frame where calculations are straightforward, and thus in order to extract inflationary observables one needs to perform a detailed and lengthy perturbation investigation. In this work we bypass this problem by performing a Hamilton-Jacobi analysis, namely rewriting the cosmological equations considering the scalar field to be the time variable. We apply the method to two specific models, namely the power-law and the exponential cases, and for each model we calculate various observables suc…
We consider an extension of Higgs inflation in which the Higgs field is non-minimally coupled to gravity through its kinetic term. We analyzed power-law coupling functions with positive or negative integer power and found that the Higgs boson can drive a successful inflation only for the cases $n=2,1,0,-1$. Theoretical predictions for both tensor to scalar ratio $r$ and scalar spectral index $n_s$ are within the 2018 \textit{Planck} $95\%$ CL. The behavior of the self coupling $λ$ with respect to the scalar field at the horizon crossing was obtained, and It was found that it can take values in…
We revisit the D-term inflation and amend it with ghost-free higher derivative couplings of chiral superfields to super-curvature. These couplings realize a more generic inflationary phase in supergravity. After pointing out that a consistent embedding of these specific higher derivatives is known to exist only in the new-minimal supergravity, we show how a potential for the scalar component may arise due to a Fayet-Iliopoulos D-term. We then turn to inflationary cosmology and explicitly discuss different types of potentials, which capture properties of the common scenarios. These models thank…
We investigate higher-derivative extensions of Einstein-Maxwell theory that are invariant under electromagnetic duality rotations, allowing for non-minimal couplings between gravity and the gauge field. Working in a derivative expansion of the action, we characterize the Lagrangians giving rise to duality-invariant theories up to the eight-derivative level, providing the complete list of operators that one needs to include in the action. We also characterize the set of duality-invariant theories whose action is quadratic in the Maxwell field strength but which are non-minimally coupled to the …
We reassess employing the holographic technique to the description of 4D minimal composite Higgs model with $SO(5)\to SO(4)$ global symmetry breaking pattern. The particular 5D bottom-up holographic treatment is inspired by previous work in the context of QCD and it allows to study spin one and spin zero resonances. The resulting spectrum consists of the states transforming under the unbroken $SO(4)$ subgroup and those with quantum numbers in the $SO(5)/SO(4)$ coset. The spin one states are arranged in linear radial trajectories, and the states from the broken subgroup are generally heavier. T…
For composite systems made of $N$ different particles living in a space characterized by the same deformed Heisenberg algebra, but with different deformation parameters, we define the total momentum and the center-of-mass position to first order in the deformation parameters. Such operators satisfy the deformed algebra with new effective deformation parameters. As a consequence, a two-particle system can be reduced to a one-particle problem for the internal motion. As an example, the correction to the hydrogen atom $n$S energy levels is re-evaluated. Comparison with high-precision experimental…
The authors reexamine the two-dimensional model of massive fermions interacting with a massless pseudoscalar field via axial-current-pseudoscalar derivative coupling. Performing a canonical field transformation on the Bose field algebra the model is mapped into the Thirring model with an additional vector-current-scalar-derivative interaction (Schroer-Thirring model). The complete bosonized version of the model is presented. The bosonized composite operators of the quantum Hamiltonian are obtained as the leading operators in the Wilson short distance expansion.
Within the context of top-down holography, we study a one-parameter family of regular background solutions of maximal gauged supergravity in seven dimensions, dimensionally reduced on a 2-torus. The dual, four-dimensional confining field theory realises the global (spontaneous as well as explicit) symmetry breaking pattern SO(5)->SO(4). We compute the complete mass spectrum for the fluctuations of the 128 bosonic degrees of freedom of the five-dimensional gravity theory, which correspond to scalar, pseudoscalar, vector, axial-vector, and tensor bound states of the dual field theory, and includ…
We propose a four dimensional description of Composite Higgs Models which represents a complete framework for the physics of the Higgs as a pseudo-Nambu-Goldstone boson. Our setup captures all the relevant features of 5D models and more in general of composite Higgs models with partial compositeness. We focus on the minimal scenario where we include a single multiplet of resonances of the composite sector, as these will be the only degrees of freedom which might be accessible at the LHC. This turns out to be sufficient to compute the effective potential and derive phenomenological consequences…
We consider the sector of Horndeski's gravity characterized by the coupling between the kinetic scalar field term and the Einstein tensor. We numerically construct neutron star configurations where the external geometry is identical to the Schwarzschild metric but the interior structure is considerably different from standard general relativity. We constrain the only parameter of this model from the requirement that compact configurations exist, and we argue that solutions less compact than neutron stars, such as white dwarfs, are also supported. Therefore, our model provides an explicit modif…
Recent investigations have shown that inflation can be driven by four-dimensional strongly interacting theories non-minimally coupled to gravity. We explore this paradigm further by considering composite inflation driven by orientifold field theories. The advantage of using these theories resides in the fact that at large number of colors they feature certain super Yang-Mills properties. In particular we can use for inflation the bosonic part of the Veneziano-Yankielowicz effective theory. Furthermore, we include the 1/N as well as fermion mass corrections at the effective Lagrangian level all…
We introduce fundamental gauge theories that can be employed to construct informed composite bright and dark extensions of the Standard Model, within and beyond the standard paradigms. The gap between theory and experiments is bridged by providing predictions and ways to test them, for example, at the Fermi scale and via precision flavor experiments. We will review time-honoured paradigms from (walking) technicolor to composite Goldstone Higgs and discuss their features and differences. Standard model fermion mass generation in composite models will also be discussed along with the challenges …
A generalization of the non-Abelian version of the $CP^{N-1}$ models (also known as Grassmannian models) is presented. The generalization helps accommodate a partial breaking of the non-Abelian gauge symmetry. Constituents of the composite gauge fields, in many cases, are naturally constrained to belong to an anomaly free representation which in turn generates a composite scalar simulating Higgs mechanism to break the gauge symmetry dynamically for large $N$. Two cases are studied in detail: one based on the SU(2) gauge group and the other on SO(10). Breakings such as SU(2)$\to$U(1) or SO(10)$…
The Lee-Wick Standard Model assumes a minimal set of higher-derivative quadratic terms that produce a negative-norm partner for each Standard Model particle. Here we introduce additional terms of one higher order in the derivative expansion that give each Standard Model particle two Lee-Wick partners: one with negative and one with positive norm. These states collectively cancel unwanted quadratic divergences and resolve the hierarchy problem as in the minimal theory. We show how this next-to-minimal higher-derivative theory may be reformulated via an auxiliary field approach and written as a …
Using the operator formulation we discuss the bosonization of the two-dimensional derivative-coupling model. The fully bosonized quantum Hamiltonian is obtained by computing the composite operators as the leading terms in the Wilson short distance expansion for the operator products at the same point. In addition, the quantum Hamiltonian contains topological terms which give trivial contributions to the equations of motion. Taking into account the quantum corrections to the bosonic equations of motion and to the scale dimension of the Fermi field operator, the operator solution is obtained in …
We explicitly calculate the one-loop effective potential for a higher-derivative four-dimensional chiral superfield theory with a nonconventional kinetic term. We consider the cases of minimal and nonminimal general Lagrangians. In particular, we find that in the minimal case the divergent part of the one-loop effective potential vanishes by reason of the chirality.
We identify trigonometric parity as the key ingredient behind models of neutral naturalness for the Higgs potential. We show that any symmetric coset space readily includes such a trigonometric parity, which is simply a combination of a $π/2$ rotation along a broken direction and a Higgs parity transformation. We explain how to extend the top sector such that this $Z_2$ remains intact while the rest of the shift symmetry is explicitly broken, resulting in the cancelation of the quadratic divergences in the Higgs potential. Assuming additional structure (for example partial compositeness with m…
We give an explicit example of a composite Higgs model with a pseudo-Nambu-Goldstone Higgs in which the top Yukawa coupling is generated via the partial compositeness mechanism. This mechanism requires composite top partners which are relatively light compared to the typical mass scale of the strongly coupled theory. While most studies of the phenomenology of such models have focused on a bottom-up approach with a minimal effective theory, a top-down approach suggests that that the theory should contain a limit in which an unbroken global chiral symmetry protects the mass of the top partners, …
