Induced Gravity Models Research Articles

Slow-roll inflation in the Jordan frame

Inflation models based on scalar-tensor theories of gravity are formulated in the Jordan frame but most often analysed in the Einstein frame. The transformation between the frames is not always desirable. In this work we formulate slow-roll conditions in the Jordan frame. This is achieved by comparing different background quantities and approximations on the same spatial slice in both frames. We use these approximations to derive simple equations that can be applied to compute inflation model observables in terms of Jordan frame quantities only. Finally, we apply some of the results to analyse generalised induced gravity models and compare them with the latest observations.

Black hole entropy and long strings

In this paper, we discuss whether black hole entropy counts short or long-range microstates in quantum gravity. In brick wall and induced gravity models, the entropy arises due to short distance correlations across the event horizon cut off at the Planck length. However, the energy of these short range degrees of freedom is too high compared to the black hole energy. We argue that the long string phenomenon, which naturally appears in matrix quantum mechanics, resolves this issue by lowering the excitation energy per degree of freedom. This mechanism also reduces the total number of microscopic degrees of freedom in a given volume, leading to a correct estimate of the Bekenstein–Hawking formula for black hole entropy.

The investigation of stability of brane induced gravity model in the ‎presence of a scalar field with various kinds of potential‎

In this manuscript we consider the normal branch of DGP brane cosmological model in the presence of a ‎scalar field on the brane as the dark energy component. Using dynamical system approach we investigate ‎the stability properties of the system. We will see that one of the defined new variables lambda, that ‎depends on the potential function of the scalar field has a significant role in the evolution of the universe. ‎Therefore, we divide our discussion into two parts, the constant and the varying lambda. With a good ‎approximation we consider all the obtained critical points in the case of the constant lambda, as the ‎instantaneous critical points for the case of a varying lambda. We investigate two special scalar field ‎potential function: a double exponential potential and an inverse power law potential. In both of the cases we ‎study the evolution of the system and discuss the fate of the universe. We find that the inverse power law ‎potential function is in a good agreement with the current universe, but the double exponential potential ‎function can predict different future for the universe.‎

Induced gravity and quantum cosmology

We study the Wheeler-DeWitt equation for a class of induced gravity models in the minisuperspace approximation. In such models a scalar field nonminimally coupled to gravity determines the effective Newton's constant. For simplicity our analysis is limited to power-law potentials for the scalar field which have exact classical solutions. We show that these models have exact solutions also when quantised. Finally the Einstein Frame form of these solutions is obtained and a classical-quantum correspondence is found. Realistic induced gravity models also must include a symmetry breaking term which is needed in order to obtain a gravitational constant, successful inflation and a subsequent standard cosmological evolution. Nonetheless the potentials considered are important as they may describe the inflationary phase when the symmetry breaking part of the potential is negligible.

Palatini inflation in models with an R2 term

The Starobinsky model, considered in the framework of the Palatini formalism, in contrast to the metric formulation, does not provide us with a model for inflation, due to the absence of a propagating scalar degree of freedom that can play the role of the inflaton. In the present article we study the Palatini formulation of the Starobinsky model coupled, in general nonminimally, to scalar fields and analyze its inflationary behavior. We consider scalars, minimally or nonminimally coupled to the Starobinsky model, such as a quadratic model, the induced gravity model or the standard Higgs-like inflation model and analyze the corresponding modifications favorable to inflation. In addition we examine the case of a classically scale-invariant model driven by the Coleman-Weinberg mechanism. In the slow-roll approximation, we analyze the inflationary predictions of these models and compare them to the latest constraints from the Planck collaboration. In all cases, we find that the effect of the R2 term is to lower the value of the tensor-to-scalar ratio.

Induced Gravity Models with Exact Bounce Solutions

We study dynamics of induced gravity cosmological models with the sixth degree polynomial potentials, that have been constructed using the superpotential method. We find conditions on the potential under which exact bounce solutions exist and study the stability of these solutions.

Ultraviolet complete dark energy model

We consider a local phenomenological model to explain a non-local gravity scenario which has been proposed to address dark energy issues. This non-local gravity action has been seen to fit the data as well as $\Lambda$-CDM and therefore demands a more fundamental local treatment. The induced gravity model coupled with higher-derivative gravity is exploited for this proposal, as this perturbatively renormalizable model has a well-defined ultraviolet (UV) description where ghosts are evaded. We consider a generalised version of this model where we consider two coupled scalar fields and their non-minimal coupling with gravity. In this simple model, one of the scalar field acquires a Vacuum Expectation Value (VEV), thereby inducing a mass for one of the scalar fields and generating Newton's constant. The induced mass however is seen to be always above the running energy scale thereby leading to its decoupling. The residual theory after decoupling becomes a platform for driving the accelerated expansion under certain conditions. Integrating out the residual scalar generates a non-local gravity action. The leading term of which is the non-local gravity action used to fit the data of dark energy.

Flattening the inflaton potential beyond minimal gravity

We review the status of the Starobinsky-like models for inflation beyond minimal gravity and discuss the unitarity problem due to the presence of a large non-minimal gravity coupling. We show that the induced gravity models allow for a self-consistent description of inflation and discuss the implications of the inflaton couplings to the Higgs field in the Standard Model.

Induced gravity from curvature density preserving diffeomorphisms

We construct not only an induced gravity model with the restricted diffeomorphisms, that is, transverse diffeomorphisms which preserves the curvature density, but also that with the full diffeomorphisms. By solving the equations of motion, it turns out that these models produce Einstein's equations with a certain Newton's constant in addition to the constraint for the curvature density. In the limit of the infinite Newton constant, the models give rise to induced gravity. Moreover, we discuss cosmological solutions on the basis of the gravitational models at hand.

Starobinsky-type inflation with products of Kähler manifolds

We present a novel realization of Starobinsky-type inflation within Supergravity using two chiral superfields. The proposed superpotential is inspired by induced-gravity models. The Kähler potential contains two logarithmic terms, one for the inflaton T and one for the matter-like field S, parameterizing the SU(1,1)/U(1) × SU(2)/U(1) Kähler manifold. The two factors have constant curvatures −m/n and 2/n2, where n, m are the exponents of T in the superpotential and Kähler potential respectively, and 0 < n2 ⩽ 6. The inflationary observables depend on the ratio 2n/m only. Essentially they coincide with the observables of the original Starobinsky model. Moreover, the inflaton mass is predicted to be 3·1013 GeV.

Intermediate accelerated solutions as generic late-time attractors in a modified Jordan-Brans-Dicke theory

In this paper we investigate the evolution of a Jordan-Brans-Dicke scalar field, Φ, with a power-law potential in the presence of a second scalar field, ϕ, with an exponential potential, in both the Jordan and the Einstein frames. We present the relation of our model with the induced gravity model with power-law potential and the integrability of this kind of models is discussed when the quintessence field ϕ is massless, and has a small velocity. The fact that for some fine-tuned values of the parameters we may get some integrable cosmological models, makes our choice of potentials very interesting. We prove that in Jordan-Brans-Dicke theory, the de Sitter solution is not a natural attractor. Instead, we show that the attractor in the Jordan frame corresponds to an ``intermediate accelerated'' solution of the form a(t) ≃ eα1 tp1, as t → ∞ where α1 > 0 and 0 < p1 < 1, for a wide range of parameters. Furthermore, when we work in the Einstein frame we get that the attractor is also an ``intermediate accelerated'' solution of the form \U0001d51e(\U0001d531) ≃ eα2 \U0001d531p2 as \U0001d531 → ∞ where α2 > 0 and 0<p2<1, for the same conditions on the parameter space as in the Jordan frame. In the special case of a quadratic potential in the Jordan frame, or for a constant potential in the Einstein's frame, the above intermediate solutions are of saddle type. These results were proved using the center manifold theorem, which is not based on linear approximation. Finally, we present a specific elaboration of our extension of the induced gravity model in the Jordan frame, which corresponds to a particular choice of a linear potential of Φ. The dynamical system is then reduced to a two dimensional one, and the late-time attractor is linked with the exact solution found for the induced gravity model. In this example the ``intermediate accelerated'' solution does not exist, and the attractor solution has an asymptotic de Sitter-like evolution law for the scale factor. Apart from some fine-tuned examples such as the linear, and quadratic potential U(Φ) in the Jordan frame, it is true that ``intermediate accelerated'' solutions are generic late-time attractors in a modified Jordan-Brans-Dicke theory.

Modified gravity, the Cascading DGP model and its critical tension

We investigate the presence of instabilities in the Cascading DGP model. We start by discussing the problem of the cosmological late time acceleration, and we introduce the modified gravity approach. We then focus on brane induced gravity models and in particular on the Cascading DGP model. We consider configurations of the latter model where the source term is given simply by vacuum energy (pure tension), and we study perturbations at first order around these configurations. We perform a four-dimensional scalar-vector-tensor decomposition of the perturbations, and show that, regarding the scalar sector, the dynamics in a suitable limit can be described by a master equation. This master equation contains an energy scale (critical tension) which is related in a lion-trivial way to the parameters of the model. We give a geometrical interpretation of why this scale emerges, and explain its relevance for the presence of ghost instabilities in the theory. We comment on the difference between our result, and the one present in the literature, and stress its importance regarding the phenomenological viability of the model. We finally provide a numerical check which confirms the validity of our analysis.

Integrable cosmological models with non-minimally coupled scalar fields

We obtain general solutions for some flat Friedmann universes filled with a scalar field in induced gravity models and models including the Hilbert–Einstein curvature term plus a scalar field conformally coupled to gravity. As is well known, these models are connected to minimally coupled models through the combination of a conformal transformation and a transformation of the scalar field. The explicit forms of the self-interaction potentials for six exactly solvable models are presented here. We obtain the general solution for one of the integrable models, namely, the induced gravity model with a power-law potential for the self-interaction of the scalar field. We argue that although being mathematically in a one-to-one correspondence with the solutions in the minimally coupled models, the solutions in the corresponding non-minimally coupled models are physically different. This is because the cosmological evolutions seen by an internal observer connected with the cosmic time can be quite different. The study of a few induced gravity models with particular potentials gives us an explicit example of such a difference.

Dynamical dark energy and spontaneously generated gravity

We study the cosmological evolution of an induced gravity model with a scale symmetry breaking potential for the scalar field and the presence of barotropic fluids. The radiation to matter transition, following inflation and reheating, influences the dynamics of such a field through its non-minimal coupling. Indeed one finds, as a consequence of such a transition, that the scalar field is shifted from the potential minimum (which is associated with a zero cosmological constant). We illustrate how, under certain conditions on the potential, such a dynamics can lead to a suitable amount of dark energy explaining the present accelerated expansion. In such an approach, however, for long enough times, the dark energy will disappear.

Holographic induced gravity model with a Ricci dark energy: Smoothing the little rip and big rip through Gauss-Bonnet effects?

We present an holographic brane-world model of the Dvali-Gabadadze-Porrati (DGP) scenario with and without a Gauss-Bonnet term (GB) in the bulk. We show that an holographic dark energy component with the Ricci scale as the infrared cutoff can describe the late-time acceleration of the Universe. In addition, we show that the dimensionless holographic parameter is very important in characterizing the DGP branches, and in determining the behavior of the Ricci dark energy as well as the asymptotic behavior of the brane. On the one hand, in the DGP scenario the Ricci dark energy will exhibit a phantomlike behavior with no big rip if the holographic parameter is strictly larger than $1/2$. For smaller values, the brane hits a big rip or a little rip. On the other hand, we have shown that the introduction of the GB term avoids the big rip and little rip singularities on both branches but cannot avoid the appearance of a big freeze singularity for some values of the holographic parameter on the normal branch, however, these values are very unlikely because they lead to a very negative equation of state at the present and therefore we can speak in practice of singularity avoidance. At this regard, the equation of state parameter of the Ricci dark energy plays a crucial role, even more important than the GB parameter, in rejecting the parameter space where future singularities appear.

Cosmology of a holographic induced gravity model with curvature effects

We present an holographic model of the Dvali-Gabadadze-Porrati scenario with a Gauss-Bonnet term in the bulk. We concentrate on the solution that generalises the normal Dvali-Gabadadze-Porrati branch. It is well known that this branch cannot describe the late-time acceleration of the universe even with the inclusion of a Gauss-Bonnet term. Here, we show that this branch in the presence of a Gauss-Bonnet curvature effect and an holographic dark energy with the Hubble scale as the infra-red cutoff can describe the late-time acceleration of the universe. It is worthwhile to stress that such an energy density component cannot do the same job on the normal Dvali-Gabadadze-Porrati branch (without Gauss-Bonnet modifications) nor in a standard 4-dimensional relativistic model. The acceleration on the brane is also presented as being induced through an effective dark energy which corresponds to a balance between the holographic one and geometrical effects encoded through the Hubble parameter.

Cosmic acceleration and the challenge of modifying gravity

I briefly discuss the challenges presented by attempting to modify general relativity to obtain an explanation for the observed accelerated expansion of the universe. Foremost among these are the questions of theoretical consistency – the avoidance of ghosts in particular – and the constraints imposed by precision local tests of gravity within the solar system. For those models that clear these highly constraining hurdles, modern observational cosmology offers its own suite of tests, improving with upcoming datasets, that offer the possibility of ruling out modified gravity approaches or providing an intriguing hint of new infrared physics. In the second half of the talk, I discuss a recent approach to extracting cosmology from higher-dimensional induced gravity models.

Schwinger-DeWitt technique for quantum effective action in brane induced gravity models

We develop the Schwinger-DeWitt technique for the covariant curvature expansion of the quantum effective action for brane induced gravity models in curved spacetime. This expansion has a part nonanalytic in DGP type scale parameter, leading to the cutoff scale which is given by the geometric average of the mass of the quantum field in the bulk and DGP scale. This cutoff is much higher than the analogous strong coupling scale of the DGP model treated by weak field expansion in the tree-level approximation. The lowest orders of this curvature expansion are calculated for the case of the scalar field in the $(d+1)$-dimensional bulk with the brane carrying the $d$-dimensional kinetic term of this field. The ultraviolet divergences in this model are obtained for a particular case of $d=4$.

Scalar-tensor theory and the anisotropic perturbations of the inflationary universe

Inflationary higher derivative scalar-tensor theory is analyzed in this paper in a de Sitter background space. A useful model-independent formula of the Friedmann equation is derived and used to study the stability problem associated with the anisotropic perturbations of the inflationary solution. The stability conditions of the de Sitter solution are derived for a general class of models. For a simple demonstration, an induced gravity model is considered in this paper for the effects of the higher derivative interactions including a cubic term.

Dark energy, induced gravity and broken scale invariance

We study the cosmological evolution of an induced gravity model with a self-interacting scalar field σ and in the presence of matter and radiation. Such model leads to Einstein gravity plus a cosmological constant as a stable attractor among homogeneous cosmologies and is therefore a viable dark-energy (DE) model for a wide range of scalar field initial conditions and values for its positive γ coupling to the Ricci curvature γσ2R.