We show that scalar, 0-form, Galileon actions --models whose field equations contain only second derivatives-- can be generalized to arbitrary even p-forms. More generally, they need not even depend on a single form, but may involve mixed p combinations, including equal p multiplets, where odd p-fields are also permitted: We construct, for given dimension D, general actions depending on scalars, vectors and higher p-form field strengths, whose field equations are of exactly second derivative order. We also discuss and illustrate their curved-space generalizations, especially the delicate non-minimal couplings required to maintain this order. Concrete examples of pure and mixed actions, field equations and their curved space extensions are presented.
The maximally complicated arbitrary-dimensional "maximal" Galileon field equations simplify dramatically for symmetric configurations. Thus, spherical symmetry reduces the equations from the D- to the two-dimensional Monge-Ampere equation, axial symmetry to its cubic extension etc. We can then obtain explicit solutions, such as spherical or axial waves, and relate them to the (known) general, but highly implicit, lower-D solutions.
We demonstrate how, for an arbitrary number of dimensions, the Galileon actions and their covariant generalizations can be obtained through a standard Kaluza-Klein compactification of higher-dimensional Lovelock gravity. In this setup, the dilaton takes on the role of the Galileon. In addition, such compactifications uncover other more general Galilean actions, producing purely second-order equations in the weak-field limit, now both for the Galileon and the metric perturbations.
We present an exact plane wave solution of the most general shift-symmetric Horndeski (generalized Galileon) theory. The solution consists of the scalar part, and the gravitational part with two polarization modes. The former is due to the presence of the non-trivial Galileon scalar field, and it is parametrized by an arbitrary function of the light-cone coordinate. For a trivial scalar field configuration the solution is equivalent to the plane gravitational wave in General Relativity. When the metric is Minkowski, we reproduce known results for the plane waves of k-essence and a soliton-like…
The recent progress in the study of Galileons, i.e. equations of second order with an action invariant under a Galilean transformation is related to work on `Universal Field Equations' \cite{dbfgov} which are second order equations arising by an iterative procedure from arbitrary Lagrangians of weight one in their first derivatives. It is pointed out that the Galileon is simply a Kaluza-Klein reduction of a Universal Field Equation. An implicit solution to the equation of motion is presented, and a class of explicit solutions pointed out. The multi-field extensions of both types of equations a…
We provide a complete classification of all abelian gauge invariant $p$-form theories with equations of motion depending only on the second derivative of the field---the $p$-form analogues of the Galileon scalar field theory. We construct explicitly the nontrivial actions that exist for spacetime dimension $D\leq11$, but our methods are general enough and can be extended to arbitrary $D$. We uncover in particular a new $4$-form Galileon cubic theory in $D\geq8$ dimensions. As a by-product we give a simple proof of the fact that the equations of motion depend on the $p$-form gauge fields only t…
We consider a particular truncation of the generalized Proca field theory in four dimensions for which we construct a static and axisymmetric rotating black hole "stealth solutions", namely solutions with (Anti) de Sitter or Kerr metric but non-trivial vector field. The static configuration is promoted to a backreacting black hole with asymptotic (Anti) de Sitter behavior by turning on a nonlinear electrodynamic source given as a fixed power of the Maxwell invariant. Finally we extend our solutions to arbitrary dimensions.
It has been pointed out that non-singular cosmological solutions in second-order scalar-tensor theories generically suffer from gradient instabilities. We extend this no-go result to second-order gravitational theories with an arbitrary number of interacting scalar fields. Our proof follows directly from the action of generalized multi-Galileons, and thus is different from and complementary to that based on the effective field theory approach. Several new terms for generalized multi-Galileons on a flat background were proposed recently. We find a covariant completion of them and confirm that t…
We study scalar-tensor theories respecting the projective invariance in the metric-affine formalism. The metric-affine formalism is a formulation of gravitational theories such that the metric and the connection are independent variables in the first place. In this formalism, the Einstein-Hilbert action has an additional invariance, called the projective invariance, under a shift of the connection. Respecting this invariance for the construction of the scalar-tensor theories, we find that the Galileon terms in curved spacetime are uniquely specified at least up to quartic order which does not …
We introduce bi-galileon theory, the generalisation of the single galileon model introduced by Nicolis et al. The theory contains two coupled scalar fields and is described by a Lagrangian that is invariant under Galilean shifts in those fields. This paper is the first of two, and focuses on the motivation and formulation of the theory. We show that the boundary effective theory of the cascading cosmology model corresponds to a bi-galileon theory in the decoupling limit, and argue that this is to be expected for co-dimension 2 braneworld models exhibiting infra-red modification of gravity. We …
Explicit formulae of the equations in the generalized Galileon models are given. We also develop the formulation of the reconstruction. By using the formulation, we can explicitly construct an action which reproduces an arbitrary development of the expansion of the universe. The conditions how the reconstructed solution becomes stable and therefore it becomes an attractor solution are also given. Working in the static and spherically symmetric space-time, we investigate how the Vainshtein mechanism works in the generalized Galileon model and the correction to the Newton law becomes small. It i…
We analyze spherically symmetric black hole solutions with time-dependent scalar hair in a class of Lovelock-Galileon theories, which are the scalar-tensor theories with second-order field equations in arbitrary dimensions. We first show that known black hole solutions in five dimensions are always plagued by the ghost/gradient instability in the vicinity of the horizon. We then generalize such black hole solutions to higher dimensions and show that the same instability found in five dimensions appears universally in any number of dimensions.
Using the Wentzel-Kramers-Brillouin (WKB) approximation we study the formation and propagation of quantum bound states in the vicinity of a Galileon black hole. We show that for given ranges of black hole horizon radii and of the derivative coupling which appears in the metric of the Galileon black hole, a Regge-Wheeler potential containing a local well is formed. Varying the strength of the derivative coupling we investigate the behaviour of the bound states trapped in the potential well or penetrating the horizon of the Galileon black hole.
We investigate the renormalization structure of scalar Galileons in flat spacetime. We explicitly calculate the ultraviolet divergent one-loop contributions to the 2-point, 3-point, 4-point, and 5-point functions. We discuss the structure of the counterterms and their hierarchy within an effective field theory expansion. We comment on different resummation schemes, including a geometric resummation for which our results could be generalized to arbitrary n-point functions.
A ghost-free metric formulation of the recently proposed covariant Galileon model \cite{RPgal} which retains the internal shift symmetry has been constructed. This presents a new result because the covariant Galileon models introduced so far in the literature lacks the full Galileon symmetry. We demonstrate that the same general procedure is applicable to all the Galileon interaction terms and the resulting ghost-free Galileon action respecting internal shift symmetry cannot predict the late time acceleration of the universe. However, weakly breaking the shift symmetry in the covariant Galileo…
We show that it is possible to formulate string theory as a "Galileon string theory". The galileon field $χ$ enters in the definition of the integration measure in the action. Following the methods of the modified measure string theory, we find that the final equations are again those of Polyakov. Moreover, the string tension appears again as an additional dynamical degree of freedom. At the same time the theory satisfies all requirements of the galileon higher derivative theory at the action level while the equations of motion are still of the second order. A galileon symmetry is displayed ex…
We calculate the one-loop quantum corrections in the cubic Galileon theory, using cutoff regularization. We confirm the expected form of the one-loop effective action and that the couplings of the Galileon theory do not get renormalized. However, new terms, not included in the tree-level action, are induced by quantum corrections. We also consider the one-loop corrections in an effective brane theory, which belongs to the Horndeski or generalized Galileon class. We find that new terms are generated by quantum corrections, while the tree-level couplings are also renormalized. We conclude that t…
We determine the most general scalar field theories which have an action that depends on derivatives of order two or less, and have equations of motion that stay second order and lower on flat space-time. We show that those theories can all be obtained from linear combinations of Lagrangians made by multiplying a particular form of the Galileon Lagrangian by an arbitrary scalar function of the scalar field and its first derivatives. We also obtain curved space-time extensions of those theories which have second order field equations for both the metric and the scalar field. This provide the mo…
We review different constructions of Galileon theories in both flat and curved space, and for both single scalar field models as well as multi-field models. Our main emphasis is on the formal mathematical properties of these theories and their construction.
We have been studied the model of light Galileon with translational shift symmetry $ϕ\to ϕ+c$. The matter Lagrangian is presented in the form $\mathcal{L}_ϕ= -η(\partial ϕ)^2+βG^{μν}\partial_μϕ\partial_νϕ$. We have been addressed two issues: the first is that, we have been proven that, this type of Galileons belong to the modified matter-curvature models of gravity in type of $f(R,R^{μν}T_{μν}^m)$. Secondly, we have been investigated exact solution for spherically symmetric geometries in this model. We have been found an exact solution with singularity at $r=0$ in null coordinates. We have bee…
In this paper we investigate the decoupling limit of a particular class of multi-gravity theories, i.e. of theories of interacting spin-2 fields. We explicitly compute the interactions of helicity-0 modes in this limit, showing that they take on the form of multi-Galileons and dual forms. In the process we extend the recently discovered Galileon dualities, deriving a set of new multi-Galileon dualities. These are also intrinsically connected to healthy, but higher-derivative, multi-scalar field theories akin to `beyond Horndeski' models.
We discuss a formulation of Galileon actions in terms of matrix determinants in four dimensions. This approach allows one to straightforwardly determine derivative couplings between Galileons and scalar or vector degrees of freedom that lead to equations of motion with at most two space-time derivatives. We use this method to easily build generalizations of Galileon set-ups preserving conformal symmetry, finding explicit examples of couplings between Galileons and additional degrees of freedom that preserve the Galileon conformal invariance. We discuss various physical applications of our meth…
We derive the 1-loop effective action of the cubic Galileon coupled to quantum-gravitational fluctuations in a background and gauge-independent manner, employing the covariant framework of DeWitt and Vilkovisky. Although the bare action respects shift symmetry, the coupling to gravity induces an effective mass to the scalar, of the order of the cosmological constant, as a direct result of the non-flat field-space metric, the latter ensuring the field-reparametrization invariance of the formalism. Within a gauge-invariant regularization scheme, we discover novel, gravitationally induced non-Gal…
We consider Galileon models on curved spacetime, as well as the counterterms introduced to maintain the second-order nature of the field equations of these models when both the metric and the scalar are made dynamical. Working in a gauge invariant framework, we first show how all the third-order time derivatives appearing in the field equations -- both metric and scalar -- of a Galileon model or one defined by a given counterterm can be eliminated to leave field equations which contain at most second-order time derivatives of the metric and of the scalar. The same is shown to hold for arbitrar…
We examine AdS Galileon Lagrangians using the method of non-linear realization. By contractions 1) flat curvature limit and 2) non-relativistic brane algebra limit and 3) (1)+(2) limits we obtain DBI, Newton-Hoock and Galilean Galileons respectively. We make clear how these Lagrangians appear as invariant 4-forms and/or pseudo-invariant Wess-Zumino terms using Maurer-Cartan equations on the coset $G/SO(3,1)$. We show the equations of motion are written in terms of the MC forms only and explain why the inverse Higgs condition is obtained as the equation of motion for all cases. The supersymmetr…
We investigate a new class of scalar multi-galileon models, which is not included in the commonly admitted general formulation of generalized multi-galileons. The Lagrangians of this class of models, some of them having already been introduced in previous works, are specific to multi-galileon theories, and vanish in the single galileon case. We examine them in details, discussing in particular some hidden symmetry properties which can be made explicit by adding total derivatives to these Lagrangians. These properties allow us to describe the possible dynamics for these new Lagrangians in the c…
We consider the Lagrangian of a vector field with derivative self-interactions with a priori arbitrary coefficients. Starting with a flat space-time we show that for a special choice of the coefficients of the self-interactions the ghost-like pathologies disappear. For this we use the degeneracy condition of the Hessian. This constitutes the Galileon-type generalization of the Proca action with only three propagating physical degrees of freedom. The longitudinal mode of the vector field is associated to the usual Galileon interactions for a specific choice of the overall functions. In differen…
The cubic Galileon model containing the lowest non-trivial order action of the full Galileon action can produce the stable late-time cosmic acceleration. This model can have a significant role in the growth of structures. The signatures of the cubic Galileon model in the structure formation can be probed by the weak lensing statistics. Weak lensing convergence statistics is one of the strongest probes to the structure formation and hence it can probe the dark energy or modified theories of gravity models. In this work, we investigate the detectability of the cubic Galileon model from the $ Λ$C…
We establish a correspondence between general relativity with diffeomorphism invariance and scalar field theories with Galilean invariance: notions such as the Levi-Civita connection and the Riemann tensor have a Galilean counterpart. This suggests Galilean theories as the unique nontrivial alternative to gauge theories (including general relativity). Moreover, it is shown that the requirement of first-order Palatini formalism uniquely determines the Galileon models with second-order field equations, similar to the Lovelock gravity theories. Possible extensions are discussed.
Galileon models are a class of effective field theories that have recently received much attention. They arise in the decoupling limit of theories of massive gravity, and in some cases they have been treated in their own right as scalar field theories with a specific nonlinearly realized global symmetry (Galilean transformation). It is well known that in the presence of a source, these Galileon theories admit superluminal propagating solutions, implying that as quantum field theories they must admit a different notion of causality than standard local Lorentz invariant theories. We show that in…
Recently, an extension to the Parameterized Post-Newtonian (PPN) formalism has been proposed. This formalism, the Parameterized Post-Newtonian-Vainshteinian (PPNV) formalism, is well suited to theories which exhibit Vainshtein screening of scalar fields. In this paper we apply the PPNV formalism to the Quartic and Quintic Galileon theories for the first time. As simple generalizations of standard scalar-tensor field theories they are important guides for the generalization of parameterized approaches to the effects of gravity beyond General Relativity. In the Quartic case, we find new PPNV pot…
We study the cosmology of a generalized Galileon field $ϕ$ with five covariant Lagrangians in which $ϕ$ is replaced by general scalar functions $f_{i}(ϕ)$ (i=1,...,5). For these theories, the equations of motion remain at second-order in time derivatives. We restrict the functional forms of $f_{i}(ϕ)$ from the demand to obtain de Sitter solutions responsible for dark energy. There are two possible choices for power-law functions $f_{i}(ϕ)$, depending on whether the coupling $F(ϕ)$ with the Ricci scalar $R$ is independent of $ϕ$ or depends on $ϕ$. The former corresponds to the covariant Galileo…
We explore field theories of a single p-form with equations of motions of order strictly equal to two and gauge invariance. We give a general method for the classification of such theories which are extensions to the p-forms of the Galileon models for scalars. Our classification scheme allows to compute an upper bound on the number of different such theories depending on p and on the space-time dimension. We are also able to build a non trivial Galileon like theory for a 3-form with gauge invariance and an action which is polynomial into the derivatives of the form. This theory has gauge invar…
Recently a cubic Galileon cosmological model was derived by the assumption that the field equations are invariant under the action of point transformations. The cubic Galileon model admits a second conservation law which means that the field equations form an integrable system. The analysis of the critical points for this integrable model is the main subject of this work. To perform the analysis, we work on dimensionless variables different from that of the Hubble normalization. New critical points are derived while the gravitational effects which follow from the cubic term are studied.
The special galileon and Dirac-Born-Infeld (DBI) theories are effective field theories of a single scalar field that have many interesting properties in flat space. These theories can be extended to all maximally symmetric spaces, where their algebras of shift symmetries are simple. We study aspects of the curved space versions of these theories: for the special galileon, we find a new compact expression for its Lagrangian in de Sitter space and a field redefinition that relates it to the previous, more complicated formulation. This field redefinition reduces to the well-studied galileon duali…
In the Horndeski's most general scalar-tensor theories with second-order field equations, we derive the conditions for the avoidance of ghosts and Laplacian instabilities associated with scalar, tensor, and vector perturbations in the presence of two perfect fluids on the flat Friedmann-Lemaitre-Robertson-Walker (FLRW) background. Our general results are useful for the construction of theoretically consistent models of dark energy. We apply our formulas to extended Galileon models in which a tracker solution with an equation of state smaller than -1 is present. We clarify the allowed parameter…
We propose a new class of inflation model, G-inflation, which has a Galileon-like nonlinear derivative interaction of the form $G(ϕ, (\nablaϕ)^2)\Boxϕ$ in the Lagrangian with the resultant equations of motion being of second order. It is shown that (almost) scale-invariant curvature fluctuations can be generated even in the exactly de Sitter background and that the tensor-to-scalar ratio can take a significantly larger value than in the standard inflation models, violating the standard consistency relation. Furthermore, violation of the null energy condition can occur without any instabilities…
Very few explicit inflationary scenarios are known to generate a large bispectrum of orthogonal shape. Dirac-Born-Infeld Galileon inflation, in which an induced gravity term is added to the DBI action, is one such model. We formulate it in the language of the effective field theory of inflation by identifying the unitary gauge operators that govern the behavior of its cosmological fluctuations. We show how to recover rather easily from this its power spectrum and bispectrum, which we calculated previously using standard cosmological perturbation theory. We push our calculations up to the deter…
We systematically construct derivative self-interactions for massless and massive 2-forms. There exists a no-go theorem in the literature for constructing Galileon-like Lagrangians in four dimensions for the 2-form with gauge invariance, the Kalb-Rammond field. The presence of non-minimal couplings strongly relies on the contraction with divergenceless tensors. In four dimensions these are the Einstein tensor and the double dual Riemann tensor. Even though they are divergenceless on their own, their combination ceases to be. In the case of massless 2-forms we are not able to establish non-mini…
We study certain bi-scalar-tensor theories emanating from conformal symmetry requirements of Horndeski's four-dimensional action. The former scalar is a Galileon with shift symmetry whereas the latter scalar is adjusted to have a higher order conformal coupling. Employing technics from local Weyl geometry certain Galileon higher order terms are thus constructed to be conformally invariant. The combined shift and partial conformal symmetry of the action, allow us to construct exact black hole solutions. The black holes initially found are of planar horizon geometry embedded in anti de Sitter sp…
We discuss cosmology based on a Cuscuta-Galileon gravity theory, which preserves just two degrees of freedom. Although there exists no additional degrees of freedom, introduction of a potential of a scalar field changes the dynamics. The scalar field is completely determined by matter fields. Giving an exponential potential as an example, we discuss the cosmological dynamics. The gravitational "constant" $G_{\rm F}$ appeared in the effective Friedmann equation becomes time dependent. We also present how to construct a potential when we know the evolution of the Hubble parameter. When we assume…
We study a nonsingular bounce inflation model, which can drive the early universe from a contracting phase, bounce into an ordinary inflationary phase, followed by the reheating process. Besides the bounce that avoided the Big-Bang singularity which appears in the standard cosmological scenario, we make use of the Horndesky theory and design the kinetic and potential forms of the lagrangian, so that neither of the two big problems in bouncing cosmology, namely the ghost and the anisotropy problems, will appear. The cosmological perturbations can be generated either in the contracting phase or …
We propose a multi-field extension of (generalized) G-inflation, based on covariant multi-galileons and their generalization preserving second-order field equations. We compute the quadratic action for cosmological perturbations. By comparing the formulas for cosmological perturbations, it is highlighted that multi-field DBI galileon inflation is not included in the multi-field version of generalized G-inflation. Our result indicates that the generalized covariant multi-galileon theory is not the most general multi-scalar-tensor theory with second-order field equations.
We consider a disformal coupling between Standard Model matter and a cubic Galileon scalar sector, assumed to be a relict of some other physics that solves the cosmological constant problem rather than a solution in its own right. This allows the energy density carried by the Galileon scalar to be sufficiently small that it evades stringent constraints from the integrated Sachs-Wolfe effect, which otherwise rules out the cubic Galileon theory. Although the model with disformal coupling does not exhibit screening, we show there is a `screening-like' phenomenon in which the energy density carrie…
Cosmological inflation provides the initial conditions for the structure formation. However, the origin of large-scale magnetic fields cannot be addressed in this framework. The key issue for this long-standing problem is the conformal invariance of the electromagnetic (EM) field in 4-D. While many approaches have been proposed in the literature for breaking conformal invariance of the EM action, here, we provide a completely new way of looking at the modifications to the EM action and generation of primordial magnetic fields during inflation. We explicitly construct a higher derivative EM act…
We show that starting from initial conditions with stable perturbations, evolution of a galileon scalar field results in the appearance of a ghost later on. To demonstrate this, we consider a theory with k-essence and cubic galileon Lagrangians on a fixed Minkowski background. Explicit analytical solutions of simple waves are constructed, on top of which a healthy scalar degree of freedom is shown to be converted onto a ghost. Such a transformation is smooth and moreover perturbations remain hyperbolic all the time (until a caustic forms). We discuss a relation between the ghost and the appear…
We consider the prospect of detecting cubic Galileons through their imprint on gravitational wave signals from a triple system. Namely, we consider a massive Black Hole (BH) surrounded by a binary system of two smaller BHs. We assume that the three BHs acquire a conformal coupling to the scalar field whose origin could be due to cosmology or to the galactic environment. In this case, the massive BH has a Vainshtein radius which englobes the smaller ones and suppresses the scalar effects on the motion of the binary system. On the other hand the two binaries can be outside each other's redressed…
Higgs G-inflation is a Higgs inflation model with a generalized Galileon term added to the standard model Higgs field, which realizes inflation compatible with observations. Recently, it was claimed that the generalized Galileon term induces instabilities during the oscillation phase, and that the simplest Higgs G-inflation model inevitably suffers from this problem. In this paper, we extend the original Higgs G-inflation Lagrangian to a more general form, namely introducing a higher-order kinetic term and generalizing the form of the Galileon term, so that the Higgs field can oscillate after …
We investigate non-singular bounce realizations in the framework of ghost-free generalized Galileon cosmology, which furthermore can be free of the anisotropy problem. Considering an Ekpyrotic-like potential we can obtain a total Equation-of-State (EoS) larger than one in the contracting phase, which is necessary for the evolution to be stable against small anisotropic fluctuations. Since such a large EoS forbids the Galileon field to generate the desired form of perturbations, we additionally introduce the curvaton field which can in general produce the observed nearly scale-invariant spectru…
In this work we revisit the topological mass generation of 2-forms and establish a connection to the unique derivative coupling arising in the quartic Lagrangian of the systematic construction of massive $2-$form interactions, relating in this way BF theories to Galileon-like theories of 2-forms. In terms of a massless $1-$form $A$ and a massless $2-$form $B$, the topological term manifests itself as the interaction $B\wedge F$, where $F = {\rm d} A$ is the field strength of the $1-$form. Such an interaction leads to a mechanism of generation of mass, usually referred to as "topological genera…
We study universal electromagnetic (test) fields, i.e., p-forms fields F that solve simultaneously (virtually) any generalized electrodynamics (containing arbitrary powers and derivatives of F in the field equations) in n spacetime dimensions. One of the main results is a sufficient condition: any null F that solves Maxwell's equations in a Kundt spacetime of aligned Weyl and traceless-Ricci type III is universal (in particular thus providing examples of p-form Galileons on curved Kundt backgrounds). In addition, a few examples in Kundt spacetimes of Weyl type II are presented. Some necessary …
For very general scalar-field theories in which the equations of motion are at second-order, we evaluate the three-point correlation function of primordial scalar perturbations generated during inflation. We show that the shape of non-Gaussianities is well approximated by the equilateral type. The equilateral non-linear parameter f_NL^equil is derived on the quasi de Sitter background where the slow-variation parameters are much smaller than unity. We apply our formula for f_NL^equil to a number of single-field models of inflation--such as k-inflation, k-inflation with Galileon terms, potentia…
We compute the three-point correlation function of primordial scalar density perturbations in a general single-field inflationary scenario, where a scalar field phi has a direct coupling with the Ricci scalar R and the Gauss-Bonnet term GB. Our analysis also covers the models in which the Lagrangian includes a function non-linear in the field kinetic energy X=-(nabla phi)^2/2, and a Galileon-type field self-interaction G(phi, X)*(Box phi), where G is a function of phi and X. We provide a general analytic formula for the equilateral non-Gaussianity parameter f_{NL}^{equil} associated with the b…
We investigate cosmological perturbations of scalar-tensor theories in Palatini formalism. First we introduce an action where the Ricci scalar is conformally coupled to a function of a scalar field and its kinetic term and there is also a k-essence term consisting of the scalar and its kinetic term. This action has three frames that are equivalent to one another: the original Jordan frame, the Einstein frame where the metric is redefined, and the Riemann frame where the connection is redefined. For the first time in the literature, we calculate the quadratic action and the sound speed of scala…
We consider a new form of theories of gravity in which the action is written in terms of the Ricci scalar and its first and second derivatives. Despite the higher derivative nature of the action, the theory is free from ghost under an appropriate choice of the functional form of the Lagrangian. This model possesses $2+2$ physical degrees of freedom, namely $2$ scalar degrees and $2$ tensor degrees. We exhaust all such theories with the Lagrangian of the form $f(R, (\nabla R)^2, \Box R)$, where $R$ is the Ricci scalar, and then show some examples beyond this ansatz. In course of analysis, we pr…
EFT-Ramses: a code to simulate the effective field theory of dark energy
Durham University（杜伦大学）；National Astronomical Observatories, Chinese Academy of Sciences（中国科学院国家天文台）；University of Chinese Academy of Sciences（中国科学院大学）
We study the dynamics of inflation in a generalized scalar-torsion gravity scenario by assuming a canonical scalar field non-minimally coupled to torsion with a Galileon-type self-interaction. After obtaining the field equations for a flat FRW background, we derive the second order action for both scalar and tensor perturbations to compute the power spectra of primordial fluctuations. As particular models, we studied at first, a power-law form of coupling function $F(x)=1+ξx^{2}/2$, with $x\equiv ϕ/M_{pl}$, and a monomial scalar field potential $V(x)=λx^{n}/n$ which is ruled out at $2σ$ level …
