This work discuss the construction of braneworld solutions in modified gravity with Lagrange multipliers. We examine the general aspects of the model and present a first order formalism that help us to find analytic solutions of the equations of motion. We also investigate some explicit models, analyse linear stability of the metric and comment on how to relate models investigated in other works to the ones examined in the present study.
We develop Hamiltonian formalism for Lagrange Multiplier Modified Gravity. We further calculate the Poisson brackets between constraints and we show that they coincide with the algebra of constraints in Hamiltonian formulation of General Relativity.
We consider RFDiff invariant Horava-Lifshitz gravity action with additional Lagrange multiplier term that is a function of scalar curvature. We find its Hamiltonian formulation and we show that the constraint structure implies the same number of physical degrees of freedom as in General Relativity.
A scalar-tensor model with Gauss-Bonnet and non-minimal kinetic couplings is considered, in which ghost modes are eliminated via a Lagrange multiplier constraint. A reconstruction procedure is deviced for the scalar potential and Lagrange multiplier, valid for any given cosmological scenario. In particular, inflationary and dark energy cosmologies of different types (power-law, Little-Rip, de Sitter, quasi de Sitter) are reconstructed in such models. It is shown that, for various choices of the kinetic coupling terms, it is possible to obtain a viable inflationary phenomenology compatible with…
We investigate the Lagrange multiplier formulation of teleparallel theories, including f(T) gravity, in which the connection is not set to zero a priori and compare it with the pure frame theory. We show explicitly that the two formulations are equivalent, in the sense that the dynamical equations have the same content. One consequence is that the manifestly local Lorentz invariant f(T) theory cannot be expected to be free of pathologies, which were previously found to plague f(T) gravity formulated in the usual pure frame approach.
A string-inspired effective theory of gravity, containing Gauss-Bonnet invariant interacting with a scalar field, is considered in view of obtaining cosmological dark energy solutions. A Lagrange multiplier is inserted into the action in order to achieve the cosmological reconstruction by selecting suitable forms of couplings and potentials. Several cosmological exact solutions (including dark energy of quintessence, phantom or Little Rip type) are derived in presence and in absence of the Lagrange multiplier showing the difference in the two dynamical approaches. In the models that we conside…
We propose two new versions of ghost-free generalized $F(R)$ gravity with Lagrange multiplier constraint. The first version of such theory for a particular degenerate choice of the Lagrange multiplier, corresponds to mimetic $F(R)$ gravity. The second version of such theory is just the Jordan frame description of mimetic gravity with potential. As we demonstrate, it is possible to realize several cosmological scenarios in such theory. In particulary, de Sitter solutions may also be found.
We introduce conformal traceless decomposition in Lagrange Multiplier modified RFDiff invariant Horava-Lifshitz gravity. We perform Hamiltonian analysis of given action and determine the action for the physical degrees of freedom.
Lagrange multipliers are present in any gauge theory. They possess peculiar gauge transformation which is not generated by the constraints in the model as it is the case with the other variables. For rank one gauge theories we show how to alter the constraints so that they become generators of the local symmetry algebra in the space of Lagrange multipliers too. We also discuss the limitations on using different gauge conditions and construct the BRST charge corresponding to the newly found constraints.
We formulate higher derivative gravity with Lagrange multiplier constraint and scalar projectors. Its gauge-fixed formulation as well as vector fields formulation is developed and corresponding spontaneous Lorentz symmetry breaking is investigated. We show that the only propagating mode is higher derivative graviton while scalar and vector modes do not propagate. Despite to higher derivatives structure of the action, its first FRW equation is the first order differential equation which admits the inflationary universe solution.
We first consider the Einstein-aether theory with a gravitational coupling and a Lagrange multiplier field, and then consider the non-minimally coupled quintessence field theory with Lagrange multiplier field. We study the influence of the Lagrange multiplier field on these models. We show that the energy density evolution of the Einstein-aether field and the quintessence field are significantly modified. The energy density of the Einstein-aether is nearly a constant during the entire history of the Universe. The energy density of the quintessence field can also be kept nearly constant in the …
The use of Lagrange multipliers in the context of quintessence/phantom scalar fields allows to constrain the behavior of the scalar field, which provides a powerful tool, not only for the reconstruction of cosmological solutions but also for the study of some problems in cosmology and gravitational physics. In the present paper, we focus on the reconstruction of cosmological solutions capable of controlling the cosmological constant value by imposing a constraint on the scalar field, providing a relaxation mechanism of the value of the cosmological constant. The formalism is also extended to t…
In this paper, we employ the {\bf mimetic-like} field equations coupled with the Lagrange multiplier and %mimetic {\bf potential} to derive non-trivial spherically symmetric black hole (BH) solutions. We divided this study into three cases: The first one in which we take the Lagrange multiplier and %mimetic {\bf the potential} to have vanishing value and derive a BH solution that completely coincides with the BH of the Einstein general relativity despite the non-vanishing value of the {\bf mimetic-like scalar field}. The first case is completely consistent with the previous studies in the lite…
We study scalar-tensor theory, k-essence and modified gravity with Lagrange multiplier constraint which role is to reduce the number of degrees of freedom. Dark Energy cosmology of different types ($Λ$CDM, unified inflation with DE, smooth non-phantom/phantom transition epoch) is reconstructed in such models. It is shown that mathematical equivalence between scalar theory and $F(R)$ gravity is broken due to presence of constraint. The cosmological dynamics of $F(R)$ gravity is modified by the second $F_2(R)$ function dictated by the constraint. Dark Energy cosmology is defined by this function…
We review on the models of gravity with a constraint by the Lagrange multiplier field. The constraint breaks general covariance or Lorentz symmetry in the ultraviolet region. We report on the $F(R)$ gravity model with the constraint and the proposal of the covariant (power-counting) renormalized gravity model by using the constraint and scalar projectors. We will show that the model admits flat space solution, its gauge-fixing formulation is fully developed, and the only propagating mode is (higher derivative) graviton, while scalar and vector modes do not propagate. The preliminary study of F…
In hep-th/0312098 it was argued that by extending the ``$a$-maximization'' of hep-th/0304128 away from fixed points of the renormalization group, one can compute the anomalous dimensions of chiral superfields along the flow, and obtain a better understanding of the irreversibility of RG flow in four dimensional supersymmetric field theory. According to this proposal, the role of the running couplings is played by certain Lagrange multipliers that are introduced in the construction. We show that one can choose a parametrization of the space of couplings in which the Lagrange multipliers can ind…
In this paper, we will use $δ\mathcal{N}$-formalism to calculate the primordial curvature perturbation for the curvaton model with a Lagrange multiplier field. We calculate the non-linearity parameters $f_{NL}$ and $g_{NL}$ in the sudden-decay approximation in this kind of model, and we find that one could get a large non-Gaussinity even if the curvaton dominates the total energy density before it decays, and this property will make the curvaton model much richer. We also calculate the probability density function of the primordial curvature perturbation in the sudden-decay approximation, as w…
We consider an extension of the Weyl-Cartan-Weitzenböck (WCW) and teleparallel gravity, in which the Weitzenböck condition of the exact cancellation of curvature and torsion in a Weyl-Cartan geometry is inserted into the gravitational action via a Lagrange multiplier. In the standard metric formulation of the WCW model, the flatness of the space-time is removed by imposing the Weitzenböck condition in the Weyl-Cartan geometry, where the dynamical variables are the space-time metric, the Weyl vector and the torsion tensor, respectively. However, once the Weitzenböck condition is imposed on the …
In this paper we propose and extensively study mimetic $f({\cal G})$ modified gravity models, with various scenarios of cosmological evolution, with or without extra matter fluids. The easiest formulation is based on the use of Lagrange multiplier constraint. In certain versions of this theory, it is possible to realize accelerated expansion of the Universe or even unified evolution which includes inflation with dark energy, and at the same time in the same theoretical framework, dark matter is described by the theory. This is achieved by the re-parametrization of the metric tensor, which intr…
We investigate cyclic and singularity-free evolutions in a universe governed by Lagrange-multiplier modified gravity, either in scalar-field cosmology, as well as in $f(R)$ one. In the scalar case, cyclicity can be induced by a suitably reconstructed simple potential, and the matter content of the universe can be successfully incorporated. In the case of $f(R)$-gravity, cyclicity can be induced by a suitable reconstructed second function $f_2(R)$ of a very simple form, however the matter evolution cannot be analytically handled. Furthermore, we study the evolution of cosmological perturbations…
Renormalization of Quantum Gravity with Lagrange Multiplier Fields
Instituto de Física, Universidade de São Paulo（圣保罗大学物理研究所）；Instituto de Física Teórica, Universidade Estadual Paulista（圣保罗州立大学理论物理研究所）；Department of Applied Mathematics, The University of Western Ontario（韦仕敦大学应用数学系）；Department of Mathematics and Computer Science, Algoma University（阿尔戈马大学数学与计算机科学系）
The problem of eliminating divergences arising in quantum gravity is generally addressed by modifying the classical Einstein-Hilbert action. These modifications might involve the introduction of local supersymmetry, the addition of terms that are higher-order in the curvature to the action, or invoking compactification of superstring theory from ten to four dimensions. An alternative to these approaches is to introduce a Lagrange multiplier field that restricts the path integral to field configurations that satisfy the classical equations of motion; this has the effect of doubling the usual on…
Supergravity with Lagrange Multiplier Fields in 2 + 1 Dimensions
The University of Western Ontario（西安大略大学）；Algoma University（阿尔戈马大学）；Universidade de São Paulo（圣保罗大学）；Universidade Estadual Paulista (UNESP)（圣保罗州立大学（UNESP））
The so-called unimodular version of General Relativity is revisited. Unimodular gravity is constructed by fixing the determinant of the metric, what leads to the trace-free part of the equations instead of the usual Einstein field equations. Then, a cosmological constant naturally arises as an integration constant. While unimodular gravity turns out equivalent to General Relativity (GR) at the classical level, it provides important differences at the quantum level. Here we extend the unimodular constraint to some extensions of General Relativity that have drawn a lot of attention over the last…
We show that very general scalar-tensor theories of gravity (including, e.g., Horndeski models) are generically invariant under disformal transformations. However there is a special subset, when the transformation is not invertible, that yields new equations of motion which are a generalization of the so-called "mimetic" dark matter theory recently introduced by Chamsedinne and Mukhanov. These conclusions hold true irrespective of whether the scalar field in the action of the assumed scalar-tensor theory of gravity is the same or different than the scalar field involved in the transformation. …
We study mimetic $F(R)$ gravity with potential and Lagrange multiplier constraint. In the context of these theories, we introduce a reconstruction technique which enables us to realize arbitrary cosmologies, given the Hubble rate and an arbitrarily chosen $F(R)$ gravity. We exemplify our method by realizing cosmologies that are in concordance with current observations (Planck data) and also well known bouncing cosmologies. The attribute of our method is that the $F(R)$ gravity can be arbitrarily chosen, so we can have the appealing features of the mimetic approach combined with the known featu…
In this work we study non-singular{ bounce cosmology} in the context of the Lagrange multiplier generalized $F(R)$ gravity theory of gravity. We specify our study by using a specific variant form of the well known matter{ bounce cosmology}, with scale factor $a(t) = \left(a_0t^2 + 1 \right)^n$, and we demonstrate that for $n < 1/2$, the primordial curvature perturbations are generated deeply in the contraction era. Particularly, we show explicitly that the perturbation modes exit the horizon at a large negative time during the contraction era, which in turn makes the ``low-curvature'' regime, …
We study the effect of the topology of universe by gauging the non-relativistic particle model on the torus and 3-torus, using the symplectic formalism of constrained systems and embedding those models on extended phase-spaces. Also, we obtain the generators of the gauge transformations for gauged models. Extracting the corresponding Poisson structure of the existed constraints, we show the effect of the topology on the canonical structure of the phase-spaces of those models and suggest some phenomenology to prove the topology of the universe and probable non-commutative structure of the space…
