Gauss-Bonnet dark energy by Lagrange multipliers

Abstract

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 consider, the Lagrange multiplier behaves as a sort of dust fluid that realizes the transitions between matter dominated and dark energy epochs. The relation between Lagrange multipliers and Noether symmetries is discussed.

14 pages, expanded version to appear in PRD

References in corpus (56)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Extended Theories of Gravity
• Introduction to Modified Gravity and Gravitational Alternative for Dark Energy
• Discovery of a Supernova Explosion at Half the Age of the Universe and its Cosmological Implications
• Dark energy cosmology: the equivalent description via different theoretical models and cosmography tests
• Baryon Acoustic Oscillations in the Sloan Digital Sky Survey Data Release 7 Galaxy Sample
• Improved Cosmological Constraints from New, Old and Combined Supernova Datasets
• Curvature Quintessence
• Modified Gauss-Bonnet theory as gravitational alternative for dark energy
• Spectra and Light Curves of Six Type Ia Supernovae at 0.511 < z < 1.12 and the Union2 Compilation
• Improved Dark Energy Constraints from ~100 New CfA Supernova Type Ia Light Curves
• Dark energy in modified Gauss-Bonnet gravity: late-time acceleration and the hierarchy problem
• Gauss-Bonnet dark energy
• Singularity-free cosmological solutions of the superstring effective action
• Dark energy cosmology from higher-order, string-inspired gravity and its reconstruction
• The Little Rip
• Towards a non-singular pre-big bang cosmology
• Viscous Little Rip Cosmology
• Cosmology and Astrophysical Constraints of Gauss-Bonnet Dark Energy
• Dust of Dark Energy
• Gauss-Bonnet Quintessence: Background Evolution, Large Scale Structure and Cosmological Constraints
• The fate of (phantom) dark energy universe with string curvature corrections
• Hamiltonian dynamics and Noether symmetries in Extended Gravity Cosmology
• On the Construction of Nonsingular Pre-Big-Bang and Ekpyrotic Cosmologies and the Resulting Density Perturbations
• Dark energy and cosmological solutions in second-order string gravity
• A Model of Graceful Exit in String Cosmology
• f(R) cosmology by Noether's symmetry
• Singularity-free cosmological solutions in quadratic gravity
• Dark energy from modified F(R)-scalar-Gauss-Bonnet gravity
• String-Inspired Higher-Curvature Terms and the Randall-Sundrum Scenario
• Models for Little Rip Dark Energy
• Dark energy from modified gravity with Lagrange multipliers
• Using the Noether symmetry approach to probe the nature of dark energy
• Correspondence between Holographic and Gauss-Bonnet dark energy models
• Gauss-Bonnet cosmologies: crossing the phantom divide and the transition from matter dominance to dark energy
• Stability of the Einstein static universe in modified Gauss-Bonnet gravity
• The graceful exit in pre-big bang string cosmology
• Noether symmetries in Bianchi universes
• Accelerating Cosmologies in the Einstein-Gauss-Bonnet Theory with Dilaton
• Cyclic cosmology from Lagrange-multiplier modified gravity
• Nonsingular Dilaton Cosmology in the String Frame
• Exact Solutions and the Cosmological Constant Problem in Dilatonic-Domain-Wall Higher-Curvature String Gravity
• From Big to Little Rip in modified F(R,G) gravity
• Cosmological models with Lagrange Multiplier Field
• Dark energy generated from a (super)string effective action with higher order curvature corrections and a dynamical dilaton
• Confronting dark energy models mimicking $\Lambda$CDM epoch with observational constraints: future cosmological perturbations decay or future Rip?
• Big Rip and Little Rip solutions in scalar model with kinetic and Gauss Bonnet couplings
• Covariant power-counting renormalizable gravity: Lorentz symmetry breaking and accelerating early-time FRW universe
• Covariant Lagrange multiplier constrained higher derivative gravity with scalar projectors
• Scalar-tensor theory with Lagrange multipliers: a way of understanding the cosmological constant problem, and future singularities
• Branes with fluxes wrapped on spheres
• Observational constraints on a cosmological model with Lagrange multipliers
• Exact solutions in a scalar-tensor model of dark energy
• Conformal frames and the validity of Birkhoff's theorem

Cited by in corpus (34)

• Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution
• f(T) teleparallel gravity and cosmology
• Further matters in space-time geometry: $f(R,T,R_{\mu \nu }{T}^{\mu \nu })$ gravity
• Anisotropic Compact Stars in $f(G)$ Gravity
• Noether Symmetry Approach in Gauss-Bonnet Cosmology
• Modified Gauss-Bonnet gravity with Lagrange multiplier constraint as mimetic theory
• Noether Symmetries in Gauss-Bonnet-teleparallel cosmology
• Accelerating Cosmology and Phase Structure of F(R) Gravity with Lagrange Multiplier Constraint: Mimetic Approach
• The bounce universe history from unimodular $F(R)$ gravity
• Unimodular $F(R)$ Gravity
• Pilgrim Dark Energy in $f(T,T_G)$ cosmology
• Weyl-Cartan-Weitzenböck gravity through Lagrange multiplier
• $f(R)$-gravity from Killing Tensors
• Unimodular-Mimetic Cosmology
• Unimodular Mimetic $F(R)$ Inflation
• Reissner-Nordström Black Holes in Mimetic $F(R)$ Gravity
• Tolman-Oppenheimer-Volkoff Equations in Modified Gauss-Bonnet Gravity
• Noether Symmetry Approach for teleparallel-curvature cosmology
• A Note on Schwarzschild de Sitter Black Holes in Mimetic $F(R)$ Gravity
• Dark Energy from Gauss-Bonnet and non-minimal couplings
• Mimetic $F(R)$ inflation confronted with Planck and BICEP2/Keck Array data
• Kinetic Scalar Curvature Extended $f(R)$ Gravity
• Higher-Order Gauss-Bonnet Cosmology
• Stability of Hyperbolic and Matter-Dominated Bounce Cosmologies From F(R,G) Modified Gravity at Late Evolution Stages
• Non-minimal coupling influence on the deviation from de Sitter cosmological expansion
• Generalized second law of thermodynamics in QCD ghost f(G) gravity
• First order formalism for thick branes in modified gravity with Lagrange multiplier
• Late cosmic acceleration in a vector--Gauss-Bonnet gravity model
• Cosmological scenarios in modified gravity with non-dynamical fields
• Validating variational principle for higher order theory of gravity
• Constraints on a scalar-tensor model with Gauss-Bonnet coupling from SN Ia and BAO observations
• First-order formalism and thick branes in mimetic gravity
• Post-Newtonian N-Body Dynamics in Extended Theories of Gravity
• Stable exponential cosmological solutions with three factor spaces of dimensions $m=3$, $k_1=k$ and $k_2=k$ in the Einstein-Gauss-Bonnet model with a $\Lambda$-term