Statefinder -- a new geometrical diagnostic of dark energy

Abstract

We introduce a new cosmological diagnostic pair $\{r,s\}$ called Statefinder. The Statefinder is dimensionless and, like the Hubble and deceleration parameters $H(z)$ and $q(z)$, is constructed from the scale factor of the Universe and its derivatives only. The parameter $r(z)$ forms the next step in the hierarchy of geometrical cosmological parameters used to study the Universe after $H$ and $q$, while the parameter $s(z)$ is a linear combination of $q$ and $r$ chosen in such a way that it does not depend upon the dark energy density ${\Omega }_X(z)$. The Statefinder pair $\{r,s\}$ is algebraically related to the the dark energy pressure-to-energy ratio $w=p/\epsilon$ and its time derivative, and sheds light on the nature of dark energy/quintessence. Its properties allow to usefully differentiate between different forms of dark energy with constant and variable $w$, including a cosmological constant ($w=-1$). The Statefinder pair can be determined to very good accuracy from a SNAP type experiment.

7 pages, 3 figures. Final version to be published in JETP Lett., presentation shortened, references added and updated, consideration of brane cosmological models included, conclusions unchanged

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• Statefinder Parameter for Varying G in Three Fluid System
• Investigating the physical and geometrical parameters of the cosmological models with anisotropic background
• A Dark Energy Model with Generalized Uncertainty Principle in the Emergent, Intermediate and Logamediate Scenarios of the Universe
• Constraints on interacting dynamical dark energy and a new test for $\Lambda$CDM
• Natural scaling for dark energy
• Comparing teh holographic principle inspired dark energy models
• Curvature dominance DE-model in $f(R)$-gravity
• Holographic dark energy in Barrow cosmology with Granda-Oliveros IR cutoff
• Accelerating model of flat universe in $f(R,T)$ gravity
• Probing the cosmic acceleration history and the properties of dark energy from the ESSENCE supernova data with a model independent method
• A Modified Generalized Chaplygin Gas as the Unified Dark Matter-Dark Energy Revisited
• FRW type of cosmology with a Chaplygin gas
• $f(Q,T)$ gravity: From early to late-time cosmic acceleration
• Bulk viscous matter in $f(T)$ gravity: A path to cosmic acceleration
• Revisiting cosmic acceleration with DESI BAO
• Cosmographic analysis of sign-switching dark energy
• Statefinder Diagnostic for Phantom Model with $V(\varphi )=V_0\exp (-\lambda {\varphi }^2)$
• Bianchi type-V Transitioning model in Brans-Dicke theory with Observational Constraint
• Renyi Holographic Dark Energy models in Teleparallel gravity
• Cosmological Tests of Gravity: A Future Perspective
• Dynamical features of $f(T,B)$ cosmology
• Cosmological models of generalized ghost pilgrim dark energy (GGPDE) in the gravitation theory of Saez-Ballester
• Observationally constrained accelerating cosmological model with higher power of non-metricity and squared trace
• Length-preserving biconnection gravity and its cosmological implications
• Non-minimally coupled quintessence DE model with a cubic galileon term --A Dynamical System Analysis
• Cosmological Constraint and Analysis on Holographic Dark Energy Model Characterized by the Conformal-age-like Length
• Multiple $\Lambda$CDM cosmology with string landscape features and future singularities
• On the holographic dark energy in chameleon scalar-tensor cosmology
• Signature flips in time-varying $\Lambda (t)$ cosmological models with observational data
• Viscous extended holographic Ricci dark energy in the framework of standard Eckart theory
• Late-time acceleration with steep exponential potentials
• Viscous fluid cosmology in symmetric teleparallel gravity
• Modified holographic Ricci dark energy coupled to interacting relativistic and non-relativistic dark matter in the nonflat universe
• Bulk viscous fluid in symmetric teleparallel cosmology: theory versus experiment
• An Inhomogeneous Model Universe Behaving Homogeneously
• Addressing the High-$f$ Problem in Pseudo-Nambu-Goldstone Boson Dark Energy Models with Dark Matter - Dark Energy Interaction
• On the uniqueness of $\Lambda$CDM-like evolution for homogeneous and isotropic cosmology in General Relativity
• Testing dark energy models with $H(z)$ data
• Reconstructing $f(T)$ modified gravity from ECHDE and ECNADE models
• Interacting Generalised Cosmic Chaplygin gas in Loop quantum cosmology: A singularity free universe
• Emergence of space and expansion of universe
• Bouncing cosmological models in a functional form of F(R) gravity
• Magnetized cosmological model with variable deceleration parameter
• Reconstructions of $f(\mathcal{P})$ and $f(\mathcal{Q})$ gravity models from $(m,n)$-type Barrow Holographic Dark Energy: Analysis and Observational Constraints
• Scale-Free model for governing universe dynamics
• Israel-Stewart approach to viscous dissipative extended holographic Ricci dark energy dominated universe
• II. Non-Linear Interacting Dark Energy: Analytical Solutions and Theoretical Pathologies
• Observational constraints and stability in viscous $f(T,\mathcal{T})$ gravity
• Constraining Modified Chaplygin gas parameters
• Some models of holographic dark energy on the Randall-Sundrum brane and observational data
• Study of Some Parameters of Modified Chaplygin Gas in Galileon Gravity Theory from Observational Perspective
• Constraining Exponential f(Q) Gravity with Cosmic Chronometers and Supernovae: A Data-Driven Analysis
• Scalar Field as Dark Energy Accelerating Expansion of the Universe
• Improved parametrization of the growth index for dark energy and DGP models
• A four-dimensional ΛCDM-type cosmological model induced from higher dimensions using a kinematical constraint
• Dark Energy and Cosmological Horizon Thermal Effects
• Dark energy in thermal equilibrium with the cosmological horizon?
• Aspects of Some New Versions of Pilgrim Dark Energy in DGP Braneworld
• Barrow Holographic Dark Energy in Brane World Cosmology
• Stability analysis of agegraphic dark energy in Brans-Dicke cosmology
• Generalized Ricci dark energy in Horava-Lifshitz gravity
• Constraining Cosmological Parameters with Viscous Modified Chaplygin Gas and Generalized Cosmic Chaplygin Gas Models in Horava-Lifshitz Gravity: Utilizing Late-time Datasets
• A matter-dominated cosmological model with variable $G$ and $\Lambda$. Confrontation of theoretical predictions with observational data
• Generalized particle dynamics: modifying the motion of particles and branes
• Analysis of the cosmological evolution parameters, energy conditions, and linear matter perturbations of an exponential-type model in $f(Q)$ gravity
• Cosmology of the interacting Tsallis holographic dark energy in $f(R,T)$ gravity framework
• I. Linear Interacting Dark Energy: Analytical Solutions and Theoretical Pathologies
• Normal DGP in varying speed of light cosmology
• Constraining the Lattice Fluid Dark Energy from SNe Ia, BAO and OHD
• Fate of an Accretion Disc around a Black Hole when both the Viscosity and Dark Energy is Effecting
• Constraining Parameters for the Accelerating Universe in $f(R,{\mathcal{L}}_m)$ Gravity
• Cosmological Analysis of Reconstructed $\mathcal{F}(T,T_{\mathcal{G}})$ Models
• Late-Time Anisotropy Sourced by a 2-Form Field Non-Minimally Coupled to Cold Dark Matter
• APPLIED COSMOGRAPHY: A Pedagogical Review
• Scalar field descriptions of two dark energy models
• Analysis cosmological tachyon and fermion model and observation data constraints
• Dynamics of Logamediate and Intermediate Scenarios in the Dark Energy Filled Universe
• Late-time dynamics of dark energy EoS in symmetric teleparallel gravity
• Parameterized Deceleration in $f(Q,C)$ Gravity: A Logarithmic Approach
• New holographic Chaplygin gas model of dark energy
• Generalized Ghost Dark Energy in DGP Model
• Addressing the $r_d$ Tension using Late-Time Observational Measurements in a Novel deceleration Parametrization
• Effects of particle creation rate in two-fluid interacting cosmologies
• Do current observations support transient acceleration of our universe?
• Cosmic Acceleration in an Extended Brans-Dicke-Higgs Theory
• Light Thoughts on Dark Energy
• Mathematical properties of cosmological models with accelerated expansion
• Statefinder analysis of the superfluid Chaplygin gas model
• Quintessence Cosmology with an Effective $\Lambda$-Term in Lyra Manifold
• Cosmological implications of non-minimally coupled f(Q) gravity
• How effective is new variable modified Chaplygin gas to play the role of dark energy- A dynamical system analysis in RS II Brane model
• Scalar field dark energy: Insights into cosmological evolution and black hole accretion
• What if gravity becomes really repulsive in the future?
• Taylor expansion of luminosity distance in Szekeres cosmological models: Effects of local structures evolution on cosmographic parameters
• Accelerating behavior from dynamical system analysis parameters
• Non-Linearly Interacting Ghost Dark Energy in Brans-Dicke Cosmology
• Stability analysis and observational constraints in scalar tensor theory
• Brane cosmology from observational surveys and its comparison with standard FRW cosmology
• Cosmic Acceleration in a Model of Fourth Order Gravity
• A Comparison of the LVDP and ΛCDM Cosmological Models
• Genetic algorithms and the analysis of SnIa data
• Holographic inflation and holographic dark energy from entropy of the anti-de Sitter black hole
• Effect of Dynamical Cosmological Constant in presence of Modified Chaplygin Gas for Accelerating Universe
• Varying Speed of Light, Modified Chaplygin Gas and Accelerating Universe
• Impact of dark energy on the equation of state in light of the latest cosmological data
• Statefinder Diagnostic for Dark Energy Models in Bianchi I Universe
• Statefinders and observational measurement of superenergy
• Constraining hybrid potential scalar field cosmological model in Lyra's geometry with recent observational data
• Probing Lambda-DGP Braneworld Model
• Variable $G$ Correction for Dark Energy Model in Higher Dimensional Cosmology
• Observational constraints using Bayesian statistics and Deep Learning in $f(Q)$ gravity
• Interacting Tsallis agegraphic dark energy in DGP Braneworld Cosmology
• Interacting and Non-interacting Reńyi Holographic Dark Energy Models in DGP Braneworld
• Interacting Viscous Dark Energy in Bianchi Type-III Universe
• Viscous interacting and stability on dark matter Bose-Einstein condensation with modified Chaplygin gas
• Observational constraints on a Yang-Mills condensate dark energy model
• Linear dark energy equation of state revealed by supernovae?
• Bouncing cosmological model with general relativistic hydrodynamics in extended gravity
• Diagnostic Approaches for Interacting generalized holographic Ricci Dark Energy Models
• An exact solution of the observable universe in Bianchi V space-time
• A unified cosmic evolution: Inflation to late time acceleration
• Cosmological Issues in $F(T)$ Gravity Theory
• Generalized Ghost Pilgrim Dark Energy Fractal Cosmology with Observational Constraint
• Exploring the Evolution of Nonlinear Electrodynamics in the Universe: A Dynamical Systems Approach
• Generalized particle dynamics in anti de Sitter spaces: A source for dark energy
• Reconstructions of Einstein-Aether Gravity from Barrow Agegraphic and New Barrow Agegraphic Dark Energy models: Examinations and Observational Limits
• Observational Study of Higher Dimensional Magnetic Universe in Non-linear Electrodynamics
• Cosmological model with Gong-Zong Parametrization in $f(R,L_m)$ gravity
• Adiabatic Particle Production with Decaying $\Lambda$ and Anisotropic Universe
• Raychaudhuri-based reconstruction of anisotropic Einstein-Maxwell equation in 1+3 covariant formalism of $f(R)$-gravity
• A comprehensive analysis of Barrow holographic Chaplygin gas model reconstruction and its cosmological consequences
• Late Time Phenomena in $f(T,\mathcal{T})$ Gravity Framework: Role of $H_0$ Priors
• G-corrected holographic dark energy model
• Instability of scalar perturbation in a phantomic cosmological scenario
• Logarithmic and Strong Coupling Models in Weyl-Type $f(Q,T)$ Gravity
• Cosmological constraints in symmetric teleparallel gravity with bulk viscosity
• Observational constraints in scalar tensor theory with tachyonic potential
• A unification of RDE model and XCDM model
• Higher Dimensional Cosmology with Some Dark Energy Models in Emergent, Logamediate and Intermediate Scenarios of the Universe
• Stochastic quintessence models: jerk and fine-structure variability constraints
• Dynamical Systems Analysis of $f(R,L_m)$ Gravity Model
• Study of Some Cosmological Parameters for Interacting New Holographic Dark Energy Model in f(T) Gravity
• Observational constraints in late time for an axially symmetric transitioning model with bulk viscous fluid
• f(R) in Holographic and Agegraphic Dark Energy Models and the Generalized Uncertainty Principle
• Loop Quantum Corrections to Statefinder Parameters of Dark Energy
• Observational constraints on models of the Universe with time variable Gravitational and Cosmological constants along MOG
• Quantum Yang-Mills Condensate Dark Energy Models
• Quintom Dark Energy: Future Attractor and Phantom Crossing in Light of DESI DR2 Observation
• Statefinder diagnosis of nearly flat and thawing non-minimal quintessence
• Multiple fluid theory of cosmic evolution and its thermodynamic analysis
• Interacting Models of Generalised Chaplygin Gas and Modified Chaplygin Gas with Barotropic Fluid
• Variable Modified Chaplygin Gas in Anisotropic Universe with Kaluza-Klein Metric
• Signatures of asymmetry: Gravitational wave memory and the parity violation
• Analysis of Pantheon+ supernova data suggests evidence of sign-changing pressure of the cosmological fluid
• The role of potential in the ghost-condensate dark energy model
• Reconstructing cosmic evolution with a density parametrization
• ${\mathbf{\Omega }}_1{\mathbf{\Omega }}_2$-$\mathbf{\Lambda }$CDM: A promising phenomenological extension of the standard model of cosmology
• Mimicking the $\Lambda$CDM Universe through inhomogeneous space-time
• Phenomenological aspects of dark energy dominated cosmologies
• Observational constraints and differential diagnosis for cosmic evolutionary models
• Numerical analysis of cosmological models for accelerating Universe in Poincare gauge theory of gravity
• Natures of Statefinder Parameters and Om Diagnostic for Cardassian Universe in Horava-Lifshitz Gravity
• Large-scale structure formation in cosmology with classical and tachyonic scalar fields
• A pressure parametric dark energy model
• Is it possible to separate baryonic from dark matter within the $\Lambda$-CDM formalism?
• Accelerating Universe with binary mixture of bulk viscous fluid and dark energy
• A semi-cosmographic approach to study cosmological evolution in phase space
• Cosmological Dynamics of Exponential Quintessence Constrained by BAO, Cosmic Chronometers, and DES-SN5YR/Pantheon+ Data
• Reconstruction of Tsallis Holographic Dark Energy via Modified Non-Metric Gravity: An $f(Q,C)$ Approach
• Statefinder Description in Generalized Holographic and Ricci Dark Energy Models
• Stability of Differentially Rotating Disks in $f(T)$ Theory
• Polytropic $f(Q)$ cosmology and its implications for the $H_0$ tension
• Agegraphic dark energy from entropy of the anti-de Sitter black hole
• On Nash theory of gravity with matter contents
• An Alternative Approach to the Exact Solution of FRW-Type Spacetime with a Generalized Chaplygin Gas
• Rényi Holographic Dark Energy Models In Multidimensional Universe
• Dark Energy Behavior from Static Equation of State in Non-Minimally Coupled Gravity with Scalar Deformation
• Expanding Universe: Thermodynamical Aspects From Different Models
• Holographic Ricci DE as running vacuum with nonlinear interactions
• Interacting tachyon with varying mass dark matter
• Quintessence dark energy model in non-linear $f(Q)$ theory with bulk-viscosity
• Stability Analysis of DGP Brane-world Model with Agegraphic Dark Energy
• Bianchi type-III THDE quintessence model with hybrid expansion law
• On Generalized Theories of Varying Fine Structure Constant
• Phase space analysis and cosmography of a two-fluid cosmological model
• Observational Constraints and Geometric Diagnostics of Barboza-Alcaniz and Logarithmic Dark Energy Parametrizations
• Study of Tachyonic Field and its statefinder diagnostics in Various Scenarios of The Anisotropic Universe
• Holographic dark energy in modified Kaniadakis cosmology
• Cosmological models with Big rip and Pseudo rip Scenarios in extended theory of gravity
• Observational Constraints and Cosmological Dynamics of Interacting Fractional Holographic Dark Energy in Light of DESI DR2
• Evolution of matter perturbations in the context of cosmic slowing down
• Exploring the Viability of $f(Q,T)$ Gravity: Constraining Parameters with Cosmological Observations
• Effective quantum gravity, cosmological constant and the Standard Model of particle physics
• Modified Power law Inflation: solution to the graceful exit problem and improvement of dark energy models
• A comparative study of emergent dark energy models
• Phase space analysis of Rényi Holographic dark energy model
• Evolution of entropic dark energy and its phantom nature