Geometric formulation of $k$-essence and late-time acceleration

Abstract

We study a class of geometries in which nonmetricity is fully determined by a vectorial degree of freedom and three independent coefficients. Formulating the simplest linear action in this geometry, implemented through Lagrange multipliers, naturally leads to an equivalence with the purely kinetic $k$-essence models with quadratic kinetic terms. A detailed dynamical systems analysis reveals that the $\Lambda$CDM phenomenology is embedded within the model. Crucially, we find that if stability conditions such as a positive sound speed squared and energy density are not enforced, the model generically exhibits instabilities and divergent behaviour in the phase space. These physical viability criteria allow us to isolate stable regions of the parameter space and derive well-motivated priors for parameter inference. Using Markov Chain Monte Carlo methods and late-time observational data, including cosmic chronometers, Pantheon${}^{+}$ Type Ia supernovae, and DESI baryon acoustic oscillations, we constrain the degrees of freedom associated with nonmetricity and demonstrate the viability of the model. We discuss the implications of these results in light of the recent cosmic tensions, and give a possible explanation as to why the equivalent $k$-essence models have been missed as serious competitors to $\Lambda$CDM in the past. Finally, we review the geometric foundations of the theory and show that the integrable Weyl, Schrödinger and completely symmetric geometries are embedded within our framework as special cases.

43 pages, 8 figures, 3 tables. v2 with revisions to code & updated results

References in corpus (124)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• emcee: The MCMC Hammer
• Dynamics of dark energy
• The Cosmological Constant and Dark Energy
• Detection of the Baryon Acoustic Peak in the Large-Scale Correlation Function of SDSS Luminous Red Galaxies
• f(R) Theories Of Gravity
• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Modified Gravity and Cosmology
• f(R) theories
• Cosmological Imprint of an Energy Component with General Equation of State
• Cosmological parameters from CMB and other data: a Monte-Carlo approach
• Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution
• Exploring the Expansion History of the Universe
• Dark energy cosmology: the equivalent description via different theoretical models and cosmography tests
• A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km/s/Mpc Uncertainty from the Hubble Space Telescope and the SH0ES Team
• A Dynamical Solution to the Problem of a Small Cosmological Constant and Late-time Cosmic Acceleration
• k-Inflation
• Essentials of k-essence
• Metric-Affine Gauge Theory of Gravity: Field Equations, Noether Identities, World Spinors, and Breaking of Dilation Invariance
• f(T) teleparallel gravity and cosmology
• Exponential potentials and cosmological scaling solutions
• Kinetically Driven Quintessence
• The Pantheon+ Analysis: Cosmological Constraints
• Dark torsion as the cosmic speed-up
• Beyond the Cosmological Standard Model
• Tensions between the Early and the Late Universe
• A 6% measurement of the Hubble parameter at $z\sim 0.45$: direct evidence of the epoch of cosmic re-acceleration
• Einstein's Other Gravity and the Acceleration of the Universe
• Perturbations in k-inflation
• DESI 2024 VI: Cosmological Constraints from the Measurements of Baryon Acoustic Oscillations
• Causality, Analyticity and an IR Obstruction to UV Completion
• Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z$\sim$2
• Information criteria for astrophysical model selection
• Improved constraints on the expansion rate of the Universe up to z~1.1 from the spectroscopic evolution of cosmic chronometers
• Constraining Cosmological Parameters Based on Relative Galaxy Ages
• Coincident General Relativity
• Supernova Constraints and Systematic Uncertainties from the First 3 Years of the Supernova Legacy Survey
• Ghost Condensation and a Consistent Infrared Modification of Gravity
• Physical Aspects of the Space-Time Torsion
• Can dark energy evolve to the Phantom?
• Purely kinetic k-essence as unified dark matter
• Cosmology in $f(Q)$ geometry
• Cosmology Intertwined II: The Hubble Constant Tension
• DESI DR2 Results II: Measurements of Baryon Acoustic Oscillations and Cosmological Constraints
• Teleparallel Gravity: From Theory to Cosmology
• Dynamical systems applied to cosmology: dark energy and modified gravity
• k-Essence, superluminal propagation, causality and emergent geometry
• f(R) Gravity and scalar-tensor theory
• Seven hints that early-time new physics alone is not sufficient to solve the Hubble tension
• Covariant conservation of energy momentum in modified gravities
• Extended tachyon field, Chaplygin gas and solvable k-essence cosmologies
• Metric-affine f(R) theories of gravity
• The CosmoVerse White Paper: Addressing observational tensions in cosmology with systematics and fundamental physics
• Metric-affine approach to teleparallel gravity
• Eppur è piatto? The cosmic chronometer take on spatial curvature and cosmic concordance
• Why reducing the cosmic sound horizon alone can not fully resolve the Hubble tension
• Cosmological constraints on f(R) gravity theories within the Palatini approach
• A model independent approach to the dark energy equation of state
• Kinetic k-essence and Quintessence
• Palatini formulation of $f(R,T)$ gravity theory, and its cosmological implications
• No-go theorem for k-essence dark energy
• Reheating in $R^2$ Palatini inflationary models
• Unified Dark Matter in Scalar Field Cosmologies
• DESI DR2 Results I: Baryon Acoustic Oscillations from the Lyman Alpha Forest
• Spacetimes with vector distortion: Inflation from generalised Weyl geometry
• Quintom cosmology and modified gravity after DESI 2024
• Status of non-Riemannian cosmology
• Cosmological Hyperfluids, Torsion and Non-metricity
• Unified Dark Matter Scalar Field Models
• Early-Universe-Physics Insensitive and Uncalibrated Cosmic Standards: Constraints on ${\Omega }_{\mathrm{m}}$ and Implications for the Hubble Tension
• Modified gravity: a unified approach
• The reliability of the AIC method in Cosmological Model Selection
• AIC and BIC for cosmological interacting scenarios
• Cosmology for quadratic gravity in generalized Weyl geometry
• To conserve, or not to conserve: A review of nonconservative theories of gravity
• Quintessence and phantoms in light of DESI 2025
• Weyl geometry
• Comparison between different methods of model selection in cosmology
• No evidence of kinetic screening in simulations of merging binary neutron stars beyond general relativity
• Test Matter in a Spacetime with Nonmetricity
• Kinetic screening in nonlinear stellar oscillations and gravitational collapse
• Unitary null energy condition violation in $P(X)$ cosmologies
• Unified Dark Energy and Dust Dark Matter Dual to Quadratic Purely Kinetic K-Essence
• Scaling solutions and weak gravity in dark energy with energy and momentum couplings
• Early dark energy in $k$-essence
• Exactly Solvable Connections in Metric-Affine Gravity
• Observational Constraints in Metric-Affine Gravity
• Recovering P(X) from a canonical complex field
• Modified gravity: a unified approach to metric-affine models
• The Perfect Hyperfluid of Metric-Affine Gravity: The Foundation
• Full Investigation on the Dynamics of Power-Law Kinetic Quintessence
• A new goodness-of-fit statistic and its application to 21-cm cosmology
• The Full Quadratic Metric-Affine Gravity (Including Parity Odd Terms): Exact solutions for the Affine-Connection
• Cosmological dynamical systems in modified gravity
• Dynamical Systems Analysis of K-essence Model
• Cosmological models in Weyl geometrical scalar-tensor theory
• Probing Modified Gravity with Integrated Sachs-Wolfe CMB and Galaxy Cross-correlations
• Parametrization of K-essence and Its Kinetic Term
• Cosmological Perturbation Theory in Metric-Affine Gravity
• Non-Riemannian Cosmology: The role of Shear Hypermomentum
• Inflation in Weyl-invariant Einstein-Cartan gravity
• Raychaudhuri equation in $k$-essence geometry: conditional singular and non-singular cosmological models
• An action principle for the Einstein-Weyl equations
• Acceleration in Weyl integrable spacetime
• Cosmological constraints of Palatini $f(\mathcal{R})$ gravity
• Inflation and late-time accelerated expansion driven by $k$-essence degenerate dynamics
• Schrödinger Connections: From Mathematical Foundations Towards Yano-Schrödinger Cosmology
• Relativistic cosmology and intrinsic spin of matter: Results and theorems in Einstein-Cartan theory
• Revisiting Stability in New General Relativity
• Length-preserving biconnection gravity and its cosmological implications
• $K$-essence model from the mechanical approach point of view: coupled scalar field and the late cosmic acceleration
• Scaling solutions as Early Dark Energy resolutions to the Hubble tension
• Phenomenological signatures of gauge invariant theories of gravity with vectorial nonmetricity
• Friedmann-like universes with non-metricity
• Einstein-aether theory in Weyl integrable geometry
• CMB power spectrum in the emergent universe with k-essence
• Causality and Stability from Acoustic Geometry
• Integrability and Cosmological Solutions in Einstein-aether-Weyl theory
• Statistics of Thawing K-essence Dark Energy Models
• Form Invariance of Raychaudhuri equation in the presence of Inflaton-type fields
• Stability in Cubic Metric-Affine Gravity
• Reconstruction of a kinetic k--essence Lagrangian from a modified of dark energy equation of state
• Friedmann cosmology with hyperfluids
• Non-Affine Extensions of the Raychaudhuri Equation in the K-essence Framework