Spacetimes with vector distortion: Inflation from generalised Weyl geometry

Abstract

Spacetime with general linear vector distortion is introduced. Thus, the torsion and the nonmetricity of the affine connection are assumed to be proportional to a vector field (and not its derivatives). The resulting two-parameter family of non-Riemannian geometries generalises the conformal Weyl geometry and some other interesting special cases. Taking into account the leading order quadratic curvature correction to the Einstein-Hilbert action results uniquely in the one-parameter extension of the Starobinsky inflation known as the alpha-attractor. The most general quadratic curvature action introduces, in addition to the canonical vector kinetic term, novel ghost-free vector-tensor interactions.

5 pages, 1 table, 0 figures. V2: Added the general quadratic theory

References in corpus (8)

• Derivative self-interactions for a massive vector field
• Generalized Proca action for an Abelian vector field
• Black Holes and Abelian Symmetry Breaking
• Cosmology for quadratic gravity in generalized Weyl geometry
• Einstein-Vector Gravity, Emerging Gauge Symmetry and de Sitter Bounce
• Linear connections with propagating spin-3 field in gravity
• Planck constraints on inflation in auxiliary vector modified $f(R)$ theories
• Universality Classes of Scale Invariant Inflation

Cited by in corpus (75)

• Coincident General Relativity
• Cosmology in $f(Q)$ geometry
• $f(Q,T)$ gravity
• Teleparallel Palatini theories
• Weyl type $f(Q,T)$ gravity, and its cosmological implications
• Polarization of gravitational waves in symmetric teleparallel theories of gravity and their modifications
• Instabilities in Metric-Affine Theories of Gravity
• Inconsistencies in four-dimensional Einstein-Gauss-Bonnet gravity
• Friedmann-like universes with torsion
• Geodesic deviation, Raychaudhuri equation, Newtonian limit, and tidal forces in Weyl-type $f(Q,T)$ gravity
• Observational constraints on generalized Proca theories
• Scale transformations in metric-affine geometry
• Anisotropic Strange Star Model Beyond Standard Maximum Mass Limit by Gravitational Decoupling in $f(Q)$ Gravity
• Palatini quadratic gravity: spontaneous breaking of gauged scale symmetry and inflation
• Generalized multi-Proca fields
• Cosmology for quadratic gravity in generalized Weyl geometry
• Torsion/non-metricity duality in f(R) gravity
• Einstein-Vector Gravity, Emerging Gauge Symmetry and de Sitter Bounce
• Black hole solutions in the quadratic Weyl conformal geometric theory of gravity
• Dark matter as a Weyl geometric effect
• Revisiting the Stability of Quadratic Poincaré Gauge Gravity
• The Raychaudhuri equation in spacetimes with torsion and non-metricity
• Anisotropic cosmological solutions in massive vector theories
• Parity Violating Metric-Affine Gravity Theories
• Cosmological tests of the osculating Barthel-Kropina dark energy model
• Non-minimal geometry-matter couplings in Weyl-Cartan space-times: $f(R,T,Q,T_m)$ gravity
• Transit cosmological models with observational constraints in f(Q, T) gravity
• Coupling matter and curvature in Weyl geometry: conformally invariant $f\left(R,L_m\right)$ gravity
• Field redefinitions in theories beyond Einstein gravity using the language of differential forms
• Friedmann-like universes with weak torsion: a dynamical system approach
• The Full Quadratic Metric-Affine Gravity (Including Parity Odd Terms): Exact solutions for the Affine-Connection
• Nonmetricity theories and aspects of gauge symmetry
• Cosmology of Quadratic Metric-Affine Gravity
• Non-trivial gravitational waves and structure formation phenomenology from dark energy
• Acceleration in Friedmann cosmology with torsion
• Instabilities in Horndeski Yang-Mills inflation
• Linear Transformations on Affine-Connections
• Cosmological inflation driven by a scalar torsion function
• Compact stellar structures in Weyl geometric gravity
• Vector stability in quadratic metric-affine theories
• $f(Q,L_m)$ gravity, and its cosmological implications
• Quantum Stability of Generalized Proca Theories
• A metric-affine version of the Horndeski theory
• FLRW Cosmology in Metric-Affine $F(R,Q)$ Gravity
• Singularities and n-dimensional black holes in torsion theories
• Scale Invariance in Newton-Cartan and Hořava-Lifshitz Gravity
• Cosmological implications of the Weyl geometric gravity theory
• Myrzakulov $F(T,Q)$ gravity: cosmological implications and constraints
• Riemann Tensor and Gauss-Bonnet density in Metric-Affine Cosmology
• Dissipative quintessence, and its cosmological implications
• Gauging the spacetime metric -- looking back and forth a century later
• Phenomenological signatures of gauge invariant theories of gravity with vectorial nonmetricity
• Absence of solid angle deficit singularities in beyond-generalized Proca theories
• Modified gravity from Weyl connection and the $f(R,\mathcal{A})$ extension
• A non-trivial connection for the metric-affine Gauss-Bonnet theory in $D=4$
• Non-minimal Energy-momentum squared gravity
• Homogeneous and Isotropic space-time, Modified torsion field and Complete cosmic scenario
• Cosmology of Metric-Affine $R+\beta R^2$ Gravity with Pure Shear Hypermomentum
• Thermodynamics of the Weyl Geometric Gravity Black Holes
• Cosmology with vector distortion
• Stability in Cubic Metric-Affine Gravity
• Broken scale invariance, $\alpha$-attractors and vector impurity
• Inflation with mixed helicities and its observational imprint on CMB
• Effective field theory of coupled dark energy and dark matter
• Axionic extension of the Proca action
• Superconformal generalizations of auxiliary vector modified polynomial f(R) theories
• Mimetic Weyl geometric gravity
• D-dimensional black holes in extended Gauss-Bonnet gravity
• The Role of Torsion in Trans-Planckian Physics
• Metric-Affine Version of Myrzakulov $F(R,T,Q,\mathcal{T})$ Gravity and Cosmological Applications
• Horndeski in motion
• Geometric formulation of $k$-essence and late-time acceleration
• The Weyl Geometric Gravity black hole in light of the Solar System tests
• New effective theories of gravitation and their phenomenological consequences
• Lost in translation: the Abelian affine connection (in the coincident gauge)