Galileon and generalized Galileon with projective invariance in a metric-affine formalism

Abstract

We study scalar-tensor theories respecting the projective invariance in the metric-affine formalism. The metric-affine formalism is a formulation of gravitational theories such that the metric and the connection are independent variables in the first place. In this formalism, the Einstein-Hilbert action has an additional invariance, called the projective invariance, under a shift of the connection. Respecting this invariance for the construction of the scalar-tensor theories, we find that the Galileon terms in curved spacetime are uniquely specified at least up to quartic order which does not coincide with either the covariant Galileon or the covariantized Galileon. We also find an action in the metric-affine formalism which is equivalent to class ${}^2$N-I/Ia of the quadratic degenerated higher order scalar-tensor (DHOST) theory. The structure of DHOST would become clear in the metric-affine formalism since the equivalent action is just linear in the generalized Galileon terms and non-minimal couplings to the Ricci scalar and the Einstein tensor with independent coefficients. The fine-tuned structure of DHOST is obtained by integrating out the connection. In these theories, non-minimal couplings between fermionic fields and the scalar field may be predicted. We discuss possible extensions which could involve theories beyond DHOST.

arXiv comment13 pages, no figure, published version

References in corpus (32)

• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• f(R) theories
• Gravitational Waves and Gamma-rays from a Binary Neutron Star Merger: GW170817 and GRB 170817A
• The galileon as a local modification of gravity
• Generalized G-inflation: Inflation with the most general second-order field equations
• From k-essence to generalised Galileons
• Covariant Galileon
• Dark Energy after GW170817: dead ends and the road ahead
• Dark Energy after GW170817 and GRB170817A
• Implications of the Neutron Star Merger GW170817 for Cosmological Scalar-Tensor Theories
• Palatini Approach to Modified Gravity: f(R) Theories and Beyond
• Healthy theories beyond Horndeski
• Degenerate higher derivative theories beyond Horndeski: evading the Ostrogradski instability
• Transforming gravity: from derivative couplings to matter to second-order scalar-tensor theories beyond the Horndeski Lagrangian
• Exploring gravitational theories beyond Horndeski
• General second order scalar-tensor theory, self tuning, and the Fab Four
• Degenerate higher order scalar-tensor theories beyond Horndeski up to cubic order
• Extended Scalar-Tensor Theories of Gravity
• Degenerate higher order scalar-tensor theories beyond Horndeski and disformal transformations
• Metric-affine f(R) theories of gravity
• Inflation with Non-Minimal Coupling: Metric vs. Palatini Formulations
• Scalar-tensor theories and modified gravity in the wake of GW170817
• Metric-Palatini gravity unifying local constraints and late-time cosmic acceleration
• Effective Description of Higher-Order Scalar-Tensor Theories
• Vainshtein mechanism after GW170817
• Vainshtein Screening in Scalar-Tensor Theories before and after GW170817: Constraints on Theories beyond Horndeski
• Universality of Einstein Equations for the Ricci Squared Lagrangians
• Metric-affine f(R,T) theories of gravity and their applications
• On the equivalence of the Einstein-Hilbert and the Einstein-Palatini formulations of general relativity for an arbitrary connection
• f(R) gravity, torsion and non-metricity
• Towards the most general scalar-tensor theories of gravity: a unified approach in the language of differential forms
• Metric-Affine Formalism of Higher Derivative Scalar Fields in Cosmology

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• Metric-affine Gravity and Inflation
• Scale transformations in metric-affine geometry
• Tracing the high energy theory of gravity: an introduction to Palatini inflation
• Scalar-metric-affine theories: Can we get ghost-free theories from symmetry?
• Dimensional Transmutation in Gravity and Cosmology
• Towards distinguishing variants of non-minimal inflation
• Metric-Affine Gravity and Cosmology/Aspects of Torsion and non-Metricity in Gravity Theories
• Initial conditions for plateau inflation: a case study
• Radiatively stable ghost and tachyon freedom in Metric Affine Gravity
• Minimal $k$-inflation in light of the conformal metric-affine geometry
• General slow-roll inflation in $f(R)$ gravity under the Palatini approach
• Testing f(R) gravity with the simulated data of gravitational waves from the Einstein Telescope
• Varying the Horndeski Lagrangian within the Palatini approach
• A metric-affine version of the Horndeski theory
• Ghostfree quadratic curvature theories with massive spin-2 and spin-0 particles
• Ghost from constraints: a generalization of Ostrogradsky theorem
• Constraining Palatini-Horndeski theory with gravitational waves after GW170817
• 3+1 decomposition in modified gravities within the Palatini formalism and some applications
• Scalar fields with derivative coupling to curvature in the Palatini and the metric formulation
• Quartic Horndeski-Cartan theories in a FLRW universe
• Propagation and emission of gravitational waves in the weak-field limit within the Palatini formalism