Modified gravity: a unified approach to metric-affine models

Abstract

The starting point of this work is the original Einstein action, sometimes called the Gamma squared action. Continuing from our previous results, we study various modified theories of gravity following the Palatini approach. The metric and the connection will be treated as independent variables leading to generalised theories which may contain torsion or non-metricity or both. Due to our particular approach involving the Einstein action, our setup allows us to formulate a substantial number of new theories not previously studied. Our results can be linked back to well-known models like Einstein-Cartan theory and metric-affine theories and also links to many recently studied modified gravity models. In particular we propose an Einstein-Cartan type modified theory of gravity which contains propagating torsion provided our function depends non-linearly on a boundary term. We also can state precise conditions for the existence of propagating torsion. Our work concludes with a brief discussion of cosmology and the role of cosmological torsion in our model. We find solutions with early-time inflation and late-time matter dominated behaviour. No matter sources are required to drive inflation and it becomes a purely geometrical effect.

Final version published in JMP

References in corpus (14)

• Palatini Approach to Modified Gravity: f(R) Theories and Beyond
• The teleparallel equivalent of general relativity
• On Born-Infeld Gravity in Weitzenbock spacetime
• Metric-affine f(R) theories of gravity
• Unifying framework for scalar-tensor theories of gravity
• New classes of modified teleparallel gravity models
• Poincare gauge theory of gravity: Friedman cosmology with even and odd parity modes. Analytic part
• Inflation in Metric-Affine Quadratic Gravity
• A type of Born-Infeld regular gravity and its cosmological consequences
• Coupling Metric-Affine Gravity to a Higgs-Like Scalar Field
• Matter matters in Einstein-Cartan gravity
• Variational Principles in Teleparallel Gravity Theories
• The regular black hole in four dimensional Born-Infeld gravity
• BTZ gems inside regular Born-Infeld black holes

Cited by in corpus (20)

• The role of the boundary term in $f(Q,B)$ symmetric teleparallel gravity
• Non-metricity with bounday terms: $f(Q,C)$ gravity and cosmology
• Dynamical systems analysis of $f(Q)$ gravity
• Coupling Metric-Affine Gravity to the Standard Model and Dark Matter Fermions
• Geometry and covariance of symmetric teleparallel theories of gravity
• The Non-Relativistic Geometric Trinity of Gravity
• Spherically symmetric teleparallel geometries
• Spatial curvature in coincident gauge $f(Q)$ cosmology
• Stability of $f(Q,B)$ Gravity via Dynamical System Approach: a Comprehensive Bayesian Statistical Analysis
• Teleparallel Robertson-Walker geometries and applications
• Cosmological solutions in teleparallel $F(T,B)$ gravity
• Observational tests of asymptotically flat ${\mathcal{R}}^2$ spacetimes
• Cosmological fluids with boundary term couplings
• A new 2D formulation of modified General Relativity
• Scalar field source Teleparallel Robertson-Walker F(T)-gravity solutions
• Generating exact polytropes in non-conservative unimodular geometries
• Cosmological dynamical systems of non-minimally coupled fluids and scalar fields
• Diffeomorphism Invariance Breaking in Gravity and Cosmological Evolution
• Geometric formulation of $k$-essence and late-time acceleration
• Dynamical systems approach to stellar modelling in $f(G,B)$ gravity