Further Extended Theories of Gravitation: Part I

Abstract

We shall here propose a class of relativistic theories of gravitation, based on a foundational paper of Ehlers Pirani and Schild (EPS).All "extended theories of gravitation" (also known as f(R) theories) in Palatini formalism are shown to belong to this class. In a forthcoming paper we shall show that this class of theories contains other more general examples. EPS framework helps in the interpretation and solution of these models that however have exotic behaviours even compared to f(R) theories.

10 pages. Some refs added

References in corpus (4)

• Extended Theories of Gravity and their Cosmological and Astrophysical Applications
• Metric-affine f(R) theories of gravity
• A no-go theorem for polytropic spheres in Palatini f(R) gravity
• From Dark Energy and Dark Matter to Dark Metric

Cited by in corpus (13)

• Palatini Approach to Modified Gravity: f(R) Theories and Beyond
• New Spherically Symmetric Solutions in f(R)-gravity by Noether Symmetries
• On stability of a neutron star system in Palatini gravity
• Palatini Actions and Quantum Gravity Phenomenology
• A further study on Palatini f(R)-theories for polytropic stars
• The physical foundations for the geometric structure of relativistic theories of gravitation. From General Relativity to Extended Theories of Gravity through Ehlers-Pirani-Schild approach
• Acceleration in Weyl integrable spacetime
• MOND-like acceleration in integrable Weyl geometric gravity
• The Palatini star: exact solutions of the modified Lane-Emden equation
• The effective Equation of State in Palatini $f(R)$ cosmology
• Hubble drift in Palatini $f(\mathcal{R})$-theories
• Extended Cosmologies
• The generally covariant meaning of space distances