A Relativistic Scalar Model for Fractional Interaction between Dark Matter and Gravity

Abstract

In a series of recent papers we put forward a ``fractional gravity'' framework striking an intermediate course between a modified gravity theory and an exotic dark matter (DM) scenario, which envisages the DM component in virialized halos to feel a non-local interaction mediated by gravity. The remarkable success of this model in reproducing several aspects of DM phenomenology motivates us to look for a general relativistic extension. Specifically, we propose a theory, dubbed Relativistic Scalar Fractional Gravity or RSFG, in which the trace of the DM stress-energy tensor couples to the scalar curvature via a non-local operator constructed with a fractional power of the d'Alembertian. We derive the field equations starting from an action principle, and then we investigate their weak field limit, demonstrating that in the Newtonian approximation the fractional gravity setup of our previous works is recovered. We compute the first-order post-Newtonian parameter $\gamma$ and its relation with weak lensing, showing that although in RSFG the former deviates from its GR values of unity, the latter is unaffected. We also perform a standard scalar-vector-tensor-decomposition of RSFG in the weak field limit, to highlight that gravitational waves propagate at the speed of light, though also an additional scalar mode becomes dynamical. Finally, we derive the modified conservation laws of the DM stress energy tensor in RSFG, showing that a new non-local force emerges, and hence that the DM fluid deviates from the geodesic solutions of the field equations.

21 pages. Accepted by Classical and Quantum Gravity

References in corpus (18)

• 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
• The Pantheon+ Analysis: Cosmological Constraints
• Fractional Calculus: Integral and Differential Equations of Fractional Order
• Cosmological perturbations and structure formation in nonlocal infrared modifications of general relativity
• Equivalence Principle Implications of Modified Gravity Models
• Towards a Resolution of the Cosmological Singularity in Non-local Higher Derivative Theories of Gravity
• Analyzing the Large-Scale Bulk Flow using CosmicFlows4: Increasing Tension with the Standard Cosmological Model
• Non-Local Gravity Cosmology: an Overview
• The distribution and morphologies of Fornax Cluster dwarf galaxies suggest they lack dark matter
• Evaluating bulk flow estimators for CosmicFlows-4 measurements
• The kinematics of massive quiescent galaxies at $1.4<z<2.1$: dark matter fractions, IMF variation, and the relation to local early-type galaxies
• Gravitational waves in non-local gravity
• The first variation of the matter energy-momentum tensor with respect to the metric, and its implications on modified gravity theories
• Micro galaxies in LCDM
• Renormalizability of nonlocal quantum gravity coupled to matter
• Dark Matter in Fractional Gravity I: Astrophysical Tests on Galactic Scales
• Classical and quantum nonlocal gravity
• Machian Gravity: A mathematical formulation for Mach's Principle

Cited by in corpus (2)

• Fractional entropy of the Brown-Kuchař dust in fractional anti-de Sitter quantum gravity
• A Relativistic Tensorial Model for Fractional Interaction between Dark Matter and Gravity