Effective field equations and scale-dependent couplings in gravity

Abstract

A new set of field equations for a space-time dependent Newton's constant $G(x)$ and cosmological constant $\Lambda (x)$ in the presence of matter is presented. We prove that it represents the most general mathematically consistent, physically plausible, set of evolution equations assuming at most second derivatives in the dynamical variables. In the new Einstein's equations, only $\Lambda$-kinetic terms arise, while in the modified conservation equation, derivative terms of $G$ also appear. As an application, this formalism is applied in the context of the Asymptotic Safety scenario to the early universe, assuming a perfect fluid with a radiation equation of state. Cosmological solutions are obtained for all types of spatial curvature, displaying a variety of interesting cosmic evolutions. As an indication of such behaviours, bouncing solutions, recollapsing solutions or non-singular expanding solutions with a transient acceleration era are discussed in details.

arXiv comment21 pages, 12 figures, to appear in PRD

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Cited by in corpus (14)

• Testing a varying-$\Lambda$ model for dark energy within Co-varying Physical Couplings framework
• Thermodynamics of scale-dependent Friedmann equations
• Swiss-cheese cosmologies with variable $G$ and $\Lambda$ from the renormalization group
• Generalized Entropy Implies Varying-G: Horizon Area Dependent Field Equations and Black Hole-Cosmology Coupling
• Observational constraints on varying fundamental constants in a minimal CPC model
• Shadows of black holes at cosmological distances in the co-varying physical couplings framework
• Renormalization Group-Improved Gravitational Action: A Lagrangian Framework
• Constraining the swiss-cheese IR-fixed point cosmology with cosmic expansion
• Does the Vacuum Gravitate on Microscopic Scales? Rydberg Atoms Indicate Probably Not
• A Universe from a Lagrangian Fixed Point
• Phenomenological footprints of Lambda varying gravity theories inspired from quantum gravity models in the multi-messenger era
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• Perturbative Renormalisation Group Improved Black Hole Solution and its Quasinormal Modes
• Asymptotic Safety and the Cosmic Coincidence Problem