$\Lambda$-Gravity from Entropy

Abstract

The Gravity from Entropy (GfE) theory treats the metric of spacetime as quantum operators and proposes the GfE action for gravity. The GfE Lagrangian is given by the Geometric Quantum Relative Entropy (GQRE) between the true metric and the metric induced by the matter fields and curvature. The theory leads to modified gravity equations and predicts the emergence of a dynamical cosmological constant ${\Lambda }_{\mathcal{G}}$. In the low energy, small curvature limit the GfE gravity equations reduce to Einstein equations with vanishing cosmological constant, i.e. in the weak field linear approximation ${\Lambda }_{\mathcal{G}}$ vanishes. In this work, we propose a generalisation of the GfE theory, called $\Lambda$-Gravity from Entropy ($\Lambda$GfE). Following a thermodynamic approach, we introduce a Lagrange multiplier $\Lambda$ to define the local volume of the theory. By enforcing local Weyl stationarity of the $\Lambda$GfE action modulo the volume constraint of the theory, we derive the equation for $\Lambda$. The $\Lambda$GfE equations of motion include two dark energy contributions: the emergent and dynamical contribution given by ${\Lambda }_{\mathcal{G}}$ plus a constant contribution given by $\Lambda$ where $\Lambda$ can be identified with the cosmological constant in the low energy small curvature limit. While this theory cannot predict the exact value of $\Lambda$, here it is shown that the vacuum contributions to the dressed stress-energy tensor cancel from the trace-free equations of motion of the $\Lambda$GfE theory. Within the GfE framework, the $\Lambda$GfE also offers a novel interpretation of the dark energy terms, with potentially testable consequences for cosmological observations.

arXiv comment(15 pages + Appendices)

References in corpus (30)

• Dynamics of dark energy
• Thermodynamics of Spacetime: The Einstein Equation of State
• The Cosmological Constant
• On the Origin of Gravity and the Laws of Newton
• Testing General Relativity with Present and Future Astrophysical Observations
• Black hole chemistry: thermodynamics with Lambda
• Black holes, gravitational waves and fundamental physics: a roadmap
• Entanglement Equilibrium and the Einstein Equation
• The CosmoVerse White Paper: Addressing observational tensions in cosmology with systematics and fundamental physics
• Making the Case for Conformal Gravity
• On the Trace-Free Einstein Equations as a Viable Alternative to General Relativity
• Local Conformal Symmetry in Physics and Cosmology
• The Trace-Free Einstein Equations and inflation
• A note on classical and quantum unimodular gravity
• Cosmographic Constraints and Cosmic Fluids
• Unimodular relativity and cosmological constant
• Vacuum Energy Sequestering: The Framework and Its Cosmological Consequences
• On unimodular quantum gravity
• A Gravitational Entropy Proposal
• What is the Entropy in Entropic Gravity?
• Can quantum fluctuations differentiate between standard and unimodular gravity?
• Gravity from entropy
• Classical Weyl Transverse Gravity
• A review about Invariance Induced Gravity: Gravity and Spin from Local Conformal-Affine Symmetry
• Anomaly-free scale symmetry and gravity
• The quantum relative entropy of the Schwarzschild black-hole and the area law
• From Quantum Relative Entropy to the Semiclassical Einstein Equations
• From spacetime thermodynamics to Weyl transverse gravity
• Inflation from entropy
• Spherically symmetric black holes in Gravity from Entropy and spontaneous emission