Friedmann Equations of FRW Universe in Scalar-tensor Gravity, f(R) Gravity and First Law of Thermodynamics

Abstract

In the paper, hep-th/0501055 (R.G. Cai and S.P. Kim, JHEP {\bf 0502}, 050 (2005)), it is shown that by applying the first law of thermodynamics to the apparent horizon of an FRW universe and assuming the geometric entropy given by a quarter of the apparent horizon area, one can derive the Friedmann equations describing the dynamics of the universe with any spatial curvature; using the entropy formula for the static spherically symmetric black holes in Gauss-Bonnet gravity and in more general Lovelock gravity, where the entropy is not proportional to the horizon area, one can also obtain the corresponding Friedmann equations in each gravity. In this note we extend the study of hep-th/0501055 to the cases of scalar-tensor gravity and $f(R)$ gravity, and discuss the implication of results.

Latex, 9 pages, to appear in PLB; v2: typos corrected, a reference added

Cited by in corpus (118)

• Thermodynamic Behavior of Friedmann Equation at Apparent Horizon of FRW Universe
• Unified First Law and Thermodynamics of Apparent Horizon in FRW Universe
• Thermodynamic route to Field equations in Lanczos-Lovelock Gravity
• Hawking Radiation of Apparent Horizon in a FRW Universe
• Thermodynamical Properties of Apparent Horizon in Warped DGP Braneworld
• Corrected Entropy-Area Relation and Modified Friedmann Equations
• Friedmann Equations and Thermodynamics of Apparent Horizons
• Deep Connection Between Thermodynamics and Gravity in Gauss-Bonnet Braneworld
• Modified cosmology from extended entropy with varying exponent
• Thermodynamics of Apparent Horizon in Brane World Scenario
• Einstein's equations as a thermodynamic identity: The cases of stationary axisymmetric horizons and evolving spherically symmetric horizons
• Entropy of Null Surfaces and Dynamics of Spacetime
• Big Bang Nucleosynthesis constraints on Barrow entropy
• Generalized Vaidya Spacetime in Lovelock Gravity and Thermodynamics on Apparent Horizon
• Modified cosmology through spacetime thermodynamics and Barrow horizon entropy
• Thermodynamics of apparent horizon and modified Friedman equations
• Influence of Generalized and Extended Uncertainty Principle on Thermodynamics of FRW universe
• Thermodynamics in $F(R)$ gravity with phantom crossing
• The generalized second law of thermodynamics in generalized gravity theories
• Generalized Second Law of Thermodynamics in $f(T)$ Gravity with Entropy Corrections
• Constraining Torsion with Gravity Probe B
• Thermodynamics of Apparent Horizon in Brane World Scenarios
• Modified cosmology through Kaniadakis horizon entropy
• Cosmological apparent and trapping horizons
• Modified dispersion relations in extra dimensions
• Generalized second law in modified theory of gravity
• Correspondence of cosmology from non-extensive thermodynamics with fluids of generalized equation of state
• Modified cosmology from the thermodynamics of apparent horizon
• Baryon asymmetry from Barrow entropy: theoretical predictions and observational constraints
• Evolution of Spacetime arises due to the departure from Holographic Equipartition in all Lanczos-Lovelock Theories of Gravity
• Thermodynamical properties of dark energy
• Barrow's black hole entropy and the equipartition theorem
• Hawking radiation as tunneling for spherically symmetric black holes: A generalized treatment
• Growth of Perturbations in Tsallis and Barrow Cosmology
• Holography in Action
• Viscous Cosmology and Thermodynamics of Apparent Horizon
• Corrected Entropy of Friedmann-Robertson-Walker Universe in Tunneling Method
• Baryogenesis in non-extensive Tsallis Cosmology
• Alleviating both $H_0$ and ${\sigma }_8$ tensions in Tsallis cosmology
• Geometrical variables with direct thermodynamic significance in Lanczos-Lovelock gravity
• Holographic Thermalization and Generalized Vaidya-AdS Solutions in Massive Gravity
• Slow-roll inflation and growth of perturbations in Kaniadakis modification of Friedmann cosmology
• Observational constraints of the modified cosmology through Barrow entropy
• Thermodynamic Interpretation of Field Equations at Horizon of BTZ Black Hole
• Nonlinear Electrodynamics in $f(T)$ Gravity and Generalized Second Law of Thermodynamics
• Entropic corrections to Friedmann equations and bouncing universe due to the zero-point length
• The generalized second law of thermodynamics and the nature of the Entropy Function
• Tsallis cosmology and its applications in dark matter physics with focus on IceCube high-energy neutrino data
• Observational constraints on Tsallis modified gravity
• Constraints on Tsallis Cosmology from Big Bang Nucleosynthesis and the Relic Abundance of Cold Dark Matter Particles
• Modified Cosmology Models from Thermodynamical Approach
• Thermodynamics of a Schwarzschild Black Hole in Phantom Cosmology with Entropy Corrections
• The P-V Phase Transition of the FRW Universe
• Primordial Big Bang Nucleosynthesis and Generalized Uncertainty Principle
• Cosmological Evolution Across Phantom Crossing and the Nature of the Horizon
• Generalized Second Law of Thermodynamics in Extended Theories of Gravity
• Finite entanglement entropy from the zero-point-area of spacetime
• Thermodynamics of the apparent horizon in infrared modified Horava-Lifshitz gravity
• On thermodynamics second law in the modified Gauss Bonnet gravity
• Thermodynamics of FRW Universe: Heat Engine
• Thermodynamics of Lemaitre-Tolman-Bondi Model
• Horizon Thermodynamics and Gravitational Field Equations in Quasi-Topological Gravity
• Thermodynamics of Evolving Lorentzian Wormholes at Apparent Horizon in $f(R)$ Theory of Gravity
• The generalized second law of thermodynamics for interacting $f(R)$ gravity
• (2+1)-dimensional solutions in $F(R)$ gravity
• Dynamical apparent horizons in inhomogeneous Brans-Dicke universes
• Friedmann equations from nonequilibrium thermodynamics of the Universe: A unified formulation for modified gravity
• Note on agegraphic dark energy inspired by modified Barrow entropy
• Modified Friedmann equations from fractional entropy
• The Hawking-Page-like Phase Transition from FRW Spacetime to McVittie Black Hole
• Emergence of cosmic space and its connection with thermodynamic principles
• Generalized Uncertainty Principle mimicking dynamical Dark Energy: matter perturbations and gravitational wave data analysis
• Thermodynamics of scale-dependent Friedmann equations
• Investigation of generalised uncertainty principle effects on FRW cosmology
• Thermodynamics of $f(R)$ Gravity with Disformal Transformation
• Holographic dark energy and validity of the generalized second law of thermodynamics in the dgp brane world
• Maximum Entropy Principle for Self-gravitating Perfect Fluid in Lovelock Gravity
• A Study of Black Holes in $F(R)-$ModMax Gravity: Gravitational Lensing and Constraints from EHT Observations
• Influence on the entropic force by the virtual degree of freedom on the holographic screen
• Understanding Gravitational Entropy of Black Holes: A New Proposal via Curvature Invariants
• Generalized second law of thermodynamics in QCD ghost f(G) gravity
• Scalar-Tensor Theory of Gravity and Generalized Second Law of Thermodynamics on the Event Horizon
• A Critical Assessment of Black Hole Solutions With a Linear Term in Their Redshift Function
• On Black Hole Thermodynamics, Singularity, and Gravitational Entropy
• First law of thermodynamics and entropy of FLRW universe in modified gravity
• An attempt to add Barrow entropy in $f(R)$ gravity
• Thermodynamic Origin of the Cardassian Universe
• A Study of Universal Thermodynamics in Lanczos-Lovelock gravity
• On topological charged braneworld black holes
• Equation of State and Joule-Thomson Expansion for the FRW Universe in the Brane World Scenario
• Thermodynamics in Quasi-Spherical Szekeres Space-Time
• Renyi Entropy Correction to Expanding Universe
• Barrow's non-linear charged Anti-de Sitter black hole and stability
• Thermodynamics of noncommutative de Sitter spacetime
• Horava-Lifshitz cosmology, entropic interpretation and quark-hadron phase transition
• Big-Bang nucleosynthesis constraints on (dual) Kaniadakis cosmology
• Barrow Cosmology and Big-Bang Nucleosynthesis
• The Unified First law in "Cosmic Triad" Vector Field Scenario
• Viaggiu entropy and the generalized second law in a flat FLRW Universe
• Exponential correction to Friedmann equations
• Modified cosmology through generalized mass-to-horizon entropy: observational constraints from DESI DR2 BAO data
• MOND Theory and Thermodynamics of Spacetime
• The generalized second law of thermodynamics in f(R) gravity for various choices of scale factor
• Observational constraints and dynamical analysis of Kaniadakis horizon-entropy cosmology
• Thermodynamics of the arbitrary dimensional FRW universe: Joule-Thomson expansion
• Scalar-tensor theories of gravity from a thermodynamic viewpoint
• Misner-Sharp Energy and P-V Criticality in Quasi-Topological Cosmology
• Thermodynamic structure of field equations near apparent horizon for radiating black holes
• Friedmann equations from GUP-modified equipartition law
• The shadow of black holes in $F(R)$-ModMax theory with cosmic strings
• Holographic vacuum energy regularization and corrected entropy of de Sitter space
• Modified cosmology through generalized mass-to-horizon entropy: implications for structure growth and primordial gravitational waves
• Cosmological QCD phase transition in steady non-equilibrium dissipative Hořava-Lifshitz early universe
• The Einstein equation of state as the Clausius relation with an entropy production
• Observational constraints on Luciano-Saridakis entropic cosmology
• Cooling-Heating Properties of the FRW Universe in Gravity with a Generalized Conformal Scalar Field
• Thermodynamical aspects of modified holographic dark energy model
• Thermodynamics and optical aspects of ModMax black holes in higher order curvature gravity with quintessence dark energy