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Do consistent $F(R)$ models mimic General Relativity plus $\Lambda$?

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arxiv 0705.3199 v2 pith:X7U2B6R7 submitted 2007-05-22 astro-ph

classification astro-ph
keywords modelsacceleratingacceptableconstraintsgenerallambdalatemimic
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abstract

Modified gravity models are subject to a number of consistency requirements which restrict the form that the function $F(R)$ can take. We study a particular class of $F(R)$ functions which satisfy various constraints that have been found in the literature. These models have a late time accelerating epoch, and an acceptable matter era. We calculate the Friedmann equation for our models, and show that in order to satisfy the constraints we impose, they must mimic General Relativity plus $\Lambda$ throughout the cosmic history, with exponentially suppressed corrections. We also find that the free parameters in our model must be fine tuned to obtain an acceptable late time accelerating phase. We discuss the generality of this conclusion.

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Forward citations

Cited by 10 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Phantom-divide crossing and suppressed structure growth in kinetically braided dark energy with momentum exchange

    astro-ph.CO 2026-07 conditional novelty 6.0 of 10

    A linearly stable kinetic-braiding dark-energy model with CDM momentum exchange realizes upward phantom-divide crossing and weak CDM gravitational clustering, altering matter and CMB spectra.

  2. Realizing the phantom-divide crossing with vector and scalar fields

    astro-ph.CO 2026-01 conditional novelty 6.0 of 10

    A scalar-vector-tensor dark-energy model crosses the phantom divide at low redshift with no ghost or Laplacian instabilities and growth signatures close to LCDM.

  3. Transit dark energy cosmological models in generalized matter-geometry coupling theory using a non-linear form of $f(R,T,L_{m})$ function

    gr-qc 2025-09 conditional novelty 4.0 of 10

    A modified f(R,T,L_m) gravity model, fitted to CC and Pantheon data, yields an accelerating late-time universe with transition redshift near 0.6 and an effective dark energy equation of state within 1e-5 of -1.

  4. Preventing Curvature Singularities in $f(R)$ Dark Energy Models

    gr-qc 2025-08 reject novelty 4.0 of 10

    Adding R² or related higher-curvature corrections can prevent singularities in toy f(R) dark-energy models only when the correction mass is tuned far below the Starobinsky inflation scale.

  5. Effective Equation of State Oscillations at Matter-Radiation Equality and Primordial Gravitational Waves

    gr-qc 2025-07 reject novelty 4.0 of 10

    An exponentially deformed R^2 gravity model is claimed to produce total equation-of-state oscillations near z~3400 that enhance the primordial gravitational wave spectrum at LiteBIRD frequencies.

  6. Cosmological implications and causality in $f(R, L_{m}, T)$ gravity theory with observational constraints

    gr-qc 2025-01 reject novelty 4.0 of 10

    Four f(R,Lm,T) fluid models are fitted to CC+Pantheon+SH0ES data, but the assumed matter conservation contradicts the theory's field equations.

  7. Modified gravity/Dynamical Dark Energy vs $\Lambda$CDM: is the game over?

    gr-qc 2024-12 reject novelty 4.0 of 10

    An AIC/χ² comparison of exponential F(R) gravity, wCDM, and CPL models against Pantheon+, DESI DR1, cosmic chronometer, and Planck-compressed data claims ΛCDM is excluded at 4σ, but the significance conversion is not ...

  8. Off-diagonal solutions in Einsteingravity modeling f(R) gravity and dynamical darkenergy vs Lambda CDM cosmology

    physics.gen-ph 2026-03 unverdicted novelty 3.0 of 10

    Off-diagonal Einstein solutions constructed via the anholonomic frame and connection deformation method can mimic f(R) gravity and dynamical dark energy effects inside GR and Lambda CDM cosmology.

  9. Modified theories of gravity at different curvature scales

    gr-qc 2025-02 unverdicted novelty 3.0 of 10

    A review that classifies modified gravity theories by the GR principles they preserve or violate, and maps their tests onto a curvature-compactness plane.

  10. Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution

    gr-qc 2017-05 accept novelty 2.0 of 10

    Modified gravity theories supply viable mathematical frameworks for inflation, bounces, and dark energy eras that match observational data.

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