Constraints on Non-Flat Starobinsky f(R) Dark Energy Model

Area of Science:

• Cosmology
• Theoretical Physics
• Astrophysics

Background:

• The standard Lambda Cold Dark Matter (ΛCDM) model successfully explains cosmic expansion but requires dark energy and dark matter.
• Alternative gravity theories, such as f(R) gravity, offer potential explanations for cosmic acceleration without invoking exotic components.
• The Starobinsky model is a compelling candidate for f(R) gravity, providing a natural dark energy mechanism.

Purpose of the Study:

• To investigate the viability of the Starobinsky f(R) dark energy model in spatially non-flat Friedmann-Lemaître-Robertson-Walker (FLRW) backgrounds.
• To constrain the model parameter (λ) and the density parameter of curvature (ΩK) using recent observational data.
• To compare the Starobinsky f(R) model with the standard ΛCDM model in non-flat universes.

Main Methods:

• Modified the CAMB and CosmoMC computational packages to incorporate the Starobinsky f(R) model and non-flatness.
• Constrained cosmological parameters using recent observational datasets.
• Performed statistical analyses, including calculating χ², Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and Deviance Information Criterion (DIC).

Main Results:

• Constrained the Starobinsky f(R) model parameter to λ⁻¹ < 0.283 at 68% confidence level.
• Determined the density parameter of curvature to be ΩK = -0.00099⁺⁰.⁰⁰⁴⁴⁻⁰.⁰⁰⁴² at 95% confidence level.
• Found that the best-fit Starobinsky f(R) model is statistically consistent with the ΛCDM model (χ²f(R) ≲ χ²ΛCDM) when spatial curvature is considered a free parameter.

Conclusions:

• The viable Starobinsky f(R) gravity model is a strong alternative to dark energy, consistent with current cosmological observations in non-flat universes.
• The inclusion of spatial curvature as a free parameter is crucial for comparing f(R) gravity with the ΛCDM model.
• Further investigation into non-flat cosmological models is warranted to fully understand the nature of dark energy and cosmic acceleration.