[Paper Review] Scalar-Tensor theories and current Cosmology

Diego Sáez-Chillón Gómez|ArXiv.org|Dec 10, 2008

Cosmology and Gravitation Theories1 references3 citations

TL;DR

This paper reviews scalar-tensor theories as a unified framework for cosmic inflation and late-time acceleration, analyzing quintessence and phantom scalar field models. It demonstrates that the chameleon mechanism enables these theories to evade local gravity constraints while reproducing current cosmological observations, offering a viable dark energy candidate despite the cosmological constant and coincidence problems remaining unresolved.

ABSTRACT

Scalar-tensor theories are studied in the context of cosmological evolution, where the expansion history of the Universe is reconstructed. It is considered quintessence/phantom models, where inflation and cosmic acceleration are reproduced. Also, the non-minimally coupling regime between the scalar field and the Ricci scalar is studied and cosmological solutions are obtained. The Chamaleon mechanism is shown as a solution of the local gravity tests problems presented in this kind of theories.

Motivation & Objective

• To investigate scalar-tensor theories as a unified framework for early (inflation) and late-time (acceleration) cosmic expansion.
• To analyze quintessence and phantom scalar field models in the context of current cosmological observations.
• To address the challenge of local gravity constraints in non-minimally coupled scalar-tensor theories.
• To demonstrate how the chameleon mechanism enables these models to evade experimental bounds on fifth forces.
• To reconstruct cosmological evolution from early to late-time expansion using scalar-tensor dynamics.

Proposed method

• Formulates the action for minimally coupled scalar-tensor models with a sign choice to distinguish quintessence (−) and phantom (+) fields.
• Derives Friedmann equations and scalar field equations from the action under a flat FRW metric, linking Hubble parameter evolution to scalar field dynamics.
• Reconstructs the scalar field potential V(φ) and coupling function ω(φ) from cosmological evolution using the Hubble parameter and scale factor.
• Applies the chameleon mechanism by introducing a non-minimal coupling f(φ) to the Ricci scalar, making the scalar field mass dependent on local matter density.
• Analyzes the effective potential Ueff(σ) = U(σ) + βρmeβσ to show that high-density regions suppress scalar field effects, satisfying local gravity tests.
• Uses conformal transformations to relate the Jordan and Einstein frames, enabling analysis of scalar field mass and fifth-force strength in different environments.

Experimental results

Research questions

• RQ1 Can scalar-tensor theories with a single scalar field reproduce both inflation and late-time cosmic acceleration?
• RQ2 How do phantom and quintessence models affect the equation of state and energy density evolution in cosmology?
• RQ3 What conditions allow non-minimally coupled scalar-tensor theories to satisfy local gravity constraints?
• RQ4 How does the chameleon mechanism dynamically suppress fifth forces in high-density environments like Earth?
• RQ5 Can the chameleon mechanism be consistently applied to unify dark energy and inflation within a single scalar-tensor framework?

Key findings

• The chameleon mechanism successfully suppresses fifth-force interactions in high-density regions, allowing non-minimally coupled scalar-tensor theories to pass local gravity tests.
• The scalar field mass mσ increases with local matter density ρm, reaching values above 10^10 GeV in dense environments, making the force short-ranged and unobservable.
• In low-density regions such as cosmological scales (ρm ~ H₀²), the scalar field mass decreases, allowing long-range effects that can drive cosmic acceleration.
• The effective potential Ueff(σ) develops a minimum dependent on local ρm, stabilizing the scalar field and enabling consistent cosmological solutions.
• The paper reconstructs viable cosmological solutions for both quintessence and phantom models, showing they can reproduce the observed Hubble parameter evolution.
• Despite success in fitting cosmological data, the cosmological constant and coincidence problems remain unresolved within this framework.