[Paper Review] Scalar-tensor theories and cosmology

Gilles Esposito-Farèse|ArXiv.org|Jun 4, 2003

Cosmology and Gravitation Theories3 citations

TL;DR

This paper investigates scalar-tensor theories of gravity that include a scalar field coupled to matter, a potential, and the Gauss-Bonnet invariant. It shows that solar-system and cosmological data together constrain the scalar–Gauss-Bonnet coupling, revealing that even tiny deviations from a minimum in the coupling function $W(\varphi)$ are ruled out by solar-system tests, thus excluding certain accelerating cosmological models with non-zero $W(\varphi)$.

ABSTRACT

Scalar-tensor theories are the best motivated alternatives to general relativity and provide a mathematically consistent framework to test the various observable predictions. They can involve three functions of the scalar field: (i) a potential (as in "quintessence" models), (ii) a matter-scalar coupling function (as in "extended quintessence", where it may also be rewritten as a nonminimal coupling of the scalar field to the scalar curvature), and (iii) a coupling function of the scalar field to the Gauss-Bonnet topological invariant. We recall the main experimental constraints on this class of theories, and underline that solar-system, binary-pulsar, and cosmological observations give qualitatively different tests. We finally show that the combination of these data is necessary to constrain the existence of a scalar-Gauss-Bonnet coupling.

Motivation & Objective

• To assess the viability of scalar-tensor theories with a scalar–Gauss-Bonnet coupling as alternatives to general relativity.
• To determine whether such couplings can coexist with observed solar-system and cosmological phenomena.
• To reconstruct the matter-scalar coupling $A(\varphi)$ and potential $V(\varphi)$ from cosmological data.
• To establish experimental bounds on the scalar–Gauss-Bonnet coupling $W(\varphi)$ using combined solar-system and cosmological constraints.

Proposed method

• Formulates the most general scalar-tensor theory preserving the weak equivalence principle and one spin-0 degree of freedom, with action involving $A(\varphi)$, $V(\varphi)$, and $W(\varphi)$.
• Applies the parametrized post-Newtonian (PPN) formalism to analyze solar-system constraints on $A(\varphi)$ and its derivatives.
• Uses cosmological luminosity distance $D_L(z)$ and matter growth $\delta_m(z)$ to reconstruct $A(\varphi)$ and $V(\varphi)$ over a finite range of $\varphi$.
• Performs nonlinear perturbative analysis to assess small-scale effects of $W(\varphi)$, especially the behavior of $\varphi$ near $r \to 0$.
• Combines solar-system constraints with cosmological reconstructions to derive bounds on $W'(\varphi)$ and $W''(\varphi)$.
• Applies dimensional analysis and stability arguments to assess the physical viability of $W(\varphi)$-induced corrections to the Newtonian potential.

Experimental results

Research questions

• RQ1 Can a scalar field coupled to the Gauss-Bonnet invariant survive solar-system tests while still enabling late-time cosmic acceleration?
• RQ2 How do solar-system and cosmological data jointly constrain the functional form of the scalar–Gauss-Bonnet coupling $W(\varphi)$?
• RQ3 To what extent can the matter-scalar coupling $A(\varphi)$ and scalar potential $V(\varphi)$ be reconstructed from cosmological observations alone?
• RQ4 What are the implications of nonlinear corrections in $W(\varphi)$ for the Newtonian potential at small scales?
• RQ5 Is it possible to have a non-constant $W(\varphi)$ that avoids conflict with solar-system experiments?

Key findings

• The scalar–Gauss-Bonnet coupling $W(\varphi)$ is severely constrained by solar-system tests, requiring $|W'_{0}| < 10^{-2 \times 10^{11}}$ to avoid observable deviations.
• Even if $W'_{0} = 0$ at present, nonlinear evolution would cause $W'_{0}$ to deviate from zero within a fraction of a second, making such models unstable.
• Models with $A(\varphi) = 1$, $V(\varphi) = 0$, and $W(\varphi) \neq 0$ are ruled out because they cannot simultaneously explain cosmic acceleration and solar-system observations.
• The cosmological reconstruction of $W(\varphi)$ predicts a large and positive $W''_{0}$, implying strong nonlinear effects at small scales that dominate over linear estimates.
• Nonlinear effects can suppress scalar-field contributions at small distances if $W''_{0}$ is large and negative, but this is inconsistent with the cosmological reconstruction, which favors large positive $W''_{0}$.
• The combination of solar-system and cosmological data is essential to constrain $W(\varphi)$, as neither alone provides sufficient sensitivity.