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Constraints on Gauss-Bonnet Gravity in Dark Energy Cosmologies

Luca Amendola, Christos Charmousis, Stephen C. Davis

TL;DR

This work analyzes a scalar-tensor cosmology in which a coupled Gauss-Bonnet term modifies gravity, deriving the linear perturbation equations in the linear post-Newtonian limit and expressing key observables γ and G_*/G in terms of GB density fractions Ω_i. Focusing on slow-roll dark energy and weak GB coupling (small α), the authors obtain tractable expressions showing how γ and the time variation of the effective gravitational coupling depend on Ω_1 and, to a lesser extent, Ω_2, with higher-order terms from Ω_3 and Ω_4 being subdominant. Using growth-rate data and ISW cross-correlations, they place a current bound |Ω_1| ≲ 0.15, indicating that the coupled GB term cannot dominate the dark energy budget at present, though future observations could tighten these constraints. The analysis demonstrates that cosmological perturbations offer a promising avenue to test higher-order gravity terms originating from KK compactifications or string-inspired effective theories, within the Einstein frame where energy-momentum conservation isolates GB effects from pure scalar dynamics.

Abstract

Models with a scalar field coupled to the Gauss-Bonnet Lagrangian appear naturally from Kaluza-Klein compactifications of pure higher-dimensional gravity. We study linear, cosmological perturbations in the limits of weak coupling and slow-roll, and derive simple expressions for the main observable sub-horizon quantities: the anisotropic stress factor, the time-dependent gravitational constant, and the matter perturbation growth factor. Using present observational data, and assuming slow-roll for the dark energy field, we find that the fraction of energy density associated with the coupled Gauss-Bonnet term cannot exceed 15%. The bound should be treated with caution, as there are significant uncertainies in the data used to obtain it. Even so, it indicates that the future prospects for constraining the coupled Gauss-Bonnet term with cosmological observations are encouraging.

Constraints on Gauss-Bonnet Gravity in Dark Energy Cosmologies

TL;DR

This work analyzes a scalar-tensor cosmology in which a coupled Gauss-Bonnet term modifies gravity, deriving the linear perturbation equations in the linear post-Newtonian limit and expressing key observables γ and G_*/G in terms of GB density fractions Ω_i. Focusing on slow-roll dark energy and weak GB coupling (small α), the authors obtain tractable expressions showing how γ and the time variation of the effective gravitational coupling depend on Ω_1 and, to a lesser extent, Ω_2, with higher-order terms from Ω_3 and Ω_4 being subdominant. Using growth-rate data and ISW cross-correlations, they place a current bound |Ω_1| ≲ 0.15, indicating that the coupled GB term cannot dominate the dark energy budget at present, though future observations could tighten these constraints. The analysis demonstrates that cosmological perturbations offer a promising avenue to test higher-order gravity terms originating from KK compactifications or string-inspired effective theories, within the Einstein frame where energy-momentum conservation isolates GB effects from pure scalar dynamics.

Abstract

Models with a scalar field coupled to the Gauss-Bonnet Lagrangian appear naturally from Kaluza-Klein compactifications of pure higher-dimensional gravity. We study linear, cosmological perturbations in the limits of weak coupling and slow-roll, and derive simple expressions for the main observable sub-horizon quantities: the anisotropic stress factor, the time-dependent gravitational constant, and the matter perturbation growth factor. Using present observational data, and assuming slow-roll for the dark energy field, we find that the fraction of energy density associated with the coupled Gauss-Bonnet term cannot exceed 15%. The bound should be treated with caution, as there are significant uncertainies in the data used to obtain it. Even so, it indicates that the future prospects for constraining the coupled Gauss-Bonnet term with cosmological observations are encouraging.

Paper Structure

This paper contains 8 sections, 43 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Second-order scalar-tensor theory
  3. Cosmological perturbation equations and the linear post-Newtonian limit
  4. Small-$\alpha$ limit
  5. Slow-roll limit
  6. Slow-roll, small-$\alpha$ regime
  7. Observing a coupled Gauss-Bonnet gravity
  8. Conclusion

Figures (1)

  • Figure 1: In this plot we show the constraints on $\Omega_{1}$ from the ISW effect (within the dotted lines) and from the growth rate $f$ of structures (grey region), assuming a present value $\Omega_{m}=0.3\pm0.1$.