Towards inflation and dark energy cosmologies from modified Gauss-Bonnet theory

TL;DR

The paper develops a four-dimensional scalar-tensor cosmology in which a field-dependent Gauss-Bonnet coupling f(σ) augments a standard scalar potential V(σ). This framework yields inflation in the early universe and late-time acceleration, with an evolving effective potential Λ(σ) = V(σ) − f(σ) 𝒢 that can dynamically relax to the observed small dark-energy scale, while GB effects can be subdominant at late times. By exploiting symmetry-based relations, the authors derive exact analytic solutions for a range of ansätze, analyze slow-roll parameters and perturbations, and discuss reheating via a friction-like δ term that transfers energy to radiation. They show that a small tensor-to-scalar ratio and a nearly scale-invariant scalar spectrum can be achieved for suitable parameter choices, and they outline observationally testable predictions and constraints, including nucleosynthesis bounds and the evolution of the deceleration parameter. The work extends quintessence-like models by incorporating a dynamical GB coupling, offering a unified route to two accelerated epochs within a string-inspired effective action.

Abstract

We consider a physically viable cosmological model that has a field dependent Gauss-Bonnet coupling in its effective action, in addition to a standard scalar field potential. The presence of such terms in the four dimensional effective action gives rise to several novel effects, such as a four dimensional flat Friedmann-Robertson-Walker universe undergoing a cosmic inflation at early epoch, as well as a cosmic acceleration at late times. The model predicts, during inflation, spectra of both density perturbations and gravitational waves that may fall well within the experimental bounds. Furthermore, this model provides a mechanism for reheating of the early universe, which is similar to a model with some friction terms added to the equation of motion of the scalar field, which can imitate energy transfer from the scalar field to matter

Figures (12)

• Figure 1: The function $\xi(\sigma)$ (solid line) is symmetric about $\sigma\to -\sigma$, while its first derivative, ${\rm d}{\xi}/d\sigma$ (dotted line) is antisymmetric. Note that in these plots we have set $\delta=1$.
• Figure 2: The contour plots of the effective potential $\Lambda(\sigma)/H_0^2$ with the height in log scale. The single solid (blue) line denotes where ${\rm d} {\Lambda}/{{\rm d} N}=0$, giving the local maximum of the potential w.r.t. $\Delta N$. For larger $\Delta N$, the potential generically decreases exponentially to zero.
• Figure 3: The kinetic term $K/H_0^2$ (left plot) and the dimensionless variable $x$ (right plot), in logarithmic scales, as functions of $\alpha$ and $\Delta N$, where $x \equiv (\gamma/2) (\dot{\sigma}/H)^2 = K/H^2=(\gamma/2){\sigma^\prime}^2$. For $\alpha> 1$ (or $\alpha < -6$), $K<0$ and hence $x<0$, leading to a phantom type cosmology. For $-6< \alpha <0.45$, $K/H_0^2$ rapidly approaches zero. In all plots, where applicable, we have set $u_t=10$.
• Figure 4: The ratio $\Lambda(\sigma)/2K(\sigma)$ in logarithmic scale, in different ranges for $\alpha$.
• Figure 5: The solution is modelled such that $\ln(1+z) \equiv \Delta N=\ln\frac{a_f}{a_i}$. One can see a change from deceleration to acceleration as the red-shift factor $z$ decreases in the range $0.5\lesssim z \lesssim 1.5$.