Abstract We analyze the attractor behaviour of the inflation field in braneworld scenarios using the Hamilton-Jacobi formalism, where the Friedmann equation has the form of H2=ρ+ε√2ρ0ρ or H2=ρ+ερ2/2σ, with ε=±1. We find that in all models the linear homogeneous perturbation can decay exponentially as the scalar field rolls down its potential. However, in the case of a -ρ2 correction to the standard cosmology with ρ < σ, the existence of an attractor solution requires (σ-ρ)/φ2 > 1. Our results show that the perturbation decays more quickly in models with positive-energy correction than in the standard cosmology, which is opposite to the case of negative-energy correction. Thus, the positive-energy modification rather than the negative one can assist the inflation and widen the range of initial conditions.
(Higher-dimensional gravity and other theories of gravity)
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 10935013, 11175093, 11222545, and 11075083), the Natural Science Foundation of Zhejiang Province of China (Grant Nos. Z6100077 and R6110518), the FANEDD (Grant No. 200922), the National Basic Research Program of China (Grant No. 2010CB832803), and K. C. Wong Magna Fund in Ningbo University of China.
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