Abstract
We show that the primordial gravitational wave with scale-invariant spectrum might emerge from a nearly Minkowski space, in which the gravity is asymptotic-past free. We illustrate it with a model, in which the derivative of background scalar field nonminimally couples to gravity. We also show that since here the tensor perturbation is dominated by its growing mode, mathematically our slowly expanding background is conformally dual to the matter contraction, but there is no the anisotropy problem.
Highlights
This suggests a scenario in which the scale-invariant adiabatic perturbation may emerge from nearly flat Minkowski spacetime
We show that since here the tensor perturbation is dominated by its growing mode, mathematically our slowly expanding background is conformally dual to the matter contraction, but there is no the anisotropy problem
M P,eff MP,eff where Θm defines a physical ruler measuring the evolution of background, the physical ruler is comprised of particles with mass m, Smatter = mds, and its length scale is set by the Compton wavelength λCompton ∼ 1/m of the particle, Θm > 0 signals that the background felt by the matter is expanding, otherwise it is contracting, while ΘP =MP−,1eff measures the evolutive behavior of 1/HT, and so the primordial GWs, the conformal invariance of perturbations suggests that conformally dual models have same
Summary
In which n > 0 and ǫ ∼ −(−t)n, which is the Minkowski spacetime in infinite past, and when 1/(−t)n ∼ 1, the slow expansion ends It has been observed earlier in [11] that such a spacetime might be responsible for scale-invariant adiabatical perturbation, and after the end of the slowly expanding phase, the universe may reheat and start to evolve with standard cosmology. During slow expansion, 1/(aHPer) ≪ 1/(aH), so the background is irrelevant with the origin of primordial perturbation, as clarified recently by Wetterich in [31]. The background (2.4) equals to that in emergent scenario [37], in which it was implemented by introducing a positive curvature, so its initial state is not flat Minkowski space, see [38]. 1 (t∗−t) is rapidly increasing during slow expansion, which may be induced by the nonminimal coupling of the scalar field to gravity, the primordial GWs may be scale-invariant [13]
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