Scale-free power spectrums in the delayed cosmology

The delayed cosmology [D. Choudhury et al., J. Cosmol. Astropart. Phys. 02 (2012) 046] assumes that the evolution of geometries is delayed relative to that of matter and/or energy. This idea allows inflation to occur without inflaton fields or vacuum energies of any kind. We consider the production and evolution of primordial perturbations in this model. The results indicate that we could obtain a nearly scale-free power spectrum consistent with observations starting from a totally radiation-dominated early universe.

Figure 1

By introducing a delay to the source term of the Friedmann equation, inflation is obtained in the absence of an extra scalar field, and it is accompanied by a smooth graceful exit for a wide range of $\alpha$. In this figure the delay parameter is chosen as $\tau =10t_{\text{pl}}$. Inflation lasts for the period $\tau <t<2\tau$.

Figure 2

The power spectrum of scalar (left panel) and tensor (right panel) perturbations in the delayed inflation with preinflation scale factor $a(0<t\le \tau )\sim t^{\alpha }$, $\alpha =0$ (green line), $\pm 0.03$ (red or blue line).

Figure 3

The distribution of error function (27) on the $H_i-\alpha$ and $\tau -\alpha$ plane.

Figure 4

Power spectrum of matter distributions predicted by the delayed inflation and delayed $\mathrm{\Lambda }\mathrm{CDM}$ cosmology with delayed ${10}^6{t}_{\mathrm{pl}}$. The magnitude and shape of this late time power spectrum are very close to observations provided in Refs. [19, 20, 21].