Emergent universe revisited through the CSL theory

Abstract

In this work we analyze how the spectrum of primordial scalar perturbations is modified, within the emergent universe scenario, when a particular version of the Continuous Spontaneous Localization (CSL) model is incorporated as the generating mechanism of initial curvature perturbations, providing also an explanation to the quantum-to-classical transition of such perturbations. On the other hand, a phase of super-inflation, prior to slow-roll inflation, is a characteristic feature of the emergent universe hypothesis. In recent works, it was shown that the super-inflation phase could generically induce a suppression of the temperature anisotropies of the CMB at large angular scales. We study here under what conditions the CSL maintains or modifies these characteristics of the emergent universe and their compatibility with the CMB observations.

Emergent universe: tensor perturbations within the CSL framework

“…The work [175] was carried out within the framework of semiclassical gravity, where it is well known from previous works [72,74,75] that tensor perturbations would be practically null, remarkably consistent with current observational constraints [6,13,[16][17][18][19]. On the other hand, the exploration of studies in the framework of standard quantization (SQ), where a joint metric-matter quantization is performed, has also been done in many works, e.g.…”

“…We will be working under the same assumptions of [131,175], i.e. the action of General Relativity with a scalar field φ minimally coupled to gravity and driving the early expansion.…”

“…On the other hand, the spatial curvature is quickly negligible after a few e-foldings and furthermore slow-roll inflation can always be made to end for some negative value of φ [132]. As in [166,175], in this work we will make a first approach to the analysis and therefore we will neglect the contributions of the space curvature to the primordial perturbations. 3 As usual in perturbation analysis, we will separate the metric and the scalar field into a homogeneous background plus small perturbations, i.e.…”

“…In this subsection, we will focus on deriving a prediction for the primordial spectrum of the tensor perturbations. Notice that, since the equations have the same mathematical structure, we will closely follow the steps shown in [175] for the scalar spectrum case.…”

“…poles. In [175], some of us showed that implementing the CSL mechanism to the emergent universe scenario introduces extra modifications in the CMB temperature angular spectrum. Specifically, the angular spectrum in the low multipoles sector can exhibit a suppression or an increment, something different from what happens in the case of the standard EU, where the super-inflation phase only causes the spectrum curve to decrease on large angular scales.…”