[Paper Review] Beyond the Simplest Inflationary Cosmological Models

Alexei A. Starobinsky|arXiv (Cornell University)|Nov 23, 1998

Cosmology and Gravitation Theories3 citations

TL;DR

This paper extends the simplest inflationary models by exploring two new cosmological scenarios: (1) the possibility of an ongoing inflation-like phase, where cosmological distance and angular size measurements can constrain the inflaton potential; and (2) broken-scale-invariant models with localized features in the primordial power spectrum, potentially caused by fast phase transitions near inflation's end. The key contribution is identifying $k = 0.05\, h\,\text{Mpc}^{-1}$ as a critical scale for detecting such features.

ABSTRACT

Though predictions of the simplest inflationary cosmological models with cold dark matter, flat space and approximately flat initial spectrum of adiabatic perturbations are remarkably close to observational data, we have to go beyond them and to introduce new physics not yet discovered in laboratories to account for all data. Two extensions of these models which seem to be the most actual at present time are discussed. The first one is the possibility that we are living at the beginning of a new inflation-like era. Then classical cosmological tests, like the luminosity distance or the angular size of distant objects as functions of redshift, as well as the behaviour of density perturbations in a dustlike matter component including baryons as a function of redshift, can provide information sufficient for the unambiguous determination of an effective potential of a corresponding present inflaton scalar field. The second, unrelated extension is a possibility of broken-scale-invariant cosmological models which have localized steps or spikes in the primordial perturbation spectrum. These features can be produced by fast phase transitions in physical fields other than an inflaton field in the early Universe during inflation and not far from the end of it. At present, it seems that the only scale in the spectrum around which we might see something of this type is $k=0.05 h Mpc^{-1}$.

Motivation & Objective

• To address limitations in the simplest inflationary models with cold dark matter, flat geometry, and a nearly scale-invariant spectrum, which, while consistent with data, cannot fully account for all observations.
• To investigate the possibility that we are at the onset of a new inflation-like era, which could be probed through classical cosmological tests.
• To examine the implications of broken-scale-invariant models that produce localized steps or spikes in the primordial perturbation spectrum.
• To determine whether such features could arise from fast phase transitions in fields other than the inflaton, particularly near the end of inflation.
• To identify the most promising scale—$k = 0.05\, h\,\text{Mpc}^{-1}$—for detecting such features in current and future observational data.

Proposed method

• Analyzes classical cosmological distance and angular size relations as functions of redshift to constrain the effective potential of a present-day inflaton-like scalar field.
• Applies perturbation theory to dustlike matter components (including baryons) to study their redshift evolution in the context of ongoing inflation.
• Considers models with broken scale invariance that introduce localized steps or spikes in the primordial power spectrum of density perturbations.
• Uses effective field theory arguments to model fast phase transitions in non-inflaton fields during or near the end of inflation.
• Derives conditions under which such features would manifest at observable scales, particularly focusing on the $k = 0.05\, h\,\text{Mpc}^{-1}$ scale.
• Evaluates the detectability of such features using current and future cosmological data, especially from large-scale structure and CMB anisotropies.

Experimental results

Research questions

• RQ1 Can cosmological distance and angular size measurements in the present epoch provide unambiguous constraints on the effective potential of a scalar field driving a new inflation-like phase?
• RQ2 What observational signatures would arise from localized steps or spikes in the primordial power spectrum due to fast phase transitions in non-inflaton fields?
• RQ3 Is there a specific scale in the primordial power spectrum where such features are most likely to be detected with current observational sensitivity?
• RQ4 How do the dynamics of density perturbations in a dustlike matter component differ in models with ongoing inflation compared to standard cold dark matter models?
• RQ5 What physical mechanisms during or near the end of inflation could generate scale-localized features in the primordial spectrum without involving the inflaton field?

Key findings

• Classical cosmological tests—luminosity distance and angular size as functions of redshift—can uniquely determine the effective potential of a present-day inflaton-like scalar field if we are in a new inflation-like era.
• Localized features in the primordial power spectrum, such as steps or spikes, can be generated by fast phase transitions in fields other than the inflaton, particularly near the end of inflation.
• The scale $k = 0.05\, h\,\text{Mpc}^{-1}$ is identified as the most promising region for detecting such features in the primordial spectrum.
• The presence of such features would not require new physics in the inflaton sector but could arise from dynamics in other scalar fields during the final stages of inflation.
• The model suggests that observational data at $k = 0.05\, h\,\text{Mpc}^{-1}$ could distinguish between standard inflation and models with broken scale invariance and localized spectral features.