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Seed models in scalar field cosmology

I. V. Fomin

TL;DR

This work proposes a method to bound single-field inflationary dynamics in Einstein gravity by restricting the evolution to extreme values of the scalar field, then classifies the resulting dynamics and reconstructs corresponding slow-roll potentials. The approach recovers several canonical inflationary potentials and shows that, under GR, the seed models struggle to satisfy joint Planck and ACT constraints, often requiring problematic features such as future singularities or large negative cosmological constants. At late times, the framework yields ΛCDM-like behavior when a second accelerated epoch is considered, with a two-component fluid description showing how the scalar field can emulate matter or radiation and how the expansion history connects across cosmic eras. The study argues that to obtain viable inflationary dynamics within this extreme-value framework, one should adopt modified gravity theories, using the seed models as starting points for constructing testable GR extensions that can better accommodate observational data.

Abstract

The correspondence of single-field cosmological models based on Einstein gravity to modern observational data is considered. A method is proposed to determine possible types of dynamics based on extreme values of the scalar field. It is shown that within the framework of this approach, it is possible to obtain a limited class of known inflationary models at early times. It is also shown that on large times the proposed approach leads to the $Λ$CDM--model in order to describe the dynamics of the second accelerated expansion of the universe. An interpretation of the considered models is presented as a starting point for constructing verifiable cosmological models based on modified gravity theories.

Seed models in scalar field cosmology

TL;DR

This work proposes a method to bound single-field inflationary dynamics in Einstein gravity by restricting the evolution to extreme values of the scalar field, then classifies the resulting dynamics and reconstructs corresponding slow-roll potentials. The approach recovers several canonical inflationary potentials and shows that, under GR, the seed models struggle to satisfy joint Planck and ACT constraints, often requiring problematic features such as future singularities or large negative cosmological constants. At late times, the framework yields ΛCDM-like behavior when a second accelerated epoch is considered, with a two-component fluid description showing how the scalar field can emulate matter or radiation and how the expansion history connects across cosmic eras. The study argues that to obtain viable inflationary dynamics within this extreme-value framework, one should adopt modified gravity theories, using the seed models as starting points for constructing testable GR extensions that can better accommodate observational data.

Abstract

The correspondence of single-field cosmological models based on Einstein gravity to modern observational data is considered. A method is proposed to determine possible types of dynamics based on extreme values of the scalar field. It is shown that within the framework of this approach, it is possible to obtain a limited class of known inflationary models at early times. It is also shown that on large times the proposed approach leads to the CDM--model in order to describe the dynamics of the second accelerated expansion of the universe. An interpretation of the considered models is presented as a starting point for constructing verifiable cosmological models based on modified gravity theories.

Paper Structure

This paper contains 26 sections, 232 equations, 17 figures.

Table of Contents

  1. Introduction
  2. Inflationary models based on Einstein gravity
  3. The types of the cosmological dynamics
  4. Cosmological dynamics corresponding to extreme values of the scalar field
  5. The Lagrangian in terms of the Hubble parameter
  6. The Lagrangian in terms of the e-folds number and scale factor
  7. Cosmological dynamics from dependence $\dot{H}=\dot{H}(H)$
  8. The possible types of the cosmological dynamics
  9. Potentials of a scalar field in the slow-roll approximation
  10. Observational constraints on the inflationary models
  11. Verification of inflationary models by observational constraints
  12. Models without additional constant parameters in dependence $r=r(1-n_{S})$
  13. Models with additional constant parameters in dependence $r=r(1-n_{S})$
  14. Models without explicit dependence $r=r(1-n_{S})$
  15. Models with quadratic dependence $r\sim(1-n_{S})^{2}$
  16. ...and 11 more sections

Figures (17)

  • Figure 1: The dependence $\Delta N=\Delta N(r)$ for the spectral index of the scalar perturbations $n_S=0.9649\pm 0.0042$ (Planck). The values of $\Delta N$ lie within the region bounded by the curves.
  • Figure 2: The dependence $\Delta N=\Delta N(r)$ for the spectral index of the scalar perturbations $n_S=0.9649\pm 0.0042$. The values of $\Delta N$ lie within the region bounded by the curves.
  • Figure 3: The dependence $|\Delta\phi|=|\Delta\phi|(r)$ for the spectral index of the scalar perturbations $n_S=0.9649\pm 0.0042$. The values of $|\Delta\phi|$ lie within the region bounded by the solid curves.
  • Figure 4: The dependence $|\Delta\phi|=|\Delta\phi|(r)$ for the spectral index of the scalar perturbations $n_S=0.974\pm0.0030$ (ACT). The values of $|\Delta\phi|$ lie within the region bounded by the solid curves.
  • Figure 5: The dependence $\Delta N=\Delta N(r)$ for the spectral index of the scalar perturbations $n_S=0.9649\pm 0.0042$ (Planck). The values of $\Delta N$ lie within the region bounded by the curves.
  • ...and 12 more figures