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Kinetic Axion $F(R)$ Gravity Inflation

V. K. Oikonomou

arXiv:2208.05544v1gr-qcastro-ph.COhep-th

TL;DR

The paper asks how a kinetic misalignment axion affects R^2 inflation when the R^2 term dominates the equations of motion. It analyzes the axion’s constant-roll evolution and its effects on inflationary perturbations and the background near inflation’s end. The axion’s contribution cancels from leading-order observational indices, while its stiff era prolongs inflation.

  • Problem

    The paper examines whether a kinetic misalignment axion affects R^2 inflation, given that R^2 dominates the equations of motion but the axion may contribute through the second slow-roll index.

    Source: §III · p. 5, §IV · p. 10

  • Method

    The authors analyze kinetic misalignment axion dynamics in R^2-dominated F(R) inflation, tracking the slow-roll indices and the background evolution near inflation’s end.

    Source: §III · pp. 5–6

  • Results

    The axion’s constant-roll contribution cancels from leading-order observational indices, while its stiff equation of state prolongs inflation beyond 60 e-foldings.

    Source: §III · pp. 6–7

  • Takeaways & Limitations

    The axion’s effect on inflation is expressed through its influence on the duration and e-folding count rather than a contribution to the leading-order observational indices.

    Source: §III · pp. 6–7

    The late-time evolution of the unified model, including the axion’s evolution when it begins oscillating as dark matter, is left for future work.

    Source: §IV · p. 11

Abstract

from arXiv · show

In this work we investigate the quantitative effects of the misalignment kinetic axion on $R^2$ inflation. Due to the fact that the kinetic axion possesses a large kinetic energy which dominates its potential energy, during inflation its energy density redshifts as stiff matter fluid and evolves in a constant-roll way, making the second slow-roll index to be non-trivial. At the equations of motion level, the $R^2$ term dominates the evolution, thus the next possible effect of the axion could be found at the cosmological perturbations level, via the second slow-roll index which is non-trivial. As we show, the latter elegantly cancels from the observational indices, however, the kinetic axion extends the duration of the inflationary era to an extent that it may cause a 15$\%$ decrease in the tensor-to-scalar ratio of the vacuum $R^2$ model. This occurs because as the $R^2$ model approaches its unstable quasi-de Sitter attractor in the phase space of $F(R)$ gravity due to the $\langle R^2 \rangle $ fluctuations, the kinetic axion dominates over the $R^2$ inflation and in effect the background equation of state is described by a stiff era, or equivalently a kination era, different from the ordinary radiation domination era. This in turn affects the duration of the inflationary era, increasing the $e$-foldings number up to $5$ $e$-foldings in some cases, depending on the reheating temperature, which in turn has a significant quantitative effect on the observational indices of inflation and especially on the tensor-to-scalar ratio.

I. INTRODUCTION

The introduction motivates a study of kinetic misalignment axions in R^2 inflation, where the axion’s main effects are expected in perturbations and the duration of inflation. It presents modified gravity as a framework for inflation and dark energy and identifies the axion’s stiff, constant-roll evolution as central to the analysis.

I. INTRODUCTION

  • The axion is introduced as a light axion-like particle whose primordial Peccei-Quinn symmetry breaks during inflation, allowing a non-zero vacuum expectation value.Source: §I · p. 1
  • Modified gravity is presented as a framework for describing both inflation and dark energy without the stated shortcomings of scalar-field descriptions.Source: §I · p. 2
  • The paper investigates how a kinetic misalignment axion affects R^2 inflation within F(R) gravity.Source: §I · p. 2
  • The axion’s constant-roll evolution makes the second slow-roll parameter non-trivial, but its contribution cancels from the observational indices.Source: §I · p. 2
  • The axion’s stiff kination era can prolong inflation and increase the total number of e-foldings.Source: §I · p. 2

II. ESSENTIAL FEATURES OF THE F(R) GRAVITY-KINETIC AXION MODEL

This section specifies an F(R) model combining R^2 inflation with a kinetic misalignment axion. The axion’s large initial kinetic energy dominates its potential, producing stiff-fluid behavior and delaying oscillations relative to canonical misalignment.

II. ESSENTIAL FEATURES OF THE F(R) GRAVITY-KINETIC AXION MODEL

  • The assumed F(R) model combines an R^2 term for primordial inflation with a power-law R^δ term for late-time dynamics.Source: §II · p. 3
  • The model treats the axion as a misalignment axion with broken primordial Peccei-Quinn symmetry, a non-zero vacuum expectation value, and an initial velocity.Source: §II · p. 3
  • Kinetic misalignment delays axion oscillations relative to canonical misalignment; after oscillations begin, the axion energy density redshifts as dark matter.Source: §II · p. 4
  • For the kinetic axion to account for the present dark matter abundance, its decay constant must satisfy f_a ≤ 1.5 × 10^11 GeV.Source: §II · p. 4
  • During inflation, the axion’s kinetic energy exceeds its potential energy, and its energy density redshifts as a^-6 with stiff-fluid equation of state w = 1.Source: §II · p. 4
  • The authors state that the stiff axion fluid prolongs the inflationary era.Source: §II · p. 5

III. DYNAMICS OF INFLATION FOR THE KINETIC AXION F(R) GRAVITY MODEL

The R^2 term controls the inflationary background, while the kinetic axion’s stiff constant-roll evolution introduces a nontrivial slow-roll index that cancels from leading observational indices. After the unstable de Sitter phase, axion kination prolongs inflation and changes the tensor prediction in a reheating-temperature-dependent, Planck-compatible model.

  • During inflation, radiation and axion densities redshift as e^-4N and e^-6N, respectively, leaving R^2 dominant in the field equations and producing a quasi-de Sitter solution.The solution's integration constant H_I sets the inflationary scale.Source: §III · p. 5
  • The stiff axion equation gives ε2 = -3, but its contribution cancels from the leading-order scalar spectral index.Source: §III · p. 6
  • At leading order, n_s ∼ 1 − 2/N and r ∼ 12/N^2, matching Starobinsky phenomenology for N ∼ 60.Source: §III · p. 7
  • The tensor-to-scalar ratio differs by about 15% from standard R^2 inflation at N = 60, while the kinetic-axion model fits the Planck likelihood sweet spot across reheating temperatures of 10^7–10^12 GeV.The paper describes the kinetic-axion model as a measurable deformation of vacuum R^2 predictions.Source: Figure 3 · p. 9, §III · p. 10
  • After the unstable de Sitter point repels the system, the axion kinetic term drives a w = 1 stiff era before oscillations allow ordinary reheating to begin.The R^2 model has an unstable de Sitter fixed point; the axion-driven stiff phase extends the number of e-foldings.Source: Figure 2 · p. 7, §III · pp. 8–9
  • The R^2 term enhances the kinetic-axion dynamics and delays the onset of oscillations, while the resulting e-fold extension depends strongly on reheating temperature.Source: §III · pp. 9–10

IV. CONCLUSIONS

The kinetic axion leaves R^2 inflation’s perturbation-level observational indices unchanged, but can extend inflation and alter the tensor-to-scalar ratio. Its late-time evolution in the unified model remains a topic for future study.

IV. CONCLUSIONS

  • Up to 5 additional e-foldings in some cases accompany an approximately 15% decrease in the tensor-to-scalar ratio versus vacuum R^2 inflation.As R^2 inflation approaches its unstable quasi-de Sitter attractor, the axion can dominate and produce a stiff, kination-like era with total equation-of-state parameter w = 1.Source: §IV · p. 10
  • The axion’s large, constant-roll second slow-roll index cancels from the observational indices, leaving R^2 inflation unaffected at the perturbation level.At the equations-of-motion level, vacuum R^2 dynamics dominate; the axion’s effect instead arises through the duration of inflation.Source: §IV · p. 10
  • The unified model’s late-time evolution remains for future study, including the axion’s oscillatory phase, when its energy density redshifts as dark matter.The authors also identify an Einstein-Gauss-Bonnet extension as an avenue for future investigation.Source: §IV · pp. 10–11
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