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Ghost-free non-local $F(R)$ Gravity Compatible with ACT

Shin'ichi Nojiri, S. D. Odintsov, V. K. Oikonomou

TL;DR

This work investigates ghost-free non-local gravity within the $F(R)$ framework and tests its inflationary predictions against ACT and Planck/BICEP constraints. By introducing a scalar $\phi$ and auxiliary fields, the authors formulate a ghost-free, localizable theory that can be recast as an $F(R,\phi)$ model and admit a de Sitter background. They analyze two analytic realizations— a power-law $F(R)$ and a non-local $R^2$ model—deriving slow-roll observables and showing parameter choices that yield $n_s$ and $r$ in agreement with observations, thereby establishing viable inflationary phenomenology for ghost-free non-local gravity. The results highlight the potential of non-local, ghost-free gravity to explain early-universe dynamics and motivate further scrutiny of non-local modifications in cosmology.

Abstract

We confront the ghost-free non-local $F(R)$ gravity theories with the latest Atacama Cosmology Telescope (ACT) constraints on the spectral index of the scalar perturbations and the updated constraints of Planck/BICEP on the tensor-to-scalar ratio. After reviewing how the ghost-free non-local version of $F(R)$ gravity can be obtained, we show that the de Sitter solution can be obtained in this framework. Also, we show that the resulting theory can be cast in terms of an $F(R,φ)$ theory of gravity. We analyze two models of non-local $F(R)$ gravity, one power-law and the $R^2$ model, and we show that both models can be compatible with the ACT and updated Planck/BICEP constraints.

Ghost-free non-local $F(R)$ Gravity Compatible with ACT

TL;DR

This work investigates ghost-free non-local gravity within the framework and tests its inflationary predictions against ACT and Planck/BICEP constraints. By introducing a scalar and auxiliary fields, the authors formulate a ghost-free, localizable theory that can be recast as an model and admit a de Sitter background. They analyze two analytic realizations— a power-law and a non-local model—deriving slow-roll observables and showing parameter choices that yield and in agreement with observations, thereby establishing viable inflationary phenomenology for ghost-free non-local gravity. The results highlight the potential of non-local, ghost-free gravity to explain early-universe dynamics and motivate further scrutiny of non-local modifications in cosmology.

Abstract

We confront the ghost-free non-local gravity theories with the latest Atacama Cosmology Telescope (ACT) constraints on the spectral index of the scalar perturbations and the updated constraints of Planck/BICEP on the tensor-to-scalar ratio. After reviewing how the ghost-free non-local version of gravity can be obtained, we show that the de Sitter solution can be obtained in this framework. Also, we show that the resulting theory can be cast in terms of an theory of gravity. We analyze two models of non-local gravity, one power-law and the model, and we show that both models can be compatible with the ACT and updated Planck/BICEP constraints.
Paper Structure (9 sections, 70 equations, 2 figures)

This paper contains 9 sections, 70 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Non-local Gravity Models without Ghost
  3. Inflationary Phenomenology of Ghost-free non-Local $F(R)$ Gravity Theory
  4. de Sitter Spacetime as an Exact Solution
  5. General Inflationary Dynamics of the Ghost-free $f(R)$ Gravity
  6. Analytic Examples of ACT-Compatible Non-local $F(R)$ Gravity
  7. A Power-law $F(R)$ Model
  8. Non-local Ghost-free $R^2$ Model
  9. Conclusions

Figures (2)

  • Figure 1: Marginalized curves of the Planck 2018 data and the non-local power-law $F(R)$ gravity model, confronted with the ACT data, the Planck 2018 data, and the updated Planck constraints on the tensor-to-scalar ratio for $n=1.7657$, $\alpha=2$, $N=50$ and $\beta$ in the range $\beta=[0.625,0.626]$.
  • Figure 2: Marginalized curves of the Planck 2018 data and the non-local $R^2$ gravity model, confronted with the ACT data, the Planck 2018 data, and the updated Planck constraints on the tensor-to-scalar ratio for $\alpha=0.064667699$, $N=60$ and $\beta$ in the range $\beta=[299,300.1]$.