Generalized non-local $R^2$-like inflation

Abstract

The $R^2$ inflation which is an extension of general relativity (GR) by quadratic scalar curvature introduces a quasi-de Sitter expansion of the early Universe governed by Ricci scalar being an eigenmode of d'Alembertian operator. In this paper, we derive a most general theory of gravity admitting $R^2$ inflationary solution which turned out to be higher curvature non-local extension of GR. We study in detail inflationary perturbations in this theory and analyse the structure of form-factors that leads to a massive scalar (scalaron) and massless tensor degrees of freedom. We argue that the theory contains only finite number of free parameters which can be fixed by cosmological observations. We derive predictions of our generalized non-local $R^2$-like inflation and obtain the scalar spectral index $n_s\approx 1-\frac{2}{N}$ and any value of the tensor-to-scalar ratio $r<0.036$. In this theory, tensor spectral index can be either positive or negative $n_t\lessgtr 0$ and the well-known consistency relation $r=-8n_t$ is violated in a non-trivial way. We also compute running of the tensor spectral index and discuss observational implications to distinguish this model from several classes of scalar field models of inflation. These predictions allow us to probe the nature of quantum gravity in the scope of future CMB and gravitational wave observations. Finally we comment on how the features of generalized non-local $R^2$-like inflation cannot be captured by established notions of the so-called effective field theory of single field inflation and how we must redefine the way we pursue inflationary cosmology.

37 pages, 3 figures, Discussions extended, typos corrected, matches with the version published in JHEP

References in corpus (16)

• The Effective Field Theory of Inflation
• Observational Signatures and Non-Gaussianities of General Single Field Inflation
• Effective Field Theory for Inflation
• Inflationary cosmology in modified gravity theories
• No-ghost theorem for the fourth-order derivative Pais-Uhlenbeck oscillator model
• Resilience of the standard predictions for primordial tensor modes
• Predictions of quantum gravity in inflationary cosmology: effects of the Weyl-squared term
• Stochastic gravitational-wave background in quantum gravity
• Inflation and Alternatives with Blue Tensor Spectra
• Cosmological perturbations in non-local higher-derivative gravity
• Cosmological Signature of Tachyon Condensation
• New Cosmological Solutions of a Nonlocal Gravity Model
• Confining complex ghost degrees of freedom
• Non-Gaussianities in generalized non-local $R^2$-like inflation
• Positivity vs. Lorentz-violation: an explicit example
• Tree-level scattering amplitudes in nonlocal field theories

Cited by in corpus (13)

• On the superstring-inspired quantum correction to the Starobinsky model of inflation
• Tabletop potentials for inflation from $f(R)$ gravity
• Can nonlocal gravity really explain dark energy?
• Finding origins of CMB anomalies in the inflationary quantum fluctuations
• Cornering Extended Starobinsky Inflation with CMB and SKA
• Stability investigations of isotropic and anisotropic exponential inflation in the Starobinsky-Bel-Robinson gravity
• Precision predictions of Starobinsky inflation with self-consistent Weyl-squared corrections
• Primordial black holes save $R^2$ inflation
• Cosmology with Higher-Derivative Gravities
• Stability investigations of de Sitter inflationary solutions in power-law extensions of the Starobinsky model
• Observational Constraints on Asymptotic Safety Inflation in Gravity Rainbow
• Cosmic inflation in non-perturbative quantum gravity
• Gödel's Universe and the Local Limit of Nonlocal Gravity