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Starobinsky R-squared Inflation

Starobinsky 1980, the foundational paper. An R-squared term drives early-universe inflation.

Family status
Strongly supported
Proposed
1980
Sources
2
Reader votes
0
Basis: indirect
The CMB spectrum and flat space match what inflation predicts, but the field and potential that drove it are unknown.

1The claim

The original higher-curvature gravity proposal: an R-squared term in the action drives a phase of cosmic inflation in the very early universe. Starobinsky 1980 is the foundational work that originated the higher-curvature gravity research program.

2Why it might be true

Starobinsky's 1980 framework was developed in the context of the early universe, not late-time cosmology. Adding an R-squared term to the gravitational action introduces a higher-derivative dynamics whose perturbative behavior matches the slow-roll inflation paradigm. The constant of proportionality of the R-squared term determines the inflationary phenomenology; current Planck data constrain this constant tightly.

The construction is connected to the late-time f(R) work in the Ch.5 Geometric Modified Gravity family: both modify the gravitational action with higher-curvature terms, but with different parameterizations and at different cosmological epochs. The 1980 paper is the conceptual ancestor; the modern work extends and refines the framework to specific cosmological problems.

Starobinsky inflation predicts a specific tensor-to-scalar ratio that has been a benchmark for inflation searches. ACT's 2025 data put the simplest version at the edge of the two-sigma range. The verdict depends on how the universe reheated after inflation, which is still highly uncertain.

3Evidence so far

  • Current Planck 2018 data (with 2020 follow-up analyses) is consistent with Starobinsky inflation in the small-r region of parameter space; the model is among the most successful inflation candidates
  • The 1980 paper is the canonical reference for higher-curvature inflation
  • The framework connects naturally to the modern late-time f(R) work via the higher-curvature gravity research program (cross-reference: Ch.5 Geometric Modified Gravity family)
  • Independent supergravity completions (no-scale models, alpha-attractor inflation) often reduce to Starobinsky-style attractors in their inflationary regimes; the framework has multiple UV-physics motivations

A tightly curved early-universe spacetime sheet that smooths and gently expands, the R-squared higher-curvature term driving a burst of cosmic inflation in Starobinsky's 1980 model.

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4What would test it

4 predictions

  • An R-squared term in the gravitational action produces a phase of slow-roll inflation in the very early universe with specific perturbation spectra
  • The model predicts a tensor-to-scalar ratio of order 0.003 to 0.004, in tension with some other inflation models that predict larger values
  • The predicted shape of primordial density ripples (the scalar spectral index n_s, a measure of how the strength of those ripples changes with scale, and its running, how that slope itself drifts) matches what the Planck satellite's map of the cosmic microwave background sees, under appropriate parameter ranges
  • The framework should be testable by future CMB B-mode polarization measurements (LiteBIRD, CMB-S4, Simons Observatory) that probe the tensor-to-scalar ratio

5Where it breaks

4 objections, plus 3 shared

  • Current data constrains the Starobinsky parameter range tightly; the model is testable rather than free, and next-generation B-mode measurements will either confirm or restrict it sharply
  • The R-squared model requires a specific scale for the higher-curvature term that does not have a deep first-principles explanation
  • The framework is one of several viable inflation candidates; selecting Starobinsky over other models awaits sharper observational constraints
  • The 1980 paper predates the modern formulation of f(R) gravity; some technical subtleties of the inflationary slow-roll evolution were worked out in subsequent literature rather than in the original paper

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Technical register

Stated precisely

Alexei Starobinsky proposed in 1980, in a paper published before the arXiv existed, that an R-squared term added to the Einstein-Hilbert action drives a phase of cosmic inflation in the very early universe. The 1980 paper is the foundational work for the entire higher-curvature gravity research program and predates the modern late-time f(R) constructions (Ch.5 Geometric Modified Gravity family) by 27 years.

The R-squared term in the gravitational action has dimension four (in 4D spacetime), so it is renormalizable in the standard power-counting sense. This was originally noted by Stelle in the context of curvature-squared gravity in 1977 (cross-reference: Ch.4 Asymptotic Safety family, Higher-Derivative Gravity Extensions variant). Starobinsky's 1980 paper applied this insight specifically to inflation.

The Starobinsky inflation framework has been extensively connected to UV physics: no-scale supergravity reduces to Starobinsky-style attractors; alpha-attractor inflation models also flow to Starobinsky-like behavior in their slow-roll regimes. The framework has multiple motivated UV completions, which is unusual for inflation models.

inflation
A brief burst of accelerating expansion in the very early universe, smoothing out and stretching whatever existed before.

6Who built it, and when

  1. 1

    established

    no count, pre-arXiv

  2. 2

    established

    no count yet

Inflationary Big Bang, all 6 variants

Lead variant first, then by year

  1. Modern Slow-Roll Inflation1983 and 2018
  2. Starobinsky R-squared Inflationthis page1980
  3. Warm Inflation1995 and 2020
  4. Higgs Inflation2008
  5. Old Inflation1980 and 1981
  6. New Inflation1982

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