Starobinsky inflation
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| Starobinsky inflation | |
|---|---|
| Name | Starobinsky inflation |
| Field | Cosmology |
| Introduced | 1980 |
| Proponents | Alexei Starobinsky |
| Related | Inflationary cosmology; f(R) gravity |
Starobinsky inflation is a cosmological inflationary scenario proposed in 1980 by Alexei Starobinsky that modifies the gravitational action to generate an early accelerated expansion. It achieves a quasi-de Sitter phase via higher-order curvature corrections rather than a fundamental scalar field, producing specific predictions for the spectral index and tensor-to-scalar ratio that are highly relevant for cosmic microwave background experiments. The model sits at the intersection of quantum field theory in curved spacetime, modified gravity, and observational cosmology, and has informed connections to later proposals such as Higgs inflation and conformal inflation.
Background and theoretical motivation
Starobinsky introduced the model in the context of semiclassical gravity, drawing on results from Alexander Friedmann-era cosmology and developments in quantum corrections to general relativity studied by groups associated with Andrei Sakharov, Nikolay Bogoliubov, Lev Landau, Richard Feynman, and Pieter van Nieuwenhuizen. Influences include investigations of renormalization by researchers at Steklov Institute of Mathematics and work on trace anomalies by scholars connected to Moscow State University and Lebedev Physical Institute. The idea leveraged insights from the de Sitter space solution used by Georges Lemaître and Howard Robertson, and it paralleled independent inflationary proposals by Alan Guth and Andrei Linde while differing in mechanism. Historical antecedents also include semiclassical analysis by members of Landau Institute and concepts appearing in effective action treatments by scientists affiliated with Princeton University and Harvard University. The model gained renewed attention following precision measurements by COBE, WMAP, and Planck collaborations.
Starobinsky model formulation
The Starobinsky proposal modifies the Einstein–Hilbert action by adding an R^2 term inspired by one-loop corrections computed in curved backgrounds; this modification echoes approaches by authors associated with Soviet Union research schools and later by groups at Cambridge University and Institute for Advanced Study. In modern notation the action is closely related to f(R) theories studied at University of Tokyo and Stanford University. The R^2 term can be transformed by a conformal transformation into an equivalent scalar-tensor form resembling models developed at California Institute of Technology and Yale University, linking to potentials considered in work by Andrei Linde and scholars from Imperial College London. The scalaron degree of freedom introduced corresponds to a scalar field whose potential is similar to those used in chaotic inflation scenarios examined by researchers at Landau Institute and Syracuse University. The mathematical structure connects to techniques employed at ETH Zurich and Max Planck Institute for Astrophysics.
Cosmological dynamics and predictions
Cosmological dynamics in the Starobinsky model produce a slow-roll inflationary epoch with graceful exit and reheating processes analyzed by theorists from University of Cambridge and Kavli Institute for Cosmology. Predictions for the scalar spectral index and tensor-to-scalar ratio have been compared extensively with data from experimental groups including Atacama Cosmology Telescope, South Pole Telescope, and the Planck Collaboration, and with forecasts by teams at European Space Agency and NASA. Reheating mechanisms invoke interactions studied by physicists at CERN and SLAC National Accelerator Laboratory and connect to particle production analyses by researchers at Los Alamos National Laboratory and University of Chicago. The model's success in matching a low tensor-to-scalar ratio influenced survey strategies at facilities such as Subaru Telescope and Very Large Telescope.
Perturbations and observational constraints
Perturbation theory in the Starobinsky framework yields nearly scale-invariant adiabatic fluctuations with specific non-Gaussianity predictions debated in literature from groups at Princeton, Oxford University, University of California, Berkeley, and University of Pennsylvania. Constraints arise from observations by the Planck Collaboration, BICEP2, Keck Array, and analyses by teams at Institut d'Astrophysique de Paris and Kavli Institute for Cosmology, Cambridge. CMB polarization and lensing measurements from WMAP and Planck limit the allowed parameter space, while large-scale structure surveys like Sloan Digital Sky Survey and Dark Energy Survey provide complementary bounds. Studies by collaborations with members from Max Planck Institute for Gravitational Physics, Fermi National Accelerator Laboratory, and University of Toronto have explored implications for primordial black hole formation and baryogenesis scenarios treated at Perimeter Institute.
Extensions, variants, and relations to other models
Extensions and variants include embedding R^2 inflation into supergravity frameworks developed at University of Bonn and Tel Aviv University, and relations to Higgs-driven inflation investigated by research teams at CERN and University of Cambridge. Connections exist to conformal inflation and attractor models advanced by scholars at Institut des Hautes Études Scientifiques and University of Oxford, and to higher-derivative gravity studied at Yukawa Institute for Theoretical Physics and Sezione INFN di Roma. Renormalization group approaches linking to asymptotically safe gravity have been pursued by researchers at Perimeter Institute and University of Copenhagen. Phenomenological comparisons involve models proposed by Andrei Linde, Alexei Starobinsky's own later work, and those from groups at Princeton and Columbia University.
Mathematical derivations and exact solutions
Derivations employ techniques from differential geometry and variational calculus refined at Moscow State University, ETH Zurich, and Universität Wien, and utilize conformal transformations familiar in analyses by authors at Scuola Normale Superiore and University of Pisa. Exact solutions for homogeneous isotropic cosmologies with R^2 corrections have been constructed building on methods developed at Steklov Institute, Lebedev Physical Institute, and Landau Institute. Linear perturbation treatments rely on formalisms advanced at University of Cambridge and Princeton University, while nonperturbative analyses connect to work at Perimeter Institute and Institute for Advanced Study. Mathematical results continue to be refined by collaborations spanning Max Planck Institute for Gravitational Physics, Kavli Institute, and University of Tokyo.