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Ch.02 The Origin of Our UniverseInflationary Big Bang

The Higgs field we already know might also have driven inflation.

Higgs Inflation

2008Fedor Bezrukov, Mikhail ShaposhnikovStrongly supported11 primary sources, 11 established Reviewed

The Higgs boson of the Standard Model, coupled strongly to spacetime curvature, drives inflation without any new particle.

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§1 · The claim, in one sentence

Bezrukov and Shaposhnikov proposed in 2008 that the Standard Model Higgs field drove inflation, provided it couples strongly to the curvature of spacetime, using only the particles of the Standard Model.

§2 · Why it might be true

needs a to drive the early expansion. Bezrukov and Shaposhnikov argued in 2008 that the Standard Model already has one, the Higgs. Their model adds no particle beyond those already present in the electroweak theory.

The key ingredient is a strong coupling between the Higgs and the curvature of spacetime, measured by the . Agreement with observations needs a dimensionless coupling of about ten thousand. At large field values this coupling gives the Higgs potential a long, nearly flat plateau. A ball on such a plateau rolls slowly, and that is the inflation needs.

The predictions sit very close to those of Starobinsky's R-squared model in the Geometric Modified Gravity family. Both give a spectral index near 0.97 and a tensor-to-scalar ratio near 0.003. Bezrukov and Gorbunov showed the two differ slightly, mainly because Higgs inflation reheats the universe to a higher temperature.

The family stance

Our universe began with a brief epoch of exponential expansion driven by a scalar field, followed by reheating into the hot Big Bang phase. The same inflaton field that drove expansion also generated the seed perturbations that became galaxies.

§2.5 · Evidence

  • Planck 2018 measured n_s = 0.9649 ± 0.0042, close to the predicted value of about 0.97, though many inflation models with a flat potential predict similar values
  • The predicted r of about 0.003 sits well below the BICEP/Keck and Planck upper limit of r < 0.036 (95% confidence, 2021)
  • Bezrukov, Magnin, Shaposhnikov and Sibiryakov found in 2011 that the theory's cutoff depends on the background Higgs field and stays above the relevant energies during inflation and reheating
  • Bezrukov, Rubio and Shaposhnikov showed in 2015 that inflation can still work if the electroweak vacuum is not absolutely stable, which the measured Higgs and top masses leave open

§3 · What you'd need to test it

  • In the , a spectral index n_s near 0.97 and a tensor-to-scalar ratio r near 0.003, almost independent of Standard Model parameters when the Higgs mass sits well above its critical value
  • A lower bound on the Higgs mass, because the Standard Model must stay a consistent theory up to the energy of inflation
  • If the Higgs mass sits within a few hundred MeV of that bound, n_s and r depend on the top-quark and Higgs masses, and r can be well above 0.003
  • A higher reheating temperature than in Starobinsky R-squared inflation, which gives slightly different n_s and r and a different allowed range for the Higgs mass

§4 · Where it breaks

  • Barbon and Espinosa argued in 2009 that the effective theory stops being valid at the Planck mass divided by the coupling, far below the field values inflation uses
  • Burgess, Lee and Trott found in 2009 that the Hubble rate during inflation sits close to the scale where the semiclassical treatment breaks down
  • Linking the inflationary parameters to collider measurements needs extra assumptions about the unknown high-energy completion, as Bezrukov and collaborators acknowledge
  • The predictions nearly coincide with Starobinsky R-squared inflation and with a class of supergravity attractor models, so CMB data alone struggle to single out the Higgs
  • ACT data combined with Planck, lensing and DESI give n_s = 0.974 ± 0.003. Some 2025 analyses read this as slightly above the simplest Higgs-inflation value, a tension that depends on the data combination and the model's high-energy details
Go deeper

The model adds a term ξ|H|²R to the action, where H is the Higgs doublet, R the Ricci scalar and ξ the non-minimal coupling. Agreement with observations needs ξ of order 10^4. Inflation takes place at field values |H| > M_P/√ξ, on the plateau of the potential. Kallosh, Linde and Roest showed that a broad class of supergravity plateau models shares attractor predictions, and for their α = 1 case these coincide with Starobinsky and Higgs inflation.

Barbon and Espinosa place the cutoff of the effective theory at Λ = M_P/ξ, well below the inflationary field values, so the potential there depends on the ultraviolet completion. Burgess, Lee and Trott reach a related conclusion from power counting, and note that curvature-squared models face similar issues. Bezrukov, Magnin, Shaposhnikov and Sibiryakov reply that the cutoff grows with the background field and stays above the dynamical scales throughout cosmic history. They also give a scheme for including loop corrections within effective field theory.

Bezrukov and Shaposhnikov (2014) show that the indices take universal values, r ≈ 0.003 and n_s ≈ 0.97, when the Higgs mass exceeds a critical value by more than a few hundred MeV. Near the critical value the indices depend on m_t and M_h, and the gravitational-wave amplitude can be considerably larger. The measured masses put the electroweak vacuum near the edge of absolute stability. Bezrukov, Rubio and Shaposhnikov (2015) keep inflation viable for a metastable vacuum, through a renormalization effect at M_P/ξ and thermal symmetry restoration after inflation. The same near-criticality underlies the Higgs Vacuum Decay variant in Chapter 7.

▸§5 · Who built it, and when(11 sources, 11 established)
Higgs Inflation, Fedor Bezrukov19801982198319952008

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