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COBE, Gravitational Waves, Inflation and Extended Inflation
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abstract
We analyse the implications for inflationary models of the cosmic microwave background (cmb) anisotropy measured by COBE. Vacuum fluctuations during inflation generate an adiabatic density perturbation, and also gravitational waves. The ratio of these two contributions to the cmb anisotropy is given for an arbitrary slow-roll inflaton potential. Results from the IRAS/QDOT and POTENT galaxy surveys are used to normalise the spectrum of the density perturbation on the scale $20h^{-1}\Mpc$, so that the COBE measurement on the scale $10^3h^{-1}\Mpc$ provides a lower bound on the spectral index $n$. For `power law' and `extended' inflation, gravitational waves are significant and the bound is $n>0.84$ at the $2$-sigma level. For `natural' inflation, gravitational waves are negligible and the constraint is weakened to $n>0.70$, at best marginally consistent with a recent proposal for explaining the excess clustering observed in the APM galaxy survey. Many versions of extended inflation, including those based on the Brans--Dicke theory, are ruled out, because they require $n\lsim 0.75$ in order that bubbles formed at the end of inflation should not be observed now in the cmb.
Forward citations
Cited by 4 Pith papers
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When inflationary perturbations refuse to classicalise: the role of non-Gaussianity in Wigner negativity
In ultra-slow-roll inflation, the Wigner function of the inflationary Goldstone field becomes negative and its negativity grows with the scale factor squared, so the perturbations do not automatically become classical.
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Connecting Early Dark Energy to Late Dark Energy by the Diluting Matter Potential
A scale-invariant model uses a diluting-matter-dependent potential to connect early and late dark energy via tunneling, alleviating the Hubble tension with best-fit early dark energy fraction ~0.3 at z~5000.
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Primordial Gravitational Waves in Quadratic Gravity
In quadratic gravity, the inflationary tensor power spectrum is suppressed by (1 + 2H_*^2/m_gh^2)^{-1}, which restores the standard consistency relation r = -8n_t.
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The Goldstone Awakens: Unimodular dark energy in scale-invariant $R^2$ gravity
In a scale-invariant R² + unimodular-gravity model, the Goldstone boson of scale symmetry becomes thawing dark energy, with its equation of state fixed by the same coupling that sets the inflationary spectral tilt.
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