Primordial Power Spectrum Characteristics in Inflationary Cosmology

The primordial power spectrum describes the distribution of curvature perturbations generated during cosmic inflation as a function of comoving wavenumber. Inflationary models naturally yield an almost scale-invariant, Gaussian spectrum, with slight departures from exact scale invariance characterised by the spectral index and its running. These small deviations encode information about the inflaton potential, the dynamics of slow-roll parameters and possible high-energy physics beyond the Standard Model. More intricate imprints, such as oscillatory or step-like features, may arise from transient particle production, sharp changes in the inflaton trajectory or pre-inflationary phases. Observations of the cosmic microwave background anisotropies and large-scale structure trace the primordial spectrum over a wide range of scales, setting constraints on its amplitude, tilt and higher-order modulations. Advances in nonlinear reconstruction techniques, joint analyses of the power spectrum and bispectrum, and combined probes from galaxy clustering and weak lensing are sharpening sensitivity to subtle features. The evolving observational landscape promises to test inflationary scenarios with unprecedented precision, offering a direct window on physics at energy scales far beyond terrestrial experiments.

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Technical terms

Primordial power spectrum: The distribution of initial curvature perturbations generated during inflation, expressed as power per unit logarithmic interval of wavenumber.

Scale invariance: A property of a spectrum whose amplitude is independent of scale, often approximated by a spectral index of unity.

Spectral index: A parameter quantifying the tilt of the primordial spectrum relative to exact scale invariance; departures reflect the dynamics of inflation.

Slow-roll inflation: A regime in which the inflaton field evolves gradually down its potential, characterised by small slow-roll parameters that determine the spectrum’s tilt and running.

Primordial features: Localised or oscillatory deviations from a simple power law in the primordial spectrum, arising from transient events or high-energy physics during inflation.

References

1. Euclid: The search for primordial features⋆. Astronomy & Astrophysics (2024).
2. Searching for local features in primordial power spectrum using genetic algorithms. Monthly Notices of the Royal Astronomical Society (2024).