Primordial fluctuations
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Primordial fluctuations are
The statistical properties of the primordial fluctuations can be inferred from observations of
Formalism
Primordial fluctuations are typically quantified by a
where is the energy density, its average and the wavenumber of the fluctuations. The power spectrum can then be defined via the ensemble average of the Fourier components:
There are both scalar and tensor modes of fluctuations.[clarification needed]
Scalar modes
Scalar modes have the power spectrum defined as the mean squared density fluctuation for a specific wavenumber , i.e., the average fluctuation amplitude at a given scale:
Many inflationary models predict that the scalar component of the fluctuations obeys a power law[why?] in which
For scalar fluctuations, is referred to as the scalar spectral index, with corresponding to scale invariant fluctuations (not scale invariant in but in the comoving curvature perturbation for which the power is indeed invariant with when ).[1]
The scalar spectral index describes how the density fluctuations vary with scale. As the size of these fluctuations depends upon the inflaton's motion when these quantum fluctuations are becoming super-horizon sized, different inflationary potentials predict different spectral indices. These depend upon the slow roll parameters, in particular the gradient and curvature of the potential. In models where the curvature is large and positive . On the other hand, models such as monomial potentials predict a red spectral index . Planck provides a value of .[2]
Tensor modes
The presence of primordial tensor fluctuations is predicted by many inflationary models. As with scalar fluctuations, tensor fluctuations are expected to follow a power law and are parameterized by the tensor index (the tensor version of the scalar index). The ratio of the tensor to scalar power spectra is given by
where the 2 arises due to the two polarizations of the tensor modes. 2015 CMB data from the Planck satellite gives a constraint of .[2]
Adiabatic/isocurvature fluctuations
See also
- Big Bang
- Cosmological perturbation theory
- Cosmic microwave background spectral distortions
- Press–Schechter formalism
- Primordial gravitational wave
- Primordial black hole
References
External links
- Crotty, Patrick, "Bounds on isocurvature perturbations from CMB and LSS data". Physical Review Letters. arXiv:astro-ph/0306286
- Linde, Andrei, "Quantum Cosmology and the Structure of Inflationary Universe". Invited talk. arXiv:gr-qc/9508019
- arXiv:astro-ph/0302225
- Tegmark, Max, "Cosmological parameters from SDSS and WMAP". Physical Review D. arXiv:astro-ph/0310723