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| '''Primordial fluctuations''' are density variations in the early universe which are considered the seeds of all [[large-scale structure of the cosmos|structure]] in the universe. Currently, the most widely accepted explanation for their origin is in the context of [[cosmic inflation]]. According to the inflationary paradigm, the exponential growth of the [[Scale factor (cosmology)|scale factor]] during inflation caused [[quantum fluctuation]]s of the inflaton field to be stretched to macroscopic scales, and, upon leaving the [[Observable universe#Cosmological horizon|horizon]], to "freeze in".
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| At the later stages of radiation- and matter-domination, these fluctuations re-entered the horizon, and thus set the [[initial conditions]] for [[structure formation]].
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| The statistical properties of the primordial fluctuations can be inferred from observations of anisotropies in the [[Cosmic microwave background radiation|cosmic microwave background]] and from measurements of the distribution of matter, e.g., galaxy [[redshift survey]]s. Since the fluctuations are believed to arise from inflation, such measurements can also set constraints on parameters within inflationary theory.
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| ==Formalism==
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| Primordial fluctuations are typically quantified by a [[power spectrum]] which gives the power of the variations as a function of spatial scale. Within this formalism, one usually considers the fractional energy density of the fluctuations, given by:
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| :<math>\delta(\vec{x}) \ \stackrel{\mathrm{def}}{=}\ \frac{\rho(\vec{x})}{\bar{\rho}} - 1 =
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| \int \text{d}k \; \delta_k \, e^{i\vec{k} \cdot \vec{x}},</math> | |
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| where <math> \rho </math> is the energy density, <math>\bar{\rho}</math> its average and <math> k </math> the [[wavenumber]] of the fluctuations. The power spectrum <math> \mathcal{P}(k)</math> can then be defined via the ensemble average of the [[Fourier transform| Fourier components]]:
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| :<math> \langle \delta_k \delta_{k'} \rangle = \frac{2 \pi^2}{k^3} \, \delta(k-k') \, \mathcal{P}(k).</math>
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| Many inflationary models predict that the scalar component of the fluctuations obeys a [[power law]] in which
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| :<math>\mathcal{P}_\mathrm{s}(k) \propto k^{n_\mathrm{s} - 1}.</math>
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| For scalar fluctuations, <math>n_\mathrm{s}</math> is referred to as the scalar spectral index, with <math>n_\mathrm{s} = 1</math> corresponding to [[scale invariance|scale invariant]] fluctuations.
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| ==Adiabatic/isocurvature fluctuations==
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| [[Adiabatic]] fluctuations are density variations in all forms of [[matter]] and [[energy]] which have equal fractional over/under densities. So for example, an adiabatic [[photon]] overdensity of a factor of two would also correspond to an [[electron]] overdensity of two. For [[isocurvature]] fluctuations, the density variations for one component do not necessarily correspond to density variations in other components. While it is usually assumed that the initial fluctuations are adiabatic, the possibility of isocurvature fluctuations can be considered given current cosmological data. While the overall constraints are inconclusive, uncorrelated isocurvature [[cold dark matter]] modes are found to be unlikely.
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| ==Tensor modes==
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| The presence of primordial [[tensor fluctuation]]s (manifested as [[gravitational wave]]s) 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), and the ratio of the tensor to scalar power.
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| ==See also==
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| *[[Big Bang]]
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| *[[Cosmic microwave background radiation]]
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| *[[Cosmic inflation]]
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| *[[Large-scale structure of the cosmos]]
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| *[[Gravitational radiation]]
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| ==References and external links==
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| * Crotty, Patrick, "''[http://xxx.lanl.gov/abs/astro-ph/0306286 Bounds on isocurvature perturbations from CMB and LSS data]''". Physical Review Letters.
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| * Linde, Andrei, "''[http://xxx.lanl.gov/abs/gr-qc/9508019 Quantum Cosmology and the Structure of Inflationary Universe]''". Invited talk.
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| * Peiris, Hiranya, "''[http://xxx.lanl.gov/abs/astro-ph/0302225 First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Implications for Inflation]''". Astrophysical Journal.
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| * Tegmark, Max, "''[http://xxx.lanl.gov/abs/astro-ph/0310723 Cosmological parameters from SDSS and WMAP]''". Physical Review D.
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| [[Category:Physical cosmology]]
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| [[Category:Cosmic inflation]]
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