[itex]\sigma_8[/itex] is the current amplitude of the matter power spectrum on that scale (as inferred by linear cosmological evolution). This parameter basically encodes information about how much large-scale structure has formed.bapowell said:[itex]n_s[/itex] is the spectral index of the scalar power spectrum ([itex]P(k) \sim k^{n_s -1}[/itex]). [itex]\sigma_8[/itex] is the amplitude of the power spectrum on the scale of 8 Mpc/h.
Sigma_8 and n_s are two important parameters in cosmology that describe the distribution and fluctuations of matter in the universe. Sigma_8, also known as the rms matter fluctuation amplitude on a scale of 8 Mpc/h, measures the amplitude of density fluctuations in the universe. n_s, or the scalar spectral index, describes the tilt or slope of the primordial power spectrum of density fluctuations.
These two parameters are important because they provide crucial information about the structure and evolution of the universe. They help us understand how matter is distributed on different scales and how it has evolved over time. They also provide constraints for various cosmological models and theories, helping us to better understand the origins and fate of the universe.
Sigma_8 and n_s are typically measured through observations of the cosmic microwave background (CMB) radiation, which is the oldest light in the universe. The CMB carries imprints of the early universe and can be used to infer the values of these parameters. Other methods include studying the large-scale structure of the universe through galaxy surveys and using gravitational lensing effects.
The current best-fit values for Sigma_8 and n_s are 0.811 and 0.966, respectively. These values were obtained from data collected by the Planck satellite, which is a space observatory operated by the European Space Agency. However, these values may vary slightly depending on the cosmological model being used.
Changes in these parameters can have significant implications for our understanding of the universe. For example, a higher value of Sigma_8 would mean a more clumpy and clustered distribution of matter, while a lower value would indicate a smoother distribution. Similarly, a higher value of n_s would suggest a more scale-invariant density fluctuation spectrum, while a lower value would imply a steeper spectrum. These changes can affect our understanding of the composition, evolution, and eventual fate of the universe.