Astron. Astrophys. 347, 799-808 (1999)

An analytic approximation of MDM power spectra in four dimensional parameter space

B. Novosyadlyj ¹, R. Durrer ² and V.N. Lukash <sup>3

1</sup> Astronomical Observatory of L'viv State University, Kyryla and Mephodia str. 8, 290005, L'viv, Ukraine
² Department of Theoretical Physics, University of Geneva, Ernest Ansermet, CH-1211 Geneva 4, Switzerland
³ Astro Space Center of Lebedev Physical Institute of RAS, Profsoyuznaya 84/32, 117810 Moscow, Russia

Received 6 November 1998 / Accepted 9 March 1999

Abstract

An accurate analytic approximation of the transfer function for the power spectra of primordial density perturbations in mixed dark matter models is presented. The fitting formula in a matter-dominated Universe () is a function of wavenumber k, redshift z and four cosmological parameters: the density of massive neutrinos, , the number of massive neutrino species, , the baryon density, and the dimensionless Hubble constant, h. Our formula is accurate in a broad range of parameters: , , , , , . The deviation of the variance of density fluctuations calculated with our formula from numerical results obtained with CMBfast is less than for the entire range of parameters. It increases with and is less than for .

The performance of the analytic approximation of MDM power spectra proposed here is compared with other approximations found in the literature (Holtzman 1989; Pogosyan & Starobinsky 1995; Ma 1996; Eisenstein & Hu 1997b). Our approximation turns out to be closest to numerical results in the parameter space considered here.

Key words: cosmology: large-scale structure of Universe

Send offprint requests to: Bohdan Novosyadlyj

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Contents

• 1. Introduction
• 2. Physical scales which determine the form of MDM transfer function
• 3. An analytic approximation for the MDM transfer function
  • 3.1. Dependence on and z
  • 3.2. Dependence on and h
  • 3.3. Dependence on
• 4. Performance
• 5. Comparison with other analytic approximations
• 6. Conclusions
• Acknowledgements
• Appendix
• References

© European Southern Observatory (ESO) 1999

Online publication: June 6, 1999
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