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

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

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

1 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


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 ([FORMULA]) is a function of wavenumber k, redshift z and four cosmological parameters: the density of massive neutrinos, [FORMULA], the number of massive neutrino species, [FORMULA], the baryon density, [FORMULA] and the dimensionless Hubble constant, h. Our formula is accurate in a broad range of parameters: [FORMULA], [FORMULA], [FORMULA], [FORMULA], [FORMULA], [FORMULA]. The deviation of the variance of density fluctuations calculated with our formula from numerical results obtained with CMBfast is less than [FORMULA] for the entire range of parameters. It increases with [FORMULA] and is less than [FORMULA] for [FORMULA].

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

© European Southern Observatory (ESO) 1999

Online publication: June 6, 1999