arXiv:astro-ph/0109152v1 10 Sep 2001 Mon. Not. R. Astron. Soc. 000, 000–000 (0000) Printed 1 February 2008 (MN L A T E X style file v1.4) Evidence for a non-zero Λ and a low matter density from a combined analysis of the 2dF Galaxy Redshift Survey and Cosmic Microwave Background Anisotropies G. Efstathiou 1,2 , Stephen Moody 1 , John A. Peacock 3 , Will J. Percival 3 , Carlton Baugh 4 , Joss Bland-Hawthorn 5 , Terry Bridges 5 , Russell Cannon 5 , Shaun Cole 4 , Matthew Colless 6 , Chris Collins 7 , Warrick Couch 8 , Gavin Dalton 9 , Roberto De Propis 8 , Simon P. Driver 10 , Richard S. Ellis 11 , Carlos S. Frenk 4 , Karl Glazebrook 12 , Carole Jackson 6 , Ofer Lahav 1 , Ian Lewis 5 , Stuart Lumsden 13 , Steve Maddox 14 , Peder Norberg 4 , Bruce A. Peterson 6 , Will Sutherland 3 , Keith Taylor 11 (The 2dFGRS Team) 1. Institute of Astronomy, Madingley Road, Cambridge CB3 OHA. UK. 2. Theoretical Astrophysics, Caltech, Pasadena, CA 91125, USA. 3. Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh, EH9 3HJ, UK. 4. Department of Physics, University of Durham, South Road, Durham DH1 3LE, UK. 5. Anglo-Australian Observatory, P.O. Box 296, Epping, NSW 2121, Australia. 6. Research School of Astronomy and Astrophysics, The Australian National University, Weston Creek, ACT 2611, Australia 7. Astrophysics Research Institute, Liverpool John Moores University, Twelve Quays House, Birkenhead, L14 1LD, UK 8. Department of Astrophysics, University of New South Wales, Sydney, NSW 2052, Australia. 9. Astrophysics, Nuclear and Astrophysics Laboratory, University of Oxford, Keble Road, Oxford OX1 3RH, UK. 10. School of Physics and Astronomy, University of St Andrews, North Haugh, St Andrews, Fife, KY6 9SS, UK. 11. Department of Astronomy, Caltech, Pasadena, CA 91125, USA. 12. Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD 21218-2686, USA. 13. Department of Physics, University of Leeds, Woodhouse Lane, Leeds, LS2 9JT, UK. 14. School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD, UK. 1 February 2008 ABSTRACT We perform a joint likelihood analysis of the power spectra of the 2dF Galaxy Red- shift Survey (2dFGRS) and the cosmic microwave background (CMB) anisotropies under the assumptions that the initial fluctuations were adiabatic, Gaussian and well described by power laws with scalar and tensor indices of n s and n t . On its own, the 2dFGRS sets tight limits on the parameter combination Ω m h ⋆ , but relatively weak limits on the fraction of the cosmic matter density in baryons Ω b /Ω m . The CMB anisotropy data alone set poor constraints on the cosmological constant and Hubble constant because of a ‘geometrical degeneracy’ among parameters. Furthermore, if tensor modes are allowed, the CMB data allow a wide range of values for the physical densities in baryons and cold dark matter (ω b =Ω b h 2 and ω c =Ω c h 2 ). Combin- ing the CMB and 2dFGRS data sets helps to break both the geometrical and tensor mode degeneracies. The values of the parameters derived here are consistent with the predictions of the simplest models of inflation, with the baryon density derived from primordial nucleosynthesis and with direct measurements of the Hubble parameter. In particular, we find strong evidence for a positive cosmological constant with a ±2σ range of 0.65 < Ω Λ < 0.85, completely independently of constraints on Ω Λ derived from Type Ia supernovae. Key words: Galaxy clustering, large-scale structure, cosmic microwave background- cosmology: miscellaneous. ⋆ Here h is Hubble’s constant H 0 in units of 100kms -1 Mpc -1 . The cosmic densities in baryons, cold dark matter and vacuum c  0000 RAS