Beyond Einstein Gravity A Survey of Gravitational Theories for Cosmo
Beyond Einstein’s Gravity is a graduate level introduction to extended theories of gravity and cosmology, including variational principles, the weak-field limit, gravitational waves, mathematical tools, exact solutions, as well as cosmological and astroph
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Series Editors Philippe Blanchard, Universit¨at Bielefeld, Bielefeld, Germany Paul Busch, University of York, Heslington, York, United Kingdom Bob Coecke, Oxford University Computing Laboratory, Oxford, United Kingdom Detlef D¨urr, Mathematisches Institut, M¨unchen, Germany Roman Frigg, London School of Economics and Political Science, London, United Kingdom Christopher A. Fuchs, Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada Giancarlo Ghirardi, University of Trieste, Trieste, Italy Domenico Giulini, University of Hannover, Hannover, Germany Gregg Jaeger, Boston University CGS, Boston, USA Claus Kiefer, University of Cologne, Cologne, Germany Klaas Landsman, Radboud Universiteit Nijmegen, Nijmegen, The Netherlands Christian Maes, K.U. Leuven, Leuven, Belgium Hermann Nicolai, Max-Planck-Institut f¨ur Gravitationsphysik, Golm, Germany Vesselin Petkov, Concordia University, Montreal, Canada Alwyn van der Merwe, University of Denver, Denver, USA Rainer Verch, Universit¨at Leipzig, Leipzig, Germany Reinhard Werner, Leibniz University, Hannover, Germany Christian W¨uthrich, University of California, San Diego, La Jolla, USA
For further volumes: http://www.springer.com/series/6001
Salvatore Capozziello
Valerio Faraoni
Beyond Einstein Gravity A Survey of Gravitational Theories for Cosmology and Astrophysics
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Prof. Salvatore Capozziello Universit`a di Napoli Federico II Dipartimento di Scienze Fisiche Via Cinthia 80126 Napoli Italy [email protected]
Prof. Valerio Faraoni Physics Department Bishop’s University 2600 College Street Sherbrooke, QC Canada J1M 1Z7 [email protected]
ISBN 978-94-007-0164-9 e-ISBN 978-94-007-0165-6 DOI 10.1007/978-94-007-0165-6 Springer Dordrecht Heidelberg London New York Library of Congress Control Number: 2010938912 c Springer Science+Business Media B.V. 2011 No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Cover design: SPi Publisher Services Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
To Donovan, Emanuele, and Francesca Sofia
Preface
There are good theoretical reasons to consider seriously the possibility that gravity is not described precisely by Einstein’s General Relativity but rather by some alternative theory. First, attempts to renormalize General Relativity in the 1960s and 1970s showed clearly that counterterms must be introduced which alter the theory significantly and make its field equations of fourth order instead of second. From the physical point of view, this fact implies that extra degrees of freedom, in addition to the usual spin two graviton, need to be introduced. Unfortunately, the corrected theory is not free of
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