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    Possible antigravity regions in <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd" xmlns:sa="http://www.elsevier.com/xml/common/struct-aff/dtd"><mml:mi>F</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>R</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math> theory?

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    Possible antigravity regions in F(R)F(R) theory?

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    We construct an F(R)F(R) gravity theory corresponding to the Weyl invariant two scalar field theory. We investigate whether such F(R)F(R) gravity can have the antigravity regions where the Weyl curvature invariant does not diverge at the Big Bang and Big Crunch singularities. It is revealed that the divergence cannot be evaded completely but can be much milder than that in the original Weyl invariant two scalar field theory.The work is supported in part by the JSPS Grant-in-Aid for Young Scientists (B) # 25800136 (K.B.); that for Scientific Research (S) # 22224003 and (C) # 23540296 (S.N.); and MINECO (Spain), FIS2010-15640 and AGAUR (Generalitat de Catalunya), contract 2009SGR-345, and MES project 2.1839.2011 (Russia) (S.D.O.). D.S.-G. also acknowledges the support from the University of the Basque Country, Project Consolider CPAN Bo. CSD2007-00042 (Spain) and the URC financial support from the University of Cape Town (South Africa).Peer reviewe
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