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Astrophysics and cosmology after Gamow: recent progress and new horizons 18 August 2009, Odessa

Cosmology of Modified Gravity. Astrophysics and cosmology after Gamow: recent progress and new horizons 18 August 2009, Odessa. Tomi S. Koivisto Insititut f ϋ r Theoretische Physik, Heidelberg. Need for energy sources in cosmology. Modification of gravity (MG)?.

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Astrophysics and cosmology after Gamow: recent progress and new horizons 18 August 2009, Odessa

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  1. Cosmology of Modified Gravity Astrophysics and cosmology after Gamow: recent progress and new horizons 18 August 2009, Odessa Tomi S. Koivisto Insititut fϋr Theoretische Physik, Heidelberg

  2. Need for energy sources in cosmology Modification of gravity (MG)? Adjustment of the matter sector? • Dark matter - Rotation curves of galaxies, structure formation etc. - Particle still unobserved • Dark energy - Observed acceleration: huge fine-tuning of Λ - MG could address dynamically • Inflation - MG natural candidate to drive inflation - or even evade it: bouncing cosmologies!

  3. Regimes of gravity 10-3cm 1AU 1kpc 1Mpc 1000Mpc Modified gravity? Large extra d? GR, tight constrains! MOND? Solar system tests Cosmological perturbations Newtons law Universal Expansion Ultraviolet modification: effects in early universe Infrared modification: may have cosmological effects but... • Structure formation: sensitively probe alternative cosmologies! • Solar system tests: exclude many gravity models!

  4. Gravity actions -A higher derivative extension of the Einstein-Hilbert action: - generically, result in ghosts and instabilities. An exception: (?) Woodard, Lect. Notes Phys.720:403-433 (2007) Woodard, Motivations • a prototype (simplest?) generalisation, special case of scalar-tensor - produces acceleration: R^2 resolves initial singularity, generates inflation - renormalizable gravity Starobinsky, Phys. Lett. B91: 99-102, (1980)

  5. Metric f(R) theories Results in the field 4th order equations (F=f’(R)) Introducing an auxiliary field one may write this as a scalar-tensor theory And by a conformal transformation this turns into a coupled quintessence

  6. Scalar-tensor: frames Matter ψ Matter ϕ ψ

  7. Can higher derivative corrections accelerate the universe at late times? Review: S. Nojiri, S.D. Odintsov, Int. J. Geom. Met. Mod. Phys. 4, 115 (2007) ►an example: f(R)=R+aR^n ►n=-1 : The CDTT model Carroll, Duvvuri, Trodden, Turner Phys.Rev. D70 (2004) 043528 Matter era Radiation era Is not compatible with the standard matter era, w=0, but w=1/3 instead! Requiring 1) Saddle point MD 2) Late de Sitter attractor restricts severely the possible forms of f(R) Acceleration Amendola, Gannouji, Polarski, Tsujikawa Phys.Rev D75: 083504 (2007)

  8. Viable forms of metric f(R) models? ► Avoid antigravity: f’(R)>0 ► Stability: f’’(R)>0 (scalaron mass M^2 ~ 1/3f’’) R ► Local constraints: M >>1/lenght m(r) = Rf’’/f’ r = -Rf’/f ► Matter era: m>0, m’(r)>0, at MD saddle point, and dS exists Some cleverly wrought lagrangians do satisfy all this: Hu and Sawicki Phys.Rev.D76:064004,2007 Starobinsky JETP Lett.86:157-163,2007 Miranda, Joras, Waga and Quartin Phys.Rev.Lett.102:221101,2009 ...where R_C is of the order of the present Hubble rate squared, RC = 10^(-66) eV^2...

  9. Potentially viable modified gravities... -A higher derivative extension of the Einstein-Hilbert action: - generically, result in ghosts and instabilities. Woodard, There are interesting ways out of those higher derivative theories: 1) An alternative variational principle: Palatini formalism 2) A particular curvature combination: Gauss-Bonnet term 3) Infinite order derivatives theories: Nonlocal modifications

  10. The Palatini form of f(R) • Consider the metric and the affine connection as independent • Iff f=R, equivalent to metric variation: one then gets GR - The trace R(T) algebraically! - The hatted Riccis the conformal metric: ...And what it might be good for? -Conceptually: 1st order -Practically: Simpler calculations -Theoretically: No ghosts! -Locally: Escapes Solar system constraints -Cosmologically? Let us see... T.K.: Class. Quant. Grav. 23 4289 (2006)

  11. MG: Geometric tests Geometric quantities to measure: Comoving distance r(z) =  dz/H(z) Standard Candles dL(z) = (1+z) r(z) Standard Rulers dA(z) = r(z)/(1+z) Standard Population dV/dzd = r2(z)/H(z) All the physics is in H(z), or equivalently, w(z) ! Observations: SNIa, BAO, CMB shift.

  12. Palatini-f(R) cosmology - The modified Friedman equation allows to solve H(R(z)) M. Amarzuioui, O. Elgaroy, D.F. Mota, T. Multamaki Astron.Astrophys. 454 (2006) 707-714 • Simple functions can generate RD->MD->dS

  13. Structure formation in MG Generic effects from Generic effects due to modified gravity: (in an f(R) case consider ψ = f’(R)-1). - Effective anisotropic stress appears (relevant for weak lensing?) - Poisson equationis different too (detectable in the ISW?) - Matter growthis given by the G* (constraints from LSS !)

  14. Palatini-f(R) cosmology: linear structure - Perturbations in pressureless matter: T.K. & H. Kurki-Suonio: Class.Quant.Grav. 23 (2006) 2355-2369 • A(t) and B(t) determine the growth rate in the large-scale limit • The ”sound speed" • is a problem at small scales If C<0, explosions If C>0, oscillations

  15. Viability of Palatini-f(R) gravity Well,again RC=10^(-66) eV^2 ... But also tight constraints from SDSS data: |β| < few*(0.00001) T.K.: Phys.Rev. D73 (2006) 083517 • Avoided by fine-tuning dark matter • such that T.K.: Phys.Rev. D76 (2007) 043527 • Dark energy: Difficult (without extra assumptions) • Early cosmology: Graceful exit problem in inflation • Matter bounce from the modified Friedmann?

  16. Gauss-Bonnet gravity 2nd order • Higher derivatives occur linearly • In D=4, the term is topological • In FRW: G = -12H^4(3w-1) alone trivial Couple non-minimally (from e.g. compactification) a) f(G) models b) more generally: Motivation: - Uniqueness of the action requires G - Most general scalar-tensor theory couples to G - String theory: leading α' corrections include G!

  17. COSMOLOGY OF GAUSS-BONNET DARK ENERGY -Consider an exponential model: An analysis of the phase space reveals: Practically ARBITRARY initial conditions The "EXACT TRACKING" solution of a self-tuning scalar field Possible PHANTOM era (transient) Potential dominates: DE SITTER expansion Instability of perturbationsmight occur: return to matter domination? T.K. & DavidF. Mota: Phys.Lett.B64 104 (2007)

  18. GAUSS-BONNET DARK ENERGY: BACKGROUND CONSTRAINTS Consider an exponentialmodel: Solid: SNeIa (GOLD) Dashed: SNeIa + CMB Peaks Colors: SNeIa + CMB Peaks + BAO Addresses the fine-tuning problems since - Scales V0 about 1/κ^4 and f0 about 1 - Parameters λ and α of order 1 ! - Initial conditions don't matter T.K. & DavidF. Mota: Phys.Lett.B64 104 (2007)

  19. PERTURBATIONS IN GAUSS-BONNET COSMOLOGY T.K. & DavidF. Mota: Phys.Lett.B64 104, Phys.Rev.D75 023518 (2007)

  20. Conclusions Extensions of the E-H action - Can be ghost-free and cosmologically viable - Could model inflation and dark energy - Exhibit interesting modifications to LSS Do they provide a dynamical solution to Λ? - f(R): complicated form, scale Λreappears - Palatini: almost Λ, or then fine-tuned dark matter - Gauss-Bonnet: addresses the Λ-problem

  21. Appendix I: Nonlocal gravity terms - Then, how to alleviate the fine-tuning? - Dimensionless combinations, like G/R^2? No, ghosts appear. - Dividing dimensions away like R/□ ? May be… - A simplemodel: - For dark energy f should be about ~ -1 nowadays No unnatural scales : Less fine tuning? R vanishes during RD : Answer to coincidence? - Quantumcorrections t’ Hooft & Veltman: Annales Poincare Phys.Theor.A20:69-94,1974 Deser & Nieuwenhuizen: Phys. Rev. D 10, 401 (1974) Etc.

  22. Appendix II: cosmological applications ...of effective actions: LC =  R□-1R - Could stabilize the Euclidean action - Constraints from BBN C. Wetterich: Gen.Rel.Grav.30:159-172,1998 LC = f(r□-1 Rrm□-1R) Soussa & Woodard: CQG 20, 2737, 2003 - Nonlocal formulation of MOND - Fails weak lensing and early universe LC =  R log(/2) R Espriu, Multamaki & Vagenas: Phys. Lett. B 628 (2005) - The leading loop correction (?) - Secular effect to inflation possible LC = Rf(R/) S. Deser & R.P. Woodard: Phys.Rev.Lett.99:111301,2007. - Recent suggestion: could provide dark energy - This we’ll pursue here... T.K. : Phys.Rev.D77:123513,2008 (dynamics) Phys.Rev.D78:123505,2008 (structure)

  23. Appendix III: Biscalar-tensor formulation Introduce a field and a Lagrange multiplier: Define : - Equivalent to a local model with two extra d.o.f ! - Massless fields with a nonlinear sigma -type (kinetic) interaction

  24. Appendix IV: summary of cosmic evolutions n>0 f(x)=Nxn Nonlocal effect N(-1)n>0 N(-1)n<0 n<0 Slows down expansion Acceleration Matter domination Regularized Singularity ?

  25. Appendix V: Scalar modes • Go to Einstein frame, diagonalise and pick up the • entropy and isocurvature modes: F(ϕ,ξ) - Classically the evolution is causal and stable - Typically F<0, which results in a ghostmode

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