Could dark energy be modified gravity or related to matter? Rachel Bean Cornell University In collaboration with: David Bernat (Cornell) Michel Liguori (Cambridge) Scott Dodelson (Fermilab) Levon Pogosian (Simon Fraser) Alessandra Silvestri (Syracuse) Mark Trodden (Syracuse)
Outline Bit of motivation F(R) gravity Can we distinguish between modified gravity and matter dark energy?
What is the underlying nature of dark energy? Adjustment to gravity? - Non-minimal couplings to gravity? Higher dimensional gravity? Cosmological constant? -Early phase transitions? -Holographic? -Anthropic? Adjustment to matter? -An exotic, dynamical matter component? Unified Dark Matter?
Tackling the fine-tuning problem Scalar!(x,t) - spin 0 particle (e.g Higgs). Accelerative expansion when potential dominates Scaling potentials Scaling potentials Evolve as dominant background matter Wetterich 1988, Ferreira & Joyce 1998 Tracker potentials Insensitive to initial conditions Ratra & Peebles 1988 Wang, Steinhardt, Zlatev 1999 Tracker potentials Potential V(!). Kinetic! 2 /2
Tackling the coincidence problem: are we special? We re not special: universe sees periodic epochs of acceleration w(z) evolution with an oscillatory potential V~M 4 e -"! (1+Asin #!) Dodelson, Kaplinghat, Stewart 2000 W tot We are special: the key is our proximity to the matter/ radiation equality Non-minimal coupling to matter (Amendola 2000, Bean & Magueijo 2001) log(a) Dodelson, Kaplinghat, Stewart 2000 w(z) evolution with a non-minimal coupling to dark matter k-essence : A dynamical push after z eq with nontrivial kinetic Lagrangian term (Armendariz-Picon, et al 2000) w tot log(a) Bean & Magueijo 2001
Tackling the dark matter and dark energy problems as one Unified dark matter/ dark energy Clustering at early times like CDM, w~0, c s 2 ~0 Accelerating expansion at late times like $, w <0 Evolution of equation of state for Chaplygin Gas Phenomenology: Chaplygin gases an adiabatic fluid, parameters w 0, % w lg(a) Bean and Dore PRD 68 2003 Strings interpretation? Born-Infeld action is of this form with % =1 (e.g. Gibbons astroph/0204008 )
Modifications to gravity rather than matter Quintessential inflation (e.g. Copeland et al 2000) Randall Sundrum like scenario Curvature on the brane (Dvali,Gabadadze Porrati 2001) Gravity 5D (Minkowski) on large scales l>l c &1/H 0 i.e. only visible at late times Although 4D on small scales not Einstein gravity Large scale modifications to GR Modifies at large scales R~H 0 2 Potential implications for solar system tests as well as horizon scales
Why modify gravity? Theories predict a modification Scalar-tensor gravity We don t have a clue what dark energy is - matter or gravity? e.g. could it be an f(r) theory? e.g. could it contain higher geometric derivatives? Conceivably, we don t yet have the correct large (and small?) scale theory of gravity?
Tight constraints on gravity from solar system Solar system tests e.g. Cassini ' ( = 2x10 )3 ( PPN 1 0 1 2 * PPN Figure: Takeshi Chiba Future constraints will be tighter 2011 (?) GAIA could get ' ( < 10 )6 2012 ESA Bepi-Columbo Mercury orbiter ' ( < 3x10 )5, ' * < 3x10 )4
Modified gravity -> time varying G BBN abundances (Copi, Davis, Krauss 2003) z= 10 10 +0.20 G/G 0 = 1.01 (68%) -0.16 Lunar radar ranging z=0 dg/dt/g<8x10-12 yr -1 G/G N =1.21 G/G N =1.01 G/G N =0.85 CMB (Nagata-Chiba-Sugiyama,2004) z=1100 (G recom -G 0 )/G 0 <0.05 Copi, Davis, Krauss 2003
f(r) theories : Jordan frame Modified gravity, minimally coupled matter Normal GR Modification to GR Normal matter
f(r) theories : Jordan frame Modified gravity, minimally coupled matter Modified Einstein field equations
f(r) theories : Jordan frame Modified gravity, minimally coupled matter Modified Einstein field equations Modified Friedmann and acceleration equations Modifies how the universe s expansion history is determined by matter Way to resolve acceleration equations need for (++3P)<0
An alternative perspective :Einstein frame Conformal transformation (Chiba 2003) [*=! ( 2/3)]
An alternative perspective :Einstein frame Conformal transformation (Chiba 2003) [*=! ( 2/3)] Einstein gravity, non-minimally coupled matter
An alternative perspective :Einstein frame Conformal transformation (Chiba 2003) [*=! ( 2/3)] Einstein gravity, non-minimally coupled matter Cosmological variables redefined with! dependence
An alternative perspective :Einstein frame Fluid equations are coupled between matter- scalar field
An alternative perspective :Einstein frame Fluid equations are coupled between matter- scalar field Expansion history has normal gravity but non-minimally coupled matter with scalar field that can have negative pressure Benefits (but no physical implication) Equations more intuitive (at least to me) in this frame Dynamical evolution also easier to understand - attractor behavior
Attractor behavior Amendola 1999, Copeland et al 2006, use Einstein frame dynamical variables Attractor behavior (fractional energy densities constant) when
Attractor behavior Amendola 1999, Copeland et al 2006, use Einstein frame dynamical variables Attractor behavior (fractional energy densities constant) when Amendola et al 2006, coupling alters matter dominated era evolution - behaves like radiation in Jordan frame! Late time acceleration determined by V(!)&exp(-"!)
Jordan frame : observed frame Usually interpret observations e.g. redshifts assuming atomic physics in distant galaxy/ supernovae, CMB is the same as on Earth Equivalent to Jordan frame (matter minimally coupled to scalar field) Translate back Einstein attractor to Jordan frame However we also usually interpret expansion history assuming GR complications of dark energy due to extra matter e.g. scalar field Actual: Assumed: This leads to apparent strange interpretation in Jordan frame
An example: f(r) =-µ 4 /R
Perturbation evolution in Jordan frame Time and spatial derivatives of the coupling come into play Jordan frame - tricky to understand
Perturbation evolution in the Einstein frame Easier evolution picture in Einstein frame First order equations unchanged from normal GR if define matter variable
Perturbation evolution in the Einstein frame Easier evolution picture in Einstein frame First order equations unchanged from normal GR if define matter variable Full Einstein equations similar to simple quintessence (+ coupling)
Perturbation evolution in the Einstein frame Easier evolution picture in Einstein frame First order equations unchanged from normal GR if define matter variable Full Einstein equations similar to simple quintessence (+ coupling) Transformation back to Jordan frame density perturbation
An example: f(r) = -µ 1 exp(-r/µ 2 ) $CDM JF CDM EF CDM EF scalar PRD 75 (2007) 064020, astro-ph/0611321
An example: f(r) = -µ 4 /R $CDM JF CDM EF CDM EF scalar PRD 75 (2007) 064020, astro-ph/0611321
An example: f(r) = -µ 1 exp(-r/µ 2 ) Same initial normalization Renormalized to fit small scales $CDM SDSS Galaxies fit OK CMB does not PRD 75 (2007) 064020, astro-ph/0611321
An example: f(r) = -µ 4 /R Same initial normalization Renormalized to fit small scales $CDM SDSS Galaxies fit OK CMB does not PRD 75 (2007) 064020, astro-ph/0611321
Distinguishing between modified gravity and matter DE f(r) theories that behave similar to $ do not suffer attractor problem e.g f(r)& exp(-r/" H 02 ) for ">>1 Could we still hope to distinguish them? Maybe Normal GR the Poisson equation gives the relationship between matter and gravity Newtonian gauge No shear stress Poisson equation Zhang, Liguori, Bean, Dodelson arxiv:0704.193
Distinguishing between modified gravity and matter DE f(r) theories that behave similar to $ do not suffer attractor problem e.g f(r)& exp(-r/" H 02 ) for ">>1 Could we still hope to distinguish them? Maybe Normal GR the Poisson equation gives the relationship between matter and gravity Newtonian gauge No shear stress Poisson equation Modified gravity theories introduce an effective shear stress Scale dependent shear stress Modified Poisson Zhang, Liguori, Bean, Dodelson arxiv:0704.193
Distinguishing between modified gravity and matter DE f(r) theories that behave similar to $ do not suffer attractor problem e.g f(r)& exp(-r/" H 02 ) for ">>1 Could we still hope to distinguish them? Maybe Normal GR the Poisson equation gives the relationship between matter and gravity Newtonian gauge No shear stress Poisson equation Modified gravity theories introduce an effective shear stress Scale dependent shear stress Modified Poisson Zhang, Liguori, Bean, Dodelson arxiv:0704.193
Observational test of modified gravity Compare correlations of matter power spectrum based variables Zhang, Liguori, Bean, Dodelson arxiv:0704.193
Observational test of modified gravity Compare correlations of matter power spectrum based variables Can hope to distinguish between theories by measuring a range of scales Zhang, Liguori, Bean, Dodelson arxiv:0704.193
Observational test of modified gravity Compare correlations of matter power spectrum based variables Can hope to distinguish between theories by measuring a range of scales With future large scale structure surveys Zhang, Liguori, Bean, Dodelson arxiv:0704.193
Observational test of modified gravity Can hope to distinguish between theories by measuring a range of scales 0.4<z<0.6 1.3<z<1.7 0.85<z<1.15 1.8<z<2.2 $CDM DGP f(r) TeVeS K=0.1 TeVeS K=0.09 TeVeS K=0.08 Zhang, Liguori, Bean, Dodelson arxiv:0704.193
Conclusions Low curvature modifications to gravity offer an alternative to dark energy Perturbation and background evolution altered by modification Einstein frame gives easier route into perturbation calculations Attractor evolution leads to large scale suppression in comparison to LCDM can rule out many theories under this banner Distinguishing between the alternatives viable E.g. comparison of galaxy-velocity and galaxy-lensing observations