Gravity and Λ Pedro G. Ferreira Oxford Oslo, 2015 Thursday, 15 January 15
Outline • Can gravity solve the Λ problem in cosmology ? • Can we use cosmology to constrain gravity ? Thursday, 15 January 15
Modifying Gravity Thursday, 15 January 15
Einstein Gravity ! Curvature ! 1 Z Z d 4 x √− gR ( g ) + d 4 x √− g L ( g, matter) 16 π G Metric of space time ! Lovelock’s theorem (1971) : “The only second-order, local gravitational field equations derivable from an action containing solely the 4D metric tensor (plus related tensors) are the Einstein field equations with a cosmological constant.” See also Hojman, Kuchar & Teitelboim (1976) 4 Thursday, 15 January 15
Einstein Gravity Curvature Metric of space-time Lovelock’s theorem (1971) : “The only second-order, local gravitational field equations derivable from an action containing solely the 4D metric tensor (plus related tensors) are the Einstein field equations with a cosmological constant.” See also Hojman, Kuchar & Teitelboim (1976) 5 Thursday, 15 January 15
The Feynman/Weinberg “Theorem” Feynman (1963) Spin-2 field Weinberg (1965) Deser (1970) Couple to matter: Self energy of the graviton: Unique non-linear completion is GR... Thursday, 15 January 15
The Problem Λ • The naturalness problem • The hierarchy problem • The why now problem • Massive gravity Thursday, 15 January 15
Effective Field Theory “Cutoff”: but Thursday, 15 January 15
Einstein-Dilaton- Cascading gravity Lorentz violation Gauss-Bonnet Conformal gravity Ho ř ava-Lifschitz Strings & Branes ✓ R ◆ f ( G ) f ⇤ DGP Randall-Sundrum Ⅰ & Ⅱ Some degravitation Higher-order scenarios 2T gravity Higher dimensions Non-local General R μν R μν , f ( R ) ☐ R,etc. Kaluza-Klein Modified Gravity Vector Einstein-Aether Generalisations Lorentz violation of S EH New degrees of freedom Massive gravity TeVeS Bigravity Gauss-Bonnet Chern-Simons Tensor Scalar-tensor & Brans-Dicke Lovelock gravity Ghost condensates Cuscuton EBI Galileons Chaplygin gases Bimetric MOND the Fab Four Scalar arXiv: KGB 1310.1086 f(T) 1209.2117 Coupled Quintessence Einstein-Cartan-Sciama-Kibble 1107.0491 Horndeski theories 1110.3830 Torsion theories Tessa Baker 2013 Thursday, 15 January 15
Three (failed) attempts • Massive gravity • Unimodular gravity • Non-local gravity Thursday, 15 January 15
Massive gravity Why bother? • Technically natural (a la t’Hooft)- a small parameter such that the restores a symmetry (GC invariance in this case) remains small. • Massive gravity may be used to degravitate (i.e. supress effect of long wavelength sources). Thursday, 15 January 15
Massive gravity Massive gravity: weak field Fierz-Pauli Action Static, spherically symmetric solution: Modified gravitation Thursday, 15 January 15
Massive gravity Massive Gravity: non-linear theory Hassan-Rosen DeRahm-Gabadadze-Tolley where we define with eigenvalues and Thursday, 15 January 15
Massive gravity • Only an effective theory valid up to: Burrage, Kaloper, Padilla 2013 Noller, Scargill, Ferreira 2014 • Not clear if bigravity is well-posed (hyperbolicity). L. Lehners (private comm.) • Simplest DRGT does not give flat FRW universe. D’Amico et al, 2011 • Bigravity is cosmological unstable Comelli et al 2013 Koennig et al 2014 Lagos & Ferreira 2014 Cusin et al 2014 Thursday, 15 January 15
Unimodular gravity Why bother? • Less degrees of freedom than GR • Completely insensitive to vacuum fluctuations (i.e. no term) Thursday, 15 January 15
Unimodular gravity Replace diff invariance by transverse diff and Weyl New theory: gauge fix: Alvarez et al, 2006 Trace free field eqn: Ellis et al 2010 Thursday, 15 January 15
Unimodular gravity • does not source gravity. • Einstein equations are recovered with as Λ an integration constant. Ellis et al 2010 • Can be made massive with a technically natural mass, just like GR. Bonifacio, Ferreira & Hinterbichler 2014 Thursday, 15 January 15
Unimodular gravity • Is protected from radiative corrections ? Λ Smolin 2010 Padilla and Saltas, 2014 • Massive unimodular has same problems as ordinary massive gravity. Bonifacio, Ferreira & Hinterbichler 2014 • Unimodular is essentially equivalent to GR. Einstein 1918 Thursday, 15 January 15
Non-local Gravity Why bother? • Generic in effective action of gravity with massless (gauge) fields • No naturalness problem • No “why now ? ” problem Thursday, 15 January 15
Non-local Gravity Non-local gravity is general! Integrating out ultra-light (or massless) d.o.f. e.g.- one loop effective action for gravity Barvinsky & Vilkovisky 1995 Barvinksy & Mukhanov 2002 No extra degrees of freedom Deser & Woodard 2010 Thursday, 15 January 15
Non-local Gravity Non-local screening of Arkani-Hamed et al 2002 Late time/large scale effect with and Deser & Woodard 2007 corrections. Generalize to Maggiore et al 2012 Thursday, 15 January 15
Non-local Gravity • No systematic way of constructing model a la EFT. • Action is not enough- causality! Maggiore et al 2012 • Generic theory will have instabilities. Ferreira & Maroto 2012 Thursday, 15 January 15
Can gravity solve the Λ problem in cosmology ? Not yet... Thursday, 15 January 15
Testing Gravity Thursday, 15 January 15
Einstein-Dilaton- Cascading gravity Lorentz violation Gauss-Bonnet Conformal gravity Ho ř ava-Lifschitz Strings & Branes ✓ R ◆ f ( G ) f ⇤ DGP Randall-Sundrum Ⅰ & Ⅱ Some degravitation Higher-order scenarios 2T gravity Higher dimensions Non-local General R μν R μν , f ( R ) ☐ R,etc. Kaluza-Klein Modified Gravity Vector Einstein-Aether Generalisations Lorentz violation of S EH New degrees of freedom Massive gravity TeVeS Bigravity Gauss-Bonnet Chern-Simons Tensor Scalar-tensor & Brans-Dicke Lovelock gravity Ghost condensates Cuscuton EBI Galileons Chaplygin gases Bimetric MOND the Fab Four Scalar arXiv: KGB 1310.1086 f(T) 1209.2117 Coupled Quintessence Einstein-Cartan-Sciama-Kibble 1107.0491 Horndeski theories 1110.3830 Torsion theories Tessa Baker 2013 Thursday, 15 January 15
Testing gravity Parameter Bound Effects Experiment Time delay, light γ − 1 2.3 x 10 − 5 Cassini tracking deflection Nordtvedt effect, β − 1 2.3 x 10 − 4 Nordtvedt effect Perihelion shift ξ 0.001 Earth tides Gravimeter data Lunar laser α 1 10 − 4 Orbit polarization ranging Solar alignment α 2 4 x 10 − 7 Spin precession with ecliptic Pulsar spin- α 3 4 x 10 − 20 Self-acceleration down statistics Combined PPN ζ 1 0.02 - bounds Binary pulsar ζ 2 4 x 10 − 5 PSR 1913+16 acceleration Lunar ζ 3 10 − 8 Newton's 3rd law acceleration Hulse-Taylor Pulsar Usually not ζ 4 0.006 - independent 26 Thursday, 15 January 15
-10 10 -12 Baker, Psaltis Triple 10 & Skordis, 2014. -14 10 AdLIGO -16 LOFT + 10 Athena -18 10 -20 10 -22 10 eLISA -24 10 Sgr A* -26 10 Inv. Sq. -28 PPN 10 PTA constraints M87 -30 Atom 10 -2 ) -32 10 Curvature, ξ (cm -34 10 -36 EHT 10 ELT S stars -38 10 -40 10 -42 10 -44 10 -46 10 -48 10 -50 10 Planck -52 P Tidal streams 10 (GAIA) -54 A 10 -56 Facility 10 Baker et al 2014 -58 BAO 10 DETF4 ArXiv:1412:3455 -60 10 -62 10 -12 10 -10 -8 -6 -4 -2 0 10 10 10 10 10 10 Potential, ε Thursday, 15 January 15
The Universe: large scale structure nonlinear X-large scales quasilinear linear 28 Thursday, 15 January 15
Extending Einstein’s equations Skordis 2010 Linear Regime Baker, Ferreira, Skordis 2012 Bardeen potentials: (ˆ Φ , ˆ Ψ ) ⇣ ˙ Γ = 1 ⌘ Linear in ˆ Φ , ˆ χ , ˙ ˆ Φ + H ˆ ˆ Γ , ˆ ˆ Ψ χ k Example: Completely general but 15 free functions... 29 Thursday, 15 January 15
“Integrability condition” can help Pearson, Battye 2011 Bloomfield et al 2012 Gleyzes et al 2013 Langlois et al 2013 Use general principles to restrict Example- assume locality, scalar field, etc leads to only 7 free functions of time. Most general action with 1 d.o.f. (use unitary gauge) 30 Thursday, 15 January 15
Quasi-static then only two functions ... k τ � 1 Caldwell et al 2007 − k 2 Φ = 4 π Gµa 2 ρ ∆ Amendola et al 2007 Bertschinger, et al 2006 Amin et al 2007 γ Ψ = Φ Pogosian et al 2009 Bean & Tangmatitham 2010 Baker et al 2013 ... actually 5 functions of time De Felice et al 2011 Baker et al 2012 Silvestri et al 2013 Baker et al 2014 31 Thursday, 15 January 15
DETF-IV (scale indep.) constraints Growth (e.g. RSDs) Lensing Leonard et al 2015 32 Thursday, 15 January 15
DETF-IV constraints Crucial to constrain Percent level constraints for scale indep. part ... ... order of magnitude greater Leonard et al 2015 for scale dependence part. 33 Thursday, 15 January 15
What does this actually mean? Example: Jordan-Brans-Dicke Theory Cosmology Now: Avillez & Skordis 2013 Euclid: (RSDs only ) Baker, Ferreira & Skordis, 2013 Solar System Cassini Now: Thursday, 15 January 15
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