Testing Gravity using Astrophysics Jeremy Sakstein Institute of Cosmology and Gravitation, Portsmouth Department of Applied Mathematics and Theoretical Physics, University of Cambridge 9 th May 2016
Why study alternative gravity theories? Dark energy candidates (explain comic acceleration) Gravity only tested in certain regimes (New class of field theories not previously known)
Dark energy + G µ =8 G(T m µ + T DE µ ) New gravity theory New matter Lots of freedom in general models All but the simplest are modified gravity theories
Completeness Relativistic gravity important for: Strong gravitational fields black holes, neutron stars Large scales Cosmology
Completeness Gravity tested in: Solar system - Newtonian and post-newtonian Binary pulsars - post-newtonian February 2016: Gravitational waves - strong field Need alternative predictions to test gravity
Local tests E.g. Cassini measures Shapiro time delay How much space is curved by a unit rest mass
What do local tests mean? GR: Field equation Force law
What do local tests mean? New scalar graviton: GR: MG: Cassini: Theory is GR on all scales
Screening mechanisms to the rescue Non-linear effects decouple cosmological scales from the solar system solar system astrophysics cosmology screened partially screened unscreened
The problem with MG GR is enough: r 2 =8 G Change kinetic term Vainshtein Kill of source Chameleons
The Vainshtein mechanism Change kinetic terms e.g. cubic galileon: r 2 + 1 3 r 2 d dr r 0 2 =8 G Poisson Non-Poisson Poisson
Vainshtein Mechanism We can integrate this once: - Vainshtein radius
Vainshtein screening
Astrophysical screening Exhibited in: DGP - tension with data Covariant galileons - too much ISW Massive gravity - no FRW solutions Massive bigravity - unstable Beyond Horndeski - new and unexplored Mechanism is partially broken in beyond Horndeski
( PPN = 1) Unscreened Screened
Vainshtein breaking Recall GR: d dr = GM(r) r d dr = GM(r) r Motion of NR matter Bending of Light
Vainshtein breaking d dr = GM(r) r 2 + 1G 4 d 2 M(r) dr 2 Stars and satellites behave differently 2 3 < 1 < 1 No stable stellar configurations Saito et al. 2015
Vainshtein breaking d dr = GM(r) r 2 5 2 G 4r dm(r) dr Light bends differently 1 < 2 < 1
Effective field theory 5 functions that control linear cosmology NR probes combinations of three of them: 1 = 2 = 4 H 2 c 2 T (1 + B) H 1 4 H ( H B ) 5(c 2 T (1 + B) H 1)
This talk: astrophysical probes Stellar structure Galactic rotation curves Galaxy Clusters Dwarf stars Neutron Stars
Stellar structure tests Main idea: Stars burn fuel to stave off gravitational collapse Changing gravity changes the burning rate This alters the temperature, luminosity and lifetime
Gravity only effects the hydrostatic equilibrium equation dp dr = GM(r) (r) r 2 1 G (r) 4 d 2 M(r) dr 2
Vainshtein stars Gravity weaker Slower burning rate Dimmer and cooler stars that live longer
Vainshtein stars Gravity stronger Faster burning rate Hotter and brighter stars that die faster
Polytropic stars P = K n+1 n polytropic index n = 3 - main sequence, white dwarfs n = 1.5 - convective stars, high mass brown dwarfs n = 1 - low mass brown dwarfs
Vainshtein main-sequence Koyama & JS 2015 L MG polytropes L GR 0.8 1 =0.1 0.6 0.4 0.2 1 =0.3 1 =0.5 20 40 60 80 100 M M
Realistic stars MG has been implemented into MESA: Fully consistent treatment of stellar structure Includes burning, convection, mass loss etc. Can compare with data
Koyama & JS 2015 Log L 2.0 No change on red giant 1.5 1.0 Dimmer + cooler on main-sequence 0.5 0.0 1 =0.3 1 =0.5 3.75 3.70 3.65 Log T eff 3.60
Rotation curves Circular velocity:
Vainshtein Circular velocity: d dr = GM(r) r 2 + 1G 4 d 2 M(r) dr 2 New features in the shape
Vainshtein rotation curves GR 1 =0.5 1 =1 Koyama & JS 2015 NFW profile for MW
Vainshtein rotation curves Measure using 21 cm Measure using stellar motions Deviations in 21 cm region compared with stellar prediction
Galaxy cluster tests Compare hydrostatic and lensing mass: dp dr = d( + ) dr GM hydro r 2 = 2GM WL r 2 Probe using X-ray brightness Probe using lensing GR: M lens = M hydro
Galaxy cluster tests GR: M lens = M hydro MG: M lens = M hydro + 4 3 r3 s s f( r r s, 1, 2 ) Non-agreement probes gravity! Sakstein et al. 2016
Cluster tests 1 = 0.11 +0.93 0.67 2 = 0.22 +1.22 1.19 Note: This applies at redshift 0.33
Dwarf stars - a new test of gravity Perfect tests: Chemically and structurally homogeneous Equation of state is well-known Polytropic models are good approximations Lots of interest in low mass objects (GAIA, KEPLER)
Low mass M-R Red dwarf n =1.5 Brown dwarf n =1 MMHB
Brown dwarfs the radius plateau Coulomb pressure ) n =1 P = K 2 Constant/non-gravitational physics K 1 2 R = G Theory of gravity
JS 2015 Brown dwarfs the radius plateau R =0.1 ( 1 ) ( 1 = 0) R
Red dwarfs MMHB Hydrogen burning when core is hot and dense enough Gravity weaker Core cooler and less dense at fixed mass Higher MMHB
Red dwarfs MMHB Stable burning when production balances loss L HB = L e : M MMHB =0.08 ( 1 ) ( 1 = 0) M Proton burning n =1.5 + theory of gravity
New constraint Lowest mass star is Gl 886 C M =0.0930 ± 0.0008M ) 1 < 0.027
Neutron Stars Answer technical questions (e.g. asymptotics) Not great probes of MG (EOS uncertainty) Need to check they exist Correct precession of Mercury ( PPN = 1) JS, Koyama, Saito, Langlois, Babichev in prep.
Improved stability bound 1 > 2(1+3P c/ c ) 3(1+5P c / c ) Ultra-relativistic: 1 > 0.44 Saito et al (2015): 1 > 0.67
Polytropic model: P = K 2
Realistic EOS (SLy4) Highest mass NS
Realistic EOS (BSK20)
Extreme parameters
Summary Modified gravity is worth exploring: Dark energy, self-acceleration Needed to test GR Can satisfy SS tests using screening mechanisms
Summary This talk test using astrophysics: NR stars are a potential probe So are rotation curves Clusters give new constraints Low mass stars (MMHB) give strongest bound Can learn a lot from NSs
Thank you! (and to my collaborators) Collaborators Kazuya Koyama (ICG) Harry Wilcox (ICG) Bob Nichol (ICG) David Bacon (ICG) David Langlois (APC) Papers 16XX.XXXXX 1511.01685 1510.05964 1502.06872 Eugeny Babichev (LPT) Ryo Saito (APC & Kyoto)