Testing Gravity using Astrophysics Jeremy Sakstein Institute of Cosmology and Gravitation, Portsmouth ICG-KASI collaboration workshop 17 th September 2015
Things I would have said at the start of the week Alternate gravity theories: Dark energy candidates Cosmological constant problem? Need to screen to pass solar system tests
Local tests E.g. Cassini measures light bending by the Sun How much space is curved by a unit rest mass
What do local tests mean? E.g. scalar-tensor theory - 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 chameleon mechanism Add a scalar potential: r 2 =8 G + V ( ), Get these to cancel out dynamically
Chameleon mechanism R r s 2 ϕ=0 2 ϕ=8παgρ
Chameleon mechanism R r s 2 ϕ=0 2 ϕ=8παgρ
Two parameters - strength of fifth-force - self-screening parameter (fully unscreened) object is unscreened if
Astrophysical Screening main-sequence post-ms dwarf galaxy Need void dwarfs due to environmental screening
The Vainshtein mechanism Change kinetic terms e.g. cubic galileon: L = 1 16 G @ µ @ µ 1 16 G 3 @ µ @ µ + T r 2 + 1 3 r 2 d dr r 0 2 =8 G
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
Vainshtein breaking ds 2 = (1 + 2 )dt 2 +(1 2 ) ij dx i dx j Motion of NR matter Bending of Light GR: d dr = GM(r) r d dr = GM(r) r
Vainshtein breaking Stars and satellites behave differently Cosmological Quartic Galileon field d dr = GM(r) r + G 4 d 2 M(r) dr 2 0 = = 1 3! 4 d dr = GM(r) r 5 G 4r dm(r) dr Light bent differently
Important difference Equivalence principle violations: Vainshtein: EP satisfied Chameleons: EP violated
This talk: astrophysical probes Stellar structure (C + V) Galactic rotation curves (C + V) Gravitational lensing (V) Dwarf stars (V) C chameleon, V Vainshtein
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 life time
Gravity only effects the hydrostatic equilibrium equation Chameleons: Vainshtein: dp dr = GM(r) (r) r 2 4 d 2 M(r) dr 2
Chameleon Stars Gravity stronger Faster burning rate Brighter stars that die faster
Vainshtein stars Gravity weaker Slower burning rate Dimmer and cooler stars that live longer
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
Mass-G-Luminosity relation Gas pressure L / G 4 M 3 Radiation pressure L / GM High-mass stars are more radiation pressure-supported
Davis, Lim, JS, Shaw 2011 Chameleon stars L L GR 2 2 = 1 3 3.0 2.5 2.0 1.5 1.0-1 0 1 2 3 Log[ M ] M
Koyama & JS 2015 L MG Vainshtein polytropes L GR =0.1 0.8 0.6 =0.3 0.4 0.2 =0.5 20 40 60 80 100 M M
Realistic stars MG has been implemented into MESA: Fully consistent treatment of stellar structure No approximations Includes burning, convection, mass loss etc. Can compare with data
Chameleons 2 2 A new and powerful tool to compare with observations
Testing chameleons using stars Parameters probed using distance indicators Need a formula to relate observational data to distances
Main idea Formula come from GR or empirical calibration e.g. luminosity distance Distance estimates: Agree in GR Disagree if galaxy is unscreened
Screened estimators: TRGB (V-I) I band at the TRGB is fixed - standard candle set by nuclear physics - independent of gravity
Unscreened estimators: Cepheids
Unscreened estimators: Cepheids Pulsate with a known period-luminosity relation: M {z} V = log + (B V ) {z } /log L+log d 2 /T eff + Stronger gravity ) distance is underestimated
Comparison with data Calculate using MESA profiles Compare screened and unscreened galaxies Galaxies found using Gongbao s screening map
Constraints Jain, Vikram, JS 2012 F 5 F 6 Excluded
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 3.75 =0.3 =0.5 3.70 3.65 Log T eff 3.60
Rotation curves Circular velocity:
Chameleons Use EP violation: Stars - screened Gas - unscreened
Comparison with data Fit NFW profiles to screened stellar rotation curve Predict gaseous rotation curve as a function of Compare measured curve with prediction Only have six unscreened galaxies - poor statistics
Vikram, JS, Davis, Neil 2014 Constraints F 6
Vainshtein Circular velocity: d dr = GM(r) r + G 4 d 2 M(r) dr 2 New features in the shape
Vainshtein rotation curves GR =0.5 =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
Gravitational lensing Compare hydrostatic and lensing mass: dp dr = GM hydro r 2 Probe using X-ray temperature + = 2GM lens r 2 Probe using lensing GR: M lens = M hydro
Chameleons M lens = 3 4 M hydro Constraint: 0 < 6 10 5 = 1 3 Terukina et al. 2014 coma cluster Wilcox et al. 21015 stacked spectra
Koyama & JS 2015 Vainshtein =0.1 =0.3 =0.5
Dwarf stars - a new test of gravity Perfect tests of the Vainshtein mechanism: Chemically and structurally homogeneous Equation of state is well-known Polytropic models are good approximations Lots of interest in low mass objects
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 ( ) ( = 0) R
Red dwarfs MMHB Hydrogen burning when core is hot and dense enough Gravity weaker Core cooler and less dense at fixed mass Lower MMHB
Red dwarfs MMHB Stable burning when production balances loss L HB = L e : M =0.08 Proton burning ( ) ( = 0) M n =1.5 + theory of gravity
New constraint Lowest mass star is Gl 886 C M =0.0930 ± 0.0008M ) < 0.027 Rules out quartic galleon
Summary f(r) Vainshtein Stars 0 < 4 10 7 Rotation curves 0 < 2 10 6 Lensing 0 < 6 10 5 Red dwarfs < 0.027
Thank you! (and to my collaborators) Chameleons Bhuvnesh Jain(UPenn) Vinu Vikram (Upenn) Papers 1409.3708 1407.6044 1309.0495 1204.6044 1102.5278 Vainshtein Kazuya Koyama (ICG) Papers 15XX.XXXXX 15XX.XXXXX 1502.06872