Institute of Cosmology and Gravitation, University of Portsmouth Cosmological Tests of Modified Gravity Kazuya Koyama Institute of Cosmology and Gravitation, University of Portsmouth “Cosmological Tests of Modified Gravity” KK, Report of Progress of Physics 79 (2016) no.4, 046902, arXiv:1504.04623

Cosmic acceleration Many independent data sets indicate the expansion of the Universe is accelerating Standard cosmology requires 70% of unknown ‘dark’ energy

Dark energy v Dark gravity Cosmological constant is the simplest candidate but the theoretical prediction is more than 50 orders of magnitude larger than the observed values “Most embarrassing observation in physics” Standard model of cosmology is based on GR but we have never tested GR on cosmological scales cf. precession of perihelion dark planet v GR

Is cosmology probing breakdown of GR on large scales ?

Assuming GR Dark Matter Dark Energy curvature potential Curvature Psaltis Living Rev. Relativity 11 (2008), 9 curvature Grav Probe B Hulse-Taylor 1 Rsun Moon Mercury 1 AU potential 10 kpc Curvature 10 Mpc Dark Matter Dark Energy Gravitational potential

General Relativity Modified Gravity Screening mechanism Grav Probe B General Relativity Hulse-Taylor 1 Rsun Moon Mercury 1 AU Screening mechanism Curvature 10 kpc 10 Mpc Dark Matter Cosmological tests of gravity Modified Gravity Gravitational potential

General picture Largest scales gravity is modified so that the universe accelerates without dark energy Large scale structure scales gravity is still modified by a fifth force from scalar graviton model independent tests of GR Small scales (solar system) GR is recovered Modified gravity Scalar tensor GR Linear scales Clifton, Ferreira, Padilla & Skordis Phys. Rept. 513 (2012) 1

Why we need screening mechanism? Brans-Dicke gravity quasi-static approximations (neglecting time derivatives) : fifth force

Constraints on BD parameter Solutions PPN parameter This constraint excludes any detectable modifications in cosmology

Screening mechanism Require screening mechanism to restore GR recovery of GR must be environmental dependent make the scalar short-ranged using (chameleon) make the kinetic term large to suppress coupling to matter using (dilaton/symmetron) or (k-mouflage) (Vainshtein) Break equivalence principle remove the fifth force from baryons (interacting DE models in Einstein frame)

Chameleon mechanism Scalar is coupled to matter Depending on density, the mass can change It is easier to understand the dynamics in Einstein frame

Chameleon mechanism Khoury & Weltman astro-ph/0309300

Thin shell condition Khoury & Weltman astro-ph/0309411 If the thin shell condition is satisfied, only the shell of the size contributes to the fifth force Screening is determined by the gravitational potential of the object Silvestri 1103.4013

Behaviour of gravity There regimes of gravity Understandings of non-linear clustering require N-body simulations where the non-linear scalar equation needs to be solved In most models, the scalar mode obeys non-linear equations describing the transition from the scalar tensor theory on large scales to GR on small scales Scalar tensor GR

N-body simulations GR Modified gravity models superposition of forces the non-linear nature of the scalar field equation implies that the superposition rule does not hold It is required to solve the non-linear scalar equation directly on a mesh a computational challenge! The breakdown of the superposition rule has interesting consequences

N-body Simulations for MG Multi-level adaptive mesh refinement solve Poisson equation using a linear Gauss-Seidel relaxation add a scalar field solver using a non-linear Gauss Seidel relaxation ECOSMOG Li, Zhao, Teyssier, KK JCAP1201 (2012) 051 MG-GADGET Puchwein, Baldi, Springel MNRAS (2013) 436 348 ISIS Llinares, Mota, Winther A&A (2014) 562 A78 DGPM, Schmidt PRD80, 043001 Modified Gravity Simulations comparison project Winther, Shcmidt, Barreira et.al. arXiv: 1506.06384

Where to test GR GR is recovered in high dense regions Scalar tensor (we consider the chameleon mechanism here) GR is recovered in high dense regions GR is restored in massive dark matter halos Environmental effects Even if dark matter halo itself is small, if it happens to live near massive halos, GR is recovered Using simulations, we can develop criteria to identify the places where GR is not recovered Scalar tensor GR Zhao, Li, KK Phy. Rev. Lett. 107 (2011) 071303

Environmental effects Zhao, Li, Koyama 1011.1257 GR is recovered even in small halos nearby big halos Large bubbles =better screened (GR is recovered)

Environmental dependence Difference between lensing and dynamical mass environment: O(1) difference no difference O(1) difference no difference

Testing chameleon gravity Outskirt of clusters Terukina. et.al. PRD86 103503, JCAP 1404 013 48 X-ray clusters from XCS compared with lensing (shear) from CFHTLS Dynamical mass can be inferred from X-ray and SZ Wilcox et.al. 1504.03937, 1603.05911

Creating a screening map It is essential to find places where GR is not recovered Small galaxies in underdense regions SDSS galaxies within 200 Mpc Cabre, Vikram, Zhao, Jain, KK JCAP 1207 (2012) 034 (we consider the chameleon mechanism here) GR is recovered

Tests of chameleon gravity dwarf galaxies in voids strong modified gravity effects Galaxies are brighter Cerpheid periods change Various other tests Jain & VanderPlas JCAP 1110 (2011) 032 Davis et.al. Phys. Rev. D85 (2012) 123006 Jain et.al. ApJ 779 (2013) 39 Vikram et.al. JCAP1308 (2013) 020 Hui, Nicolis & Stubbs Phys. Rev. D80 (2009) 104002

Constraints on chameleon gravity Non-linear regime is powerful for constraining chameleon gravity Astrophysical tests could give better constraints than the solar system tests and can be done by “piggybacking” ongoing surveys Jain et.al. 1309.5389 Interaction range of the extra force that modifies GR in the cosmological background GR

Summary In the next decade, we may be able to detect the failure of GR on cosmological scales Linear scales model independent tests of gravity Non-linear scales novel astrophysical tests of gravity (in a model dependent way) It is required to develop theoretical models from fundamental theory SUMIRE EUCLID