Æthereal Gravity: Observational Constraints on Einstein- Æther Theory Brendan Foster University of Maryland

Einstein-æther Theory Will & Nordtvedt (1972) Gasperini (1987) Jacobson & Mattingly (2000) Matter: Assume matter couples universally to g ab.

Post-Newtonian Parameters Eling & TJ (2003), Graesser, Jenkins, Wise (2005), BF & TJ (2005) Describe post-Newtonian-order effects in terms of standard set of potentials and ten “PPN” parameters.

Combined PPN, stability, Cerenkov & energy constraints BF & TJ (2005) Cerenkov & stability: (spin-2 and spin-0 mode speed) 2 ≥1 Also implies (spin-1 mode speed) 2 ≥1 AND all energy densities positive.

Radiation damping BF (2006)

Einstein-Aether Waves Mattingly & TJ (2004) spin-2: 2 gravitons spin-1: 2 transverse aether-metric modes spin-0: 1 longitudinal aether-metric mode all « massless », speeds all different: STABILITY constraint: squared speeds > 0 CERENKOV constraint: squared speeds >1 Elliott, Moore & Stoica (2005)

Wave Energy C.T. Eling (2005) POSITIVE ENERGY constraint: energy > 0 Spin-2Spin-1Spin-0 +(2c 1 - c c 3 2 )/(1-c 13 )c 14 (2- c 14 ) Found by averaging energy-momentum pseudotensor density over a wave cycle of wave solutions. Reduces to result of Lim (2004) in decoupling limit.

Total Energy C.T. Eling (2005) B.Z.Foster (2005)

Newtonian limit Eling & TJ (2003) Carroll & Lim (2004) Newtonian limit recovered, with total energy corresponds to M in asymptotic G N M/r term of metric component.

Preferred frame parameters Graesser, Jenkins, Wise (2005) Foster & TJ (2005)

Constraints on PPN Parameters From C.M. Will, gr-qc/

Preferred frame parameters Graesser, Jenkins & Wise (2005); Foster & TJ (2005)

Einstein-Aether Cosmology In RW symmetry the aether field equation is automatic, and the stress tensor is geometric: Mattingly & TJ (2001), Carroll & Lim (2004) The first term renormalizes the gravitational constant: The second term renormalizes the spatial curvature term in the Friedman eqn.

Primordial nucleosynthesis Helium abundance implies Carroll & Lim (2004) When preferred frame parameters vanish we find

Einstein-Aether Cosmology II Primordial fluctuations: Spin-1 perturbations decay exponentially (not sourced). Inflaton sources spin-0 aether perturbation which mixes with metric mode scalar and tensor mode speeds differ, and G’s differ upshot: power spectra differently rescaled. Upsets “inflationary consistency relation”: tensor/scalar power = - 9/2 tensor spectral index (1+O(c i )) (Lim, 2004)

Einstein-Aether Cosmology II Primordial fluctuations: Inflaton sources spin-0,2 perturbations, will upset “inflationary consistency” (Lim, 2004) Trans-Planckian matter sources: Stress-tensors for matter with LV couplings to aether have been found, and used to study the thermal case and trans-Planckian contributions as dark matter candidate. Mattingly & TJ (2001), Lemoine, Lubo, Martin & Uzan (2002,3), Bastero-Gil & Mersini (2003), Brandenberger & Martin (2005). Inflaton with high-frequency dispersion (Shankaranarayanan & Lubo, 2005)

Spherically symmetric solutions Chris Eling & TJ (2006)

Static aether solution Chris Eling & TJ (2006)

Static aether solution – II Chris Eling & TJ (2006)

Static aether solution – III Chris Eling & TJ (2006)

Aethereal Stars Chris Eling & TJ (2006) Fluid star interior can be matched to static aether exterior. Solution determined by eqn. of state and central pressure. Maximum mass of constant density stars less than in GR.

Aethereal Black Holes C. Eling & TJ (2006) æther not aligned with Killing vector – flows into hole analytic solution not possible to solve can shoot out from horizon or in from infinity metric horizon generically regular – 2 parameter family?? What is a black hole? must trap all modes; metric, spin-0,1,2 horizons generally differ. only spin-0 has spherically symmetric modes regularity of spin-0 horizon reduces to 1 parameter family

Aethereal Black Holes – cont’d C. Eling & TJ (2006)

Curvature divergence

Aether flow vs. free-fall

Aether flow vs. free-fall inside

Aethereal Black Holes – issues other values of c 3 ? evidence for negative mass black holes? æther singular at bifurcation surface – time asymmetry 1st law and entropy? (Foster, ‘05) numerical collapse? (e.g. imploding aether wave) rotating black holes?

General Relativity with a preferred frame Frame must be dynamical “time” function T, frame defined by T, b – will not generally remain timelike – hypersurface orthogonal – has “extra” information: | T, b | “Aether” 4-velocity u a