Gaia, the Global Sphere Reconstruction and GR The PPN-g and scalar-tensor cosmologies Gaia, the PPN-g and limits on scalar-tensor cosmologies Gaia, the PPN-g parameter and scalar-tensor cosmologies A quick overview A. Vecchiato1 1INAF - Astrophysical Observatory of Torino PONT 2017 Avignon, April 24, 2017 A. Vecchiato Gaia and scalar-tensor cosmologies Gaia, the Global Sphere Reconstruction and GR The PPN-g and scalar-tensor cosmologies Gaia, the PPN-g and limits on scalar-tensor cosmologies Outline 1 Gaia, the Global Sphere Reconstruction and General Relativity Astrometry and gravity Gaia and the global sphere reconstruction 2 The PPN-g and scalar-tensor cosmologies Scalar-tensor theories and cosmologies The PPN Framework PPN-g and scalar-tensor theories 3 Gaia, the PPN-g and limits on scalar-tensor cosmologies Constraining scalar-tensor cosmologies with Gaia Problems and pitfalls A. Vecchiato Gaia and scalar-tensor cosmologies Gaia, the Global Sphere Reconstruction and GR Astrometry and gravity The PPN- and scalar-tensor cosmologies g Gaia and the global sphere reconstruction Gaia, the PPN-g and limits on scalar-tensor cosmologies Outline 1 Gaia, the Global Sphere Reconstruction and General Relativity Astrometry and gravity Gaia and the global sphere reconstruction 2 The PPN-g and scalar-tensor cosmologies Scalar-tensor theories and cosmologies The PPN Framework PPN-g and scalar-tensor theories 3 Gaia, the PPN-g and limits on scalar-tensor cosmologies Constraining scalar-tensor cosmologies with Gaia Problems and pitfalls A. Vecchiato Gaia and scalar-tensor cosmologies Gaia, the Global Sphere Reconstruction and GR Astrometry and gravity The PPN- and scalar-tensor cosmologies g Gaia and the global sphere reconstruction Gaia, the PPN-g and limits on scalar-tensor cosmologies Why Astrometry First experimental evidences of General Relativity came from Astrometry. One can thus hope that the Thus the results of the discussion of the observations expeditions to Sobral and of Mercury simply confirm Principe can leave little doubt previous research. Now this is that a deflection of light takes not negligible: we see here place in the neighbourhood of that the approximately 3-fold the Sun and that it is of the secular movement of the amount demanded by eccentricity, added to the Einstein’s generalised theory of secular movement of the relativity, as attributable to the perihelion, gives a sum in sun’s gravitational field. which the observations are (Dyson, Eddington and greater by 3900 than those Davidson, 1920) which result from calculation. (Le Verrier, 1859) A. Vecchiato Gaia and scalar-tensor cosmologies Gaia, the Global Sphere Reconstruction and GR Astrometry and gravity The PPN- and scalar-tensor cosmologies g Gaia and the global sphere reconstruction Gaia, the PPN-g and limits on scalar-tensor cosmologies Light deflection in the Solar System Body daM (mas) daQ (mas) Sun 1:75 106 1 101 × ∼ Mercury 83 Sun Jupiter 100 Saturn Uranus Venus 493 Neptune 10 µas 10 1 1 µas Earth 574 0:6 − (mas) 2 Moon 26 δα 10− Mars 116 0:2 3 10− Jupiter 16270 240 10 4 Saturn 5780 95 − Uranus 2080 8 0 10 20 30 40 50 α (deg) Neptune 2533 10 A. Vecchiato Gaia and scalar-tensor cosmologies Gaia, the Global Sphere Reconstruction and GR Astrometry and gravity The PPN- and scalar-tensor cosmologies g Gaia and the global sphere reconstruction Gaia, the PPN-g and limits on scalar-tensor cosmologies Outline 1 Gaia, the Global Sphere Reconstruction and General Relativity Astrometry and gravity Gaia and the global sphere reconstruction 2 The PPN-g and scalar-tensor cosmologies Scalar-tensor theories and cosmologies The PPN Framework PPN-g and scalar-tensor theories 3 Gaia, the PPN-g and limits on scalar-tensor cosmologies Constraining scalar-tensor cosmologies with Gaia Problems and pitfalls A. Vecchiato Gaia and scalar-tensor cosmologies Gaia, the Global Sphere Reconstruction and GR Astrometry and gravity The PPN- and scalar-tensor cosmologies g Gaia and the global sphere reconstruction Gaia, the PPN-g and limits on scalar-tensor cosmologies Gaia at a glance What: ESA satellite, orbiting around the Sun-Earth L2 point (1:5 106 km from Earth) When: launched Dec 19th, 2013, 5yrs operations · Why: 6D map (positions and velocities) of 109 Milky Way objects @∼ 10 100 mas accuracy − A. Vecchiato Gaia and scalar-tensor cosmologies Gaia, the Global Sphere Reconstruction and GR Astrometry and gravity The PPN- and scalar-tensor cosmologies g Gaia and the global sphere reconstruction Gaia, the PPN-g and limits on scalar-tensor cosmologies Gaia at a glance What: ESA satellite, orbiting around the Sun-Earth L2 point (1:5 106 km from Earth) When: launched Dec 19th, 2013, 5yrs operations · Why: 6D map (positions and velocities) of 109 Milky Way objects @∼ 10 100 mas accuracy − How: scanning mode measurements (as opposed to “step-and-stare” mode) A. Vecchiato Gaia and scalar-tensor cosmologies Gaia, the Global Sphere Reconstruction and GR Astrometry and gravity The PPN- and scalar-tensor cosmologies g Gaia and the global sphere reconstruction Gaia, the PPN-g and limits on scalar-tensor cosmologies Gaia at a glance What: ESA satellite, orbiting around the Sun-Earth L2 point (1:5 106 km from Earth) When: launched Dec 19th, 2013, 5yrs operations · Why: 6D map (positions and velocities) of 109 Milky Way objects @∼ 10 100 mas accuracy − How: scanning mode measurements (as opposed to “step-and-stare” mode) combination of the three independent motions of the scanning law allows for a complete coverage of the sky every 6 months A. Vecchiato Gaia and scalar-tensor cosmologies Gaia, the Global Sphere Reconstruction and GR Astrometry and gravity The PPN- and scalar-tensor cosmologies g Gaia and the global sphere reconstruction Gaia, the PPN-g and limits on scalar-tensor cosmologies Principles of the sphere reconstruction The ideal picture Create a “geodetic” network of measurements N = 5 ∗ Nunk = 10 Narcs = 10 Network closed! Solve an Equation System A. Vecchiato Gaia and scalar-tensor cosmologies Gaia, the Global Sphere Reconstruction and GR Astrometry and gravity The PPN- and scalar-tensor cosmologies g Gaia and the global sphere reconstruction Gaia, the PPN-g and limits on scalar-tensor cosmologies Principles of the sphere reconstruction The (almost) real picture Observational errors ) 1 solution in the least-squares sense; 2 overdetermined system of equations. S A. Vecchiato Gaia and scalar-tensor cosmologies Gaia, the Global Sphere Reconstruction and GR Astrometry and gravity The PPN- and scalar-tensor cosmologies g Gaia and the global sphere reconstruction Gaia, the PPN-g and limits on scalar-tensor cosmologies Principles of the sphere reconstruction The (almost) real picture Observational errors ) 1 solution in the least-squares sense; 2 overdetermined system of S¯ equations. σS S A. Vecchiato Gaia and scalar-tensor cosmologies Gaia, the Global Sphere Reconstruction and GR Astrometry and gravity The PPN- and scalar-tensor cosmologies g Gaia and the global sphere reconstruction Gaia, the PPN-g and limits on scalar-tensor cosmologies Principles of the sphere reconstruction The (almost) real picture Observational errors ) 1 solution in the least-squares sense; 2 overdetermined system of S¯ equations. σS S 8 Nunk N 10 ∼ ∗ ' 2 10 Nobs 10 Nunk 10 ∼ ∼ A. Vecchiato Gaia and scalar-tensor cosmologies Gaia, the Global Sphere Reconstruction and GR Astrometry and gravity The PPN- and scalar-tensor cosmologies g Gaia and the global sphere reconstruction Gaia, the PPN-g and limits on scalar-tensor cosmologies Mathematical modeling: the Euclidean abscissa The Gaia basic observable is the abscissa f between the x axis and one viewing direction ea r cosy = ^ · (1) (^a;r) r j j cosy(^x;r) cosf = q (2) 1 cos2 y − (^z;r) Depends on the coordinates of one star(S) and on the satellite attitude(A) at the time of the observation The aberration enters in the same way as for the arcs A. Vecchiato Gaia and scalar-tensor cosmologies Gaia, the Global Sphere Reconstruction and GR Astrometry and gravity The PPN- and scalar-tensor cosmologies g Gaia and the global sphere reconstruction Gaia, the PPN-g and limits on scalar-tensor cosmologies Mathematical modeling: enters General Relativity Equivalent of Eq. (1): the relativistic viewing direction and kn (null four-vectors) have to be Γ(s) projected in the spatial hypersurface relative to uµ the observer um Tmn = gmn + um un m n µν Tmn E k T cosy = a^ (^a;k) p m n Tmn k k (3) It is possible to include one or more PPN parameters like g (Global parameters) A. Vecchiato Gaia and scalar-tensor cosmologies Gaia, the Global Sphere Reconstruction and GR Astrometry and gravity The PPN- and scalar-tensor cosmologies g Gaia and the global sphere reconstruction Gaia, the PPN-g and limits on scalar-tensor cosmologies The g parameter and the Global Sphere Reconstruction In principle, each observation is a function of Astrometric (S), Attitude (A), Instrument (C), and Global (G) parameters. n n k = k (a ;d ;p ; ma ; md ;g) ∗ ∗ ∗ ∗ ∗ n n (a) (a) (a) Ea^ = Ea^ s1 ;s2 ;s3 ;g S A C G cosy(^a;k) = Fa^ x ;x ;x ;x Estimation of PPN-g The dependence on g gives the estimation of this parameter as a by-product of the sphere reconstruction A. Vecchiato Gaia and scalar-tensor cosmologies Gaia, the Global Sphere Reconstruction and GR Astrometry and gravity The PPN- and scalar-tensor cosmologies g Gaia and the global sphere reconstruction Gaia, the PPN-g and limits on scalar-tensor cosmologies The g parameter and the Global Sphere Reconstruction In principle, each observation is a function of Astrometric (S), Attitude (A), Instrument (C), and Global (G) parameters. n n k = k (a ;d ;p ; ma ; md ;g) ∗ ∗ ∗ ∗ ∗ n n (a) (a) (a) Ea^ = Ea^ s1 ;s2 ;s3 ;g S A C G cosy(^a;k) = Fa^ x ;x ;x ;x Estimation of PPN-g The dependence on g gives the estimation of this parameter as a by-product of the sphere reconstruction A.