square kilometer array: a powerful tool to test theories of gravity and cosmological models

Transcription

1 square kilometer array: a powerful tool to test theories of gravity and cosmological models mairi sakellariadou king s college london fundamental physics with the SKA flic-en-flac, mauritius, 30/4-5/5/ 2017

2 ΛCDM model: phenomenological model successful in fitting observations GR on a FLRW metric with CDM

3 ΛCDM model: phenomenological model successful in fitting observations GR on a FLRW metric with CDM however GR is a classical theory continuous space-time undetected status of DM: 26% (extensions of SM yet undiscovered) unknown DE component: 69% inflation remains a paradigm in search of a theory at very high energy scales, quantum gravity corrections can no longer be neglected, space-time as a continuum medium may no longer be valid, and geometry may altogether lose its familiar meaning early universe cosmology is in need of a rigorous underpinning in quantum gravity

4 non-commutative spectral geometry: a bottom-up approach to quantum gravity guess small-scale structure of ST from knowledge at EW scale matter and gravity from (noncommutative) geometry space-time (4-dimensional) with extra dimensions (noncommutative) geometry: tensor product of an internal (zero-dim) geometry for the standard model of particle physics and a continuous geometry for space-time gravity on this product space = gravity + matter on ordinary 4dim space-time a different way to think about geometry instead of measuring distances between points, one could measure the way a geometric object vibrates if we bang it from the frequencies of the resulting tones, one could extract information about the geometry

5 can one hear the shape of a drum? kac (1966) the universe as a drum can one deduce the precise shape of the drum just from hearing the fundamental tone and all overtones, even though one cannot see the drum? in ordinary riemannian geometry, the shape of a drum cannot be heard milnor (1964) one can hear the shape of a spectral triple (spinorial drum) its dynamics are given by a spectral action that sums up all frequencies of vibration of space [spacetime + extra (internal space) dimensions] chamseddine, connes (1996,1997)

6 SM: a phenomenological model which dictates space-time geometry 4-dim ST with an internal kaluza-klein space attached to each point; the 5 th dim is a discrete, 0-dim space spectral triple if suitably chosen standard model (SM) coupled to gravity purely geometric interpretation of the most successful particle physics model chamseddine, connes, marcolli (2007)

7 SM: a phenomenological model which dictates space-time geometry 4-dim ST with an internal kaluza-klein space attached to each point; the 5 th dim is a discrete, 0-dim space spectral triple apply to product geometry the spectral action principal the action functional depends only on the spectrum of the dirac operator: 2 2 evaluate trace with heat kernel techniques chamseddine, connes (1996,1997)

8 gravitational terms coupled to matter: bosonic chamseddine, connes, marcolli (2007) EH action with a cosmological term topological term conformal gravity term with the weyl curvature tensor conformal coupling of higgs to gravity

9 gravitational terms coupled to matter: bosonic linear perturbations around minkowski propagation of GW nelson, ochoa, sakellariadou, PRD 82 (2010)

10 gravitational terms coupled to matter: bosonic propagation of GW constraints from binary pulsars nelson, ochoa, sakellariadou, PRL 105 (2010) 11602

11 gravitational terms coupled to matter: bosonic propagation of GW gravity probe B LARES lambiase, sakellariadou, stabile, JCAP 12 (2013) 020

12 SKA1 can discover about 10,000 normal pulsars and perhaps 1,800 millisecond pulsars the geodesic precession and frame-dragging effect will be measurable in the double pulsar with SKA1 PSRs J A and J B 23 ms period and 2.8 s period both pulsars orbit each other in less than 2.5 hours in a mildly eccentric (e = 0.088) orbit tighter constraint on the free parameter that relates coupling constants at unification (NCSG) similarly for other modified gravity models lambiase, sakellariadou, stabile, JCAP 07 (2015) 003

13 group field theory (GFT) condensate cosmology: a top-down approach to quantum gravity construct a theory of quantum geometry and identify states in its hilbert space which can represent a macroscopic, spatially homogeneous and isotropic universe space is not infinitely divisible, but has a granular structure: quanta of space they are the quantum excitations of the gravitational field, which is the physical space spacetime and geometry should be emergent, as an effective description of the collective behaviour of different pre-geometric fundamental degrees of freedom the process responsible for the emergence of a continuum geometric phase is a condensation of bosonic GFT quanta, each representing an atom of space identify this condensate phase to a continuum spacetime and derive for the corresponding GFT condensate states an effective dynamics through mean field techniques and give these states a cosmological interpretation gielen, oriti, sidoni (2013, 2014) de cesare, pithis, sakellariadou (206, 2017)

14 quantum geometry effects may lead to stochastic fluctuations of the gravitational constant, which can be thus considered as a macroscopic effective dynamical quantity non-commutative spectral geometry group field theory condensate cosmology de cesare, lizzi, sakellariadou, PLB 760 (2016) 498 effective gravitational constant from the collective behaviour of spacetime quanta de cesare, sakellariadou, PLB 764 (20117) 49 a time-dependent dark energy term in the modified field equation can be expressed in terms of a time-dependent dynamical gravitational constant the late-time accelerated expansion of the universe may be ascribed to quantum fluctuations in the geometry of space-time rather than the vacuum energy from the matter sector

15 quantum geometry effects may lead to stochastic fluctuations of the gravitational constant, which can be thus considered as a macroscopic effective dynamical quantity non-commutative spectral geometry group field theory condensate cosmology de cesare, lizzi, sakellariadou, PLB 760 (2016) 498 effective gravitational constant from the collective behaviour of spacetime quanta de cesare, sakellariadou, PLB 764 (20117) 49 time-variation in the gravitational constant contributes to the decay of a binary orbit damour et al (1988) ; nordtvedt (1990) this extra contribution can be constrained by the measurement of the decay of the binary pulsar orbit by assuming a null contribution from the dipole radiation from the lunar laser ranging williams et al (2004) from PSR J and PSR J freire et al (2012)

16 quantum geometry effects may lead to stochastic fluctuations of the gravitational constant, which can be thus considered as a macroscopic effective dynamical quantity non-commutative spectral geometry group field theory condensate cosmology de cesare, lizzi, sakellariadou, PLB 760 (2016) 498 effective gravitational constant from the collective behaviour of spacetime quanta de cesare, sakellariadou, PLB 764 (20117) 49 time-variation in the gravitational constant contributes to the decay of a binary orbit SKA (combined e.g. with VLBI instruments and GAIA setellite) will improve significantly pulsar observations, allowing us to test theories that predict a time-dependent G

17 D-material universe: motivated from string/brane theory (a top-down approach to QG) a compactified (3+1)dim brane propagates in a higher-dim bulk populated by point-like D0-brane (D-particles) defects D-particle: all spatial dim are wrapped around compact space as brane universe moves in the bulk, D particles cross it particle excitations (open strings) propagate in a medium of D-particles mavromatos, sakellariadou, PLB 652 (2007) 97 brane-puncturing (massive) D-particles captured by (neutral) matter open strings dirac-born-infeld action: tensor-vector (recoil velocity) - scalar (dilaton) model lorentz invariance locally (LLI) broken, leading to emergence of vector-like excitations that can lead to an era of inflation and contribute to large scale structure (enhancing DM component) and galaxy formation ferreras, mavromatos, sakellariadou, yusaf, PRD 860(2013) elghozi, mavromatos, sakellariadou, yusaf, JCAP 1602 (2016) 060

18 D-material universe: motivated from string/brane theory (a top-down approach to QG) violation of LLI leads to modifications of the orbital dynamics of binary pulsars and the spin evolution of solitary pulsars in characteristic ways changes in the time-derivative of the orbital eccentricity, the time-derivative of the projected semi-major axis of the pulsar orbit, and the time-derivative of the longitude of the periastron violation of LLI leads to spin precession of a solitary pulsar w.r.t. a fixed direction characteristic changes versus time in the pulse profiles best constraints on LLI are from pulsar experiments; they are proportional to timing precession of binary pulsars with SKA tests will improve dramatically with better sensitivities

19 conclusions through its sensitivity, sky and frequency coverage, the SKA will improve the timing precision of millisecond pulsars, allowing probes of potential departures from einstein s theory of general relativity, and increasing our understanding of gravitational physics in this new area of gravitational astrophysics, combining pulsar timing and laser interferometric GW detectors, we may be (finally) able to demystify gravity, understand better our universe and unweave the fabric of its space-time