gr group up fie ield ld the heory y co condensate ate co cosmolo logy gy mair iri sakella llaria iado dou king’s college london
outline motivation elements of group field theory and group field theory condensate cosmology quantum dynamics of the mean field for a GFT condensate cosmology model pithis, sakellariadou, tomov, PRD 94 94 (2016) 064056 pithis, sakellariadou, PRD 95 95 (2017) 064004 cosmological consequences of the modified friedmann equation de cesare, sakellariadou , PLB 764 764 (2017) 49 de cesare, pithis, sakellariadou , PRD 94 94 (2016) 064051 conclusions
motivation
classical cosmology is built upon general relativity (GR) and the cosmological principle but GR is a classical effective theory valid at low energies the assumption of a continuous spacetime characterised by homogeneity and isotropy on large scales is valid at low energies to describe the physics near the big bang, a quantum gravity theory with the appropriate space-time geometry is needed
at very high energy scales, quantum gravity corrections can no longer be neglected, spacetime as a continuum medium may no longer be valid, and geometry may altogether lose its familiar meaning can we resolve the initial singularity ? can we find an accelerated expansion without introducing an inflaton field with an ad hoc potential? early universe cosmology is in need of a rigorous underpinning in quantum gravity cosmological data represent the best chance for testing quantum gravity, thus guiding the formulation of the complete theory
quantum gravity approaches: top-down approach o string/brane model o non-perturbative approach -- wheeler-de witt -- loop quantum gravity -- causal dynamical triangulations -- causal sets -- group field theory bottom-up approach o non-commutative spectral geometry o asymptotic safety
quantum gravity approaches: top-down approach o string/brane model string gas scenario o non-perturbative approach -- wheeler-de witt -- loop quantum gravity -- causal dynamical triangulations -- causal sets -- group field theory bottom-up approach o non-commutative spectral geometry o asymptotic safety
quantum gravity approaches: top-down approach o string/brane model o non-perturbative approach -- wheeler-de witt -- loop quantum gravity -- causal dynamical triangulations -- causal sets -- group field theory group field theory condensate cosmology construct a theory of quantum bottom-up approach geometry and identify states in its hilbert space which o non-commutative spectral geometry represent a macroscopic, spatially homogeneous, isotropic universe
elements of group field theory (GFT) & group field theory condensate cosmology (GFC) oriti (2007, 2014) gielen, oriti, sidoni (2013, 2014) gielen, sidoni (2016)
approach: group field theory : spacetime and geometry should be emergent, as an effective description of the collective behaviour of different pre-geometric fundamental degrees of freedom functional renormalisation group analyses of GFT models support the idea of a phase transition separating a symmetric from a broken/condensate phase, as the “mass” parameter changes its sign to negative values in the IR limit of the theory the process responsible for the emergence of a continuum geometric phase is a condensation of bosonic GFT quanta, each representing an atom of space group field theory quantum cosmology : 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
group field theory (GFT) GFTs are QFTs defined over group manifolds with combinatorially nonlocal interaction terms intending to generalise matrix models for 2d QG in higher dimensions basic idea : all data encoded in the fields is exclusively of combinatorial and algebraic nature which turns GFT into a background independent FT simplest case: this data consists of group elements attached to the edges of a graph
group field theory (GFT) GFTs are QFTs defined over group manifolds with combinatorially nonlocal interaction terms intending to generalise matrix models for 2d QG in higher dimensions basic idea : all data encoded in the fields is exclusively of combinatorial and algebraic nature which turns GFT into a background independent FT choice of lie group G, interpreted as local gauge group of gravity: SU(2) (for models aiming at providing a second quantised reformulation of the kinematics of canonical LQG, G=SU(2) is the gauge group of ashtekar-barbero gravity)
group field theory (GFT) GFTs are QFTs defined over group manifolds with combinatorially nonlocal interaction terms intending to generalise matrix models for 2d QG in higher dimensions basic idea : all data encoded in the fields is exclusively of combinatorial and algebraic nature which turns GFT into a background independent FT choice of lie group G, interpreted as local gauge group of gravity: SU(2) (for models aiming at providing a second quantised reformulation of the kinematics of canonical LQG, G=SU(2) is the gauge group of ashtekar-barbero gravity) choice of the combinatorial structure of elementary building blocks : the elementary building block of 3dim space is a (quantum) tetrahedron field theory defined fundamental quanta of GFT on 4 copies of G: field which are created or annihilated by 2 nd quantised quantum tetrahedra field operators
group field theory (GFT) GFTs are QFTs defined over group manifolds with combinatorially nonlocal interaction terms intending to generalise matrix models for 2d QG in higher dimensions basic idea : all data encoded in the fields is exclusively of combinatorial and algebraic nature which turns GFT into a background independent FT choice of lie group G, interpreted as local gauge group of gravity: SU(2) (for models aiming at providing a second quantised reformulation of the kinematics of canonical LQG, G=SU(2) is the gauge group of ashtekar-barbero gravity) choice of the combinatorial structure of elementary building blocks : the elementary building block of 3dim space is a (quantum) tetrahedron dual picture from LQG and spin foams: GFT quanta as open central vertex with 4 open outgoing spin network vertices links, with group-theoretic data associated to these links
group field theory (GFT) GFTs are QFTs defined over group manifolds with combinatorially nonlocal interaction terms intending to generalise matrix models for 2d QG in higher dimensions basic idea : all data encoded in the fields is exclusively of combinatorial and algebraic nature which turns GFT into a background independent FT choice of lie group G, interpreted as local gauge group of gravity: SU(2) (for models aiming at providing a second quantised reformulation of the kinematics of canonical LQG, G=SU(2) is the gauge group of ashtekar-barbero gravity) choice of the combinatorial structure of elementary building blocks : the elementary building block of 3dim space is a (quantum) tetrahedron specify theory by the choice of a type of field - complex scalar field - and a corresponding action – a kinetic quadratic term and a sum of interaction polynomials weighted by coupling constants - encoding the dynamics
4d QG complex scalar field living on d=4 copies of the lie group G= SU(2) : where group elements g correspond to parallel transports on the gravitational I connection along a link impose invariance of the field under the right diagonal action of the group G 4 on G discrete gauge invariance at the vertex from which d links emanate equivalent to the closure constraint of a quantum tetrahedron
4d QG complex scalar field living on d=4 copies of the lie group G= SU(2) : where action interaction term: kinetic: local nonlinear and nonlocal convolution of GFT field with itself classical e.o.m. 0 =0 of the field
fock vacuum no space state (no topological, no quantum geometric information) excitation of a GFT quantum creation of a single open 4-valent over the fock vacuum LQG spin network vertex a field corresponds to a an atom of space itself
fock vacuum no space state (no topological, no quantum geometric information) excitation of a GFT quantum creation of a single open 4-valent over the fock vacuum LQG spin network vertex field operators obey canonical commutation relations: construct N-particle states (to describe extended quantum 3-geometries) obtain quantum geometric observable data via second-quantised hermitian operators vertex number operator vertex volume operator in terms of matrix elements of first quantised LQG volume operator
fock vacuum no space state (no topological, no quantum geometric information) excitation of a GFT quantum creation of a single open 4-valent over the fock vacuum LQG spin network vertex quantum theory : dynamics defined by the partition function the appropriate action yields a sum-over-histories for 4dim quantum gravity
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