Bimetric Theory (The notion of spacetime in Bimetric Gravity)
|
|
- Dinah Long
- 5 years ago
- Views:
Transcription
1 Bimetric Theory (The notion of spacetime in Bimetric Gravity) Fawad Hassan Stockholm University, Sweden 9th Aegean Summer School on Einstein s Theory of Gravity and its Modifications Sept 18-23, 2017, Sifnos
2 SFH & Mikica Kocic (arxiv: ) Also based on work with: Rachel. A. Rosen Angnis Schmidt-May Mikael von Strauss Anders Lundkvist Luis Apolo
3 Outline of the talk Motivation & Problems Gravity with an extra spin-2 field: Bimetric Theory Potential Issues Uniqueness and the local structure of spacetime Discussion
4 Bimetric gravity: Why study a theory of gravity with two metrics? (Gravitational metric coupled to extra spin-2 fields)
5 Outline of the talk Motivation & Problems Gravity with an extra spin-2 field: Bimetric Theory Potential Issues Uniqueness and the local structure of spacetime Discussion
6 Motivation GR + Λ + CDM : Very successful
7 Motivation GR + Λ + CDM : Very successful Observations and theory indicate new physics Dark matter, Dark energy (the cosmological constant problem), Origin of Inflation, The trans-planckian problem, Quantum gravity, Matter-Antimatter asymmetry
8 Motivation GR + Λ + CDM : Very successful Observations and theory indicate new physics Dark matter, Dark energy (the cosmological constant problem), Origin of Inflation, The trans-planckian problem, Quantum gravity, Matter-Antimatter asymmetry Theoretical (top down) approaches: GUTs, Susy, String Theory (with or without Multiverse), Quantum Gravity,
9 Motivation GR + Λ + CDM : Very successful Observations and theory indicate new physics Dark matter, Dark energy (the cosmological constant problem), Origin of Inflation, The trans-planckian problem, Quantum gravity, Matter-Antimatter asymmetry Theoretical (top down) approaches: GUTs, Susy, String Theory (with or without Multiverse), Quantum Gravity, But why gravity with extra spin-2 fields?
10 Recall: Spin (s) basic structure of field equations (Klein-Gordon, Dirac, Maxwell/Proca, Einstein)
11 Recall: Spin (s) basic structure of field equations (Klein-Gordon, Dirac, Maxwell/Proca, Einstein) Spin in known physics: Standard Model: multiplets of s = 0, 1 2, 1 fields Multiplet structure is crucial for the viability of SM
12 Recall: Spin (s) basic structure of field equations (Klein-Gordon, Dirac, Maxwell/Proca, Einstein) Spin in known physics: Standard Model: multiplets of s = 0, 1 2, 1 fields Multiplet structure is crucial for the viability of SM General relativity: single massless s = 2 field g µν Einstein-Hilbert for s = 2 Klein-Gordon for s = 0
13 Recall: Spin (s) basic structure of field equations (Klein-Gordon, Dirac, Maxwell/Proca, Einstein) Spin in known physics: Standard Model: multiplets of s = 0, 1 2, 1 fields Multiplet structure is crucial for the viability of SM General relativity: single massless s = 2 field g µν Einstein-Hilbert for s = 2 Klein-Gordon for s = 0 Low-energy String theory, etc: single massless spin-2 + plethora of spin 0, 1/2 and 1.
14 Recall: Spin (s) basic structure of field equations (Klein-Gordon, Dirac, Maxwell/Proca, Einstein) Spin in known physics: Standard Model: multiplets of s = 0, 1 2, 1 fields Multiplet structure is crucial for the viability of SM General relativity: single massless s = 2 field g µν Einstein-Hilbert for s = 2 Klein-Gordon for s = 0 Low-energy String theory, etc: single massless spin-2 + plethora of spin 0, 1/2 and 1. Unexplored corner: gravity with more spin-2 fields
15 Challenges in adding spin-2 fields to GR No multiple massless spin-2 fields Linear theory of massive spin-2 fields (5 helicities) [Fierz, Pauli (1939)]
16 Challenges in adding spin-2 fields to GR No multiple massless spin-2 fields Linear theory of massive spin-2 fields (5 helicities) [Fierz, Pauli (1939)] Ghosts in nonlinear theory (5 + 1 helicities) [Boulware, Deser (1972)] Ghosts in theories with multiple spin-2 fields
17 Challenges in adding spin-2 fields to GR No multiple massless spin-2 fields Linear theory of massive spin-2 fields (5 helicities) [Fierz, Pauli (1939)] Ghosts in nonlinear theory (5 + 1 helicities) [Boulware, Deser (1972)] Ghosts in theories with multiple spin-2 fields Can such theories exist or is GR unique? Consequences?
18 The Ghost Problem Ghost: A field with negative kinetic energy Example: L = T V = ( t φ) 2 (healthy) But L = T V = ( t φ) 2 (ghostly) Consequences:
19 The Ghost Problem Ghost: A field with negative kinetic energy Example: But Consequences: L = T V = ( t φ) 2 L = T V = ( t φ) 2 (healthy) (ghostly) Instability: unlimited energy transfer from ghost to other fields Negative probabilities, violation of unitarity in quantum theory
20 Outline of the talk Motivation & Problems Gravity with an extra spin-2 field: Bimetric Theory Potential Issues Uniqueness and the local structure of spacetime Discussion
21 GR with a generic spin-2 field A dynamical theory for the metric g µν & spin-2 field f µν L = m 2 p gr
22 GR with a generic spin-2 field A dynamical theory for the metric g µν & spin-2 field f µν L = m 2 p gr m 4 g V (g 1 f ) +
23 GR with a generic spin-2 field A dynamical theory for the metric g µν & spin-2 field f µν L = m 2 p gr m 4 g V (g 1 f ) + No dynamics for f µν : Massive Gravity
24 GR with a generic spin-2 field A dynamical theory for the metric g µν & spin-2 field f µν L = m 2 p gr m 4 g V (g 1 f ) + No dynamics for f µν : Massive Gravity Overcoming the ghost in massive gravity: [Creminelli, Nicolis, Papucci, Trincherini, (2005)] [de Rham, Gabadadze, Tolley (2010)] [SFH, Rosen (2011); SFH, Rosen, Schmidt-May (2011)]
25 GR with a generic spin-2 field A dynamical theory for the metric g µν & spin-2 field f µν L = m 2 p gr m 4 g V (g 1 f ) + L(f, f )
26 GR with a generic spin-2 field A dynamical theory for the metric g µν & spin-2 field f µν L = m 2 p gr m 4 g V (g 1 f ) + L(f, f ) what is V (g 1 f )? what is L(f, f )? proof of absence of the Boulware-Deser ghost
27 GR with a generic spin-2 field A dynamical theory for the metric g µν & spin-2 field f µν L = m 2 p gr m 4 g V (g 1 f ) + L(f, f ) what is V (g 1 f )? what is L(f, f )? proof of absence of the Boulware-Deser ghost V (g 1 f ) for a ghost-free theory: [SFH, Rosen (2011); de Rham, Gabadadze, Tolley (2010)]
28 Digression: elementary symmetric polynomials e n (S) Consider matrix S with eigenvalues λ 1,, λ 4. e 0 (S) = 1, e 1 (S) = λ 1 + λ 2 + λ 3 + λ 4, e 2 (S) = λ 1 λ 2 + λ 1 λ 3 + λ 1 λ 4 + λ 2 λ 3 + λ 2 λ 4 + λ 3 λ 4, e 3 (S) = λ 1 λ 2 λ 3 + λ 1 λ 2 λ 4 + λ 1 λ 3 λ 4 + λ 2 λ 3 λ 4, e 4 (S) = λ 1 λ 2 λ 3 λ 4.
29 Digression: elementary symmetric polynomials e n (S) Consider matrix S with eigenvalues λ 1,, λ 4. e 0 (S) = 1, e 1 (S) = λ 1 + λ 2 + λ 3 + λ 4, e 2 (S) = λ 1 λ 2 + λ 1 λ 3 + λ 1 λ 4 + λ 2 λ 3 + λ 2 λ 4 + λ 3 λ 4, e 3 (S) = λ 1 λ 2 λ 3 + λ 1 λ 2 λ 4 + λ 1 λ 3 λ 4 + λ 2 λ 3 λ 4, e 4 (S) = λ 1 λ 2 λ 3 λ 4. e 0 (S) = 1, e 1 (S) = Tr(S) [S], e 2 (S) = 1 2 ([S]2 [S 2 ]), e 3 (S) = 1 6 ([S]3 3[S][S 2 ] + 2[S 3 ]), e 4 (S) = det(s), e n (S) = 0 (for n > 4),
30 det(1 + S) = 4 n=0 e n(s)
31 det(1 + S) = 4 n=0 e n(s) Where: V (S) = 4 S = n=0 β n e n (S) g 1 f square root of the matrix g µλ f λν Real? Unique? How to make sense of it? (to be answered later)
32 Ghost-free bi-metric theory [SFH, Rosen ( , )] Ghost-free combination of kinetic and potential terms: L = m 2 g grg m 4 g 4 n=0 β n e n ( g 1 f ) + mf 2 f Rf bimetric nature forced by the absence of ghost
33 Ghost-free bi-metric theory [SFH, Rosen ( , )] Ghost-free combination of kinetic and potential terms: L = m 2 g grg m 4 g 4 n=0 β n e n ( g 1 f ) + mf 2 f Rf bimetric nature forced by the absence of ghost Hamiltonian analysis: 7 = nonlinear propagating modes, no BD ghost! C 1 = 0, C 2 = d dt C 1 = {H, C} = 0 Detailed analysis of constraints [SFH, Lundkvist (to appear)]
34 Mass spectrum & Limits Linear modes: f = c2ḡ, g µν = ḡ µν + δg µν, f µν = f µν + δf µν
35 Mass spectrum & Limits f = c2ḡ, g µν = ḡ µν + δg µν, f µν = f µν + δf µν Linear modes: ( ) Massless spin-2: δg µν = δg µν + m2 f δf mg 2 µν ) Massive spin-2 : δm µν = (δf µν c 2 δg µν (2) (5) g µν, f µν are mixtures of massless and massive modes
36 Mass spectrum & Limits f = c2ḡ, g µν = ḡ µν + δg µν, f µν = f µν + δf µν Linear modes: ( ) Massless spin-2: δg µν = δg µν + m2 f δf mg 2 µν ) Massive spin-2 : δm µν = (δf µν c 2 δg µν (2) (5) g µν, f µν are mixtures of massless and massive modes The General Relativity limit: m g = M P, m f /m g 0 (more later)
37 Mass spectrum & Limits f = c2ḡ, g µν = ḡ µν + δg µν, f µν = f µν + δf µν Linear modes: ( ) Massless spin-2: δg µν = δg µν + m2 f δf mg 2 µν ) Massive spin-2 : δm µν = (δf µν c 2 δg µν (2) (5) g µν, f µν are mixtures of massless and massive modes The General Relativity limit: m g = M P, m f /m g 0 (more later) Massive gravity limit: m g = M P, m f /m g
38 Can Bimetric be a fundamental theory? Similar to Proca theory in curved background, det g (Fµν F µν m 2 g µν A µ A ν + R g ) May need the equivalent of Higgs mechanism with the extra fields for better quantum or even classical behaviour
39 Some features 1) Ghost-free Matter couplings, same as in GR: L g (g, φ) + L f (f, φ)
40 Some features 1) Ghost-free Matter couplings, same as in GR: L g (g, φ) + L f (f, φ) 2) β 1, β 2, β 3 : effective cosmological constant at late times (protected by symmetry, like fermion masses) 3) Massive spin-2 particles: dark matter (stable enough)
41 Some features 1) Ghost-free Matter couplings, same as in GR: L g (g, φ) + L f (f, φ) 2) β 1, β 2, β 3 : effective cosmological constant at late times (protected by symmetry, like fermion masses) 3) Massive spin-2 particles: dark matter (stable enough) 4) Some blackhole and cosmological solutions explored 5) Gravitational waves? 6) Generalization to more than 2 fields
42 GR limit The General Relativity limit: m g = M P, α = m f /m g 0 Cosmological solutions in the GR limit: 3H 2 = ρ M 2 Pl 2 β1 2 m 2 α 2 β2 1 3 β 2 3β2 2 H 2 + O(α 4 ) The GR approximation breaks down at sufficiently strong fields
43 Outline of the talk Motivation & Problems Gravity with an extra spin-2 field: Bimetric Theory Potential Issues Uniqueness and the local structure of spacetime Discussion
44 Potential Issues (1) g, f : incompatible notions of space and time? (2) nonunique g 1 f : ambiguity in defining the action? Causality: local closed timelike curves (CTC s)? The initial value problem? Faster than light possible in the gravitational sector (good or bad?) Analogue of energy conditions and global bi hyperbolicity?
45 Problem of incompatible spacetimes Problem 1: gµν & fµν have Lorentzian signature (1, 3). But may not admit compatible 3+1 decompositions (a) (b) (c) Then, no consistent time evolution equations, no Hamiltonian formulation. (d)
46 Nonuniqueness, Reality and Covariance Problem 2: S = g 1 f is not unique, May not be real, covariant To properly define the theory (V (S)): (a) S µ ν needs to be specified uniquely, (b) Restrict g µν, f µν so that S is real, covariant What are the restrictions on g & f? Can they be imposed meaningfully & consistent with dynamics?
47 Outline of the talk Motivation & Problems Gravity with an extra spin-2 field: Bimetric Theory Potential Issues Uniqueness and the local structure of spacetime Discussion
48 Uniqueness and the local structure of spacetime Natural requirements: General Covariance: S µ ν must be a (1,1) tensor S must be real Implication : Problem 2 (reality, uniqueness) has a natural solution. This also solves Problem 1 (compatible spacetimes). [SFH, M. Kocic (arxiv: )]
49 Solution to the uniqueness problem of V (S) Matrix square roots: Primary roots: Max 16 distinct roots, generic Nonprimary roots: Infinitely many, non-generic (when eigenvalues in different Jordan blocks coincide)
50 Solution to the uniqueness problem of V (S) Matrix square roots: Primary roots: Max 16 distinct roots, generic Nonprimary roots: Infinitely many, non-generic (when eigenvalues in different Jordan blocks coincide) General Covariance: A µ ν = g µρ f ρν is a (1,1) tensor, x µ x µ A Q 1 AQ, for Q µ ν = x µ x ν
51 Uniqueness of S S µ ν = ( A) µ ν : Primary roots: Nonprimary roots: A Q 1 AQ = Q 1 A Q Q 1 AQ Q 1 A Q Step 1: General covariance only primary roots are allowed. A Consequence: Examples of backgrounds with local CTC s correspond to nonprimary roots and are excluded
52 Uniqueness of S S µ ν = ( A) µ ν : Primary roots: Nonprimary roots: A Q 1 AQ = Q 1 A Q Q 1 AQ Q 1 A Q Step 1: General covariance only primary roots are allowed. A Consequence: Examples of backgrounds with local CTC s correspond to nonprimary roots and are excluded Step 2: Only the principal root is always primary. Hence, S must be a principal root. (Nonprincipal roots degenerate to nonprimary roots when some eigenvalues coincide).
53 Reality of S Real S = g 1 f simple classification of allowed g, f configurations [SFH, M. Kocic (arxiv: )]
54 Reality of S Real S = g 1 f simple classification of allowed g, f configurations [SFH, M. Kocic (arxiv: )] Theorem: Real S = g 1 f exist if and only if the null cones of g and f (i) intersect in open sets, or, (ii) have no common space nor common time directions (Type IV) Type I Type IIa Type IIb Type III Type IV
55 Reality of S Real S = g 1 f simple classification of allowed g, f configurations [SFH, M. Kocic (arxiv: )] Theorem: Real S = g 1 f exist if and only if the null cones of g and f (i) intersect in open sets, or, (ii) have no common space nor common time directions (Type IV) Type I Type IIa Type IIb Type III Type IV *Types I-III: proper 3+1 decompositions, primary roots, allowed. *Type IV: only nonprimary real roots! (excluded).
56 Choice of the square root Reality + General Covariance * Real principal square root (unique), * Compatible 3+1 decomposition h µν = g µρ ( g 1 f ) ρ ν h null-cones for the principal root (except for the last one) Useful for choosing good coordinate systems, The specific, existing local CTC s in massive gravity rulled out.
57 Consistency with dynamics Type IV metrics arise as a limit of Type IIb metrics. But in the limit, S has a branch cut. Then, for the principal root, the variation δs is not defined at the cut Eqns. of motion not valid for Type IV. Hence cannot arise dynamically.
58 Consistency with dynamics Type IV metrics arise as a limit of Type IIb metrics. But in the limit, S has a branch cut. Then, for the principal root, the variation δs is not defined at the cut Eqns. of motion not valid for Type IV. Hence cannot arise dynamically. A simple mechanical example: A = dt (ẋ 2 /2 λ ) x 2, x 2 = x (1) ẍ = λ(x > 0), ẍ = λ(x < 0) (2) (no equation at x = 0) Implication for some acausality arguments (CTC s) in massive gravity
59 Outline of the talk Motivation & Problems Gravity with an extra spin-2 field: Bimetric Theory Potential Issues Uniqueness and the local structure of spacetime Discussion
60 Discussion The beginning of understanding theories of spin-2 fields beyond General Relativity.
61 Discussion The beginning of understanding theories of spin-2 fields beyond General Relativity. Superluminality? (yes, but not necessarily harmful, replacement for inflation?) Causality? (needs to be investigated further) Energy conditions, global bi-hyperbolicity A more fundamental formulation Application to cosmology, blackholes, GW, etc. Extra symmetries Modified kinetic terms? much less understood. [SFH, Apolo (2016)]
62 Thank you!
63 The Hojman-Kuchar-Teitelboim Metric General Relativity in 3+1 decomposition (g µν : γ ij, N, N i ): gr π ij t γ ij NR 0 N i R i Constraints: R 0 = 0, R i = 0. Algebra of General Coordinate Transformations (GCT): { R 0 (x), R 0 (y) } [ ] = R i (x) δ 3 (x y) R i (y) δ 3 (x y) x i y i { R 0 (x), R i (y) } = R 0 (y) δ 3 (x y) x i { Ri (x), R j (y) } [ ] = R j (x) δ 3 (x y) R x i i (y) δ 3 (x y) y j R i = γ ij R j, γ ij : metric of spatial 3-surfaces. Any generally covariant theory contains such an algebra. HKT: The tensor that lowers the index on R i is the physical metric of 3-surfaces.
64 The HKT metric in bimetric theory Consider g µν = (γ ij, N, N i ) and f µν = (φ ij, L, L i ), L g,f π ij γ ij + p ij φ ij M R 0 M i Ri On the surface of second class Constraints. GCT Algebra: { R0 (x), R 0 (y) } [ = Ri (x) δ 3 (x y) R ] i (y) δ 3 (x y) x i y i { R0 (x), R i (y) } = R 0 (y) δ 3 (x y) x i R i = φ ij Rj, φ ij : the 3-metric of f µν, or R i = γ ij Rj, γ ij : the 3-metric of g µν. The HKT metric of bimetric theory is g µν or f µν, consistent with ghost-free matter couplings [SFH, A. Lundkvist (to appear)]
Bimetric Massive Gravity
Bimetric Massive Gravity Tomi Koivisto / Nordita (Stockholm) 21.11.2014 Outline Introduction Bimetric gravity Cosmology Matter coupling Conclusion Motivations Why should the graviton be massless? Large
More informationA First Class Formulation of Massive Gravity - or Massive Gravity as a Gauge Theory
A First Class Formulation of Massive Gravity - or Massive Gravity as a Gauge Theory Andrew J Tolley Case Western Reserve University Based on work to appear Why Massive Gravity? Massive Gravity Theories
More informationNonlinear massive gravity and Cosmology
Nonlinear massive gravity and Cosmology Shinji Mukohyama (Kavli IPMU, U of Tokyo) Based on collaboration with Antonio DeFelice, Emir Gumrukcuoglu, Chunshan Lin Why alternative gravity theories? Inflation
More informationIntroduction to the Vainshtein mechanism
Introduction to the Vainshtein mechanism Eugeny Babichev LPT, Orsay School Paros 23-28 September 2013 based on arxiv:1107.1569 with C.Deffayet OUTLINE Introduction and motivation k-mouflage Galileons Non-linear
More informationGravitational Waves. GR: 2 polarizations
Gravitational Waves GR: 2 polarizations Gravitational Waves GR: 2 polarizations In principle GW could have 4 other polarizations 2 vectors 2 scalars Potential 4 `new polarizations Massive Gravity When
More informationNew Model of massive spin-2 particle
New Model of massive spin-2 particle Based on Phys.Rev. D90 (2014) 043006, Y.O, S. Akagi, S. Nojiri Phys.Rev. D90 (2014) 123013, S. Akagi, Y.O, S. Nojiri Yuichi Ohara QG lab. Nagoya univ. Introduction
More informationCosmological perturbations in nonlinear massive gravity
Cosmological perturbations in nonlinear massive gravity A. Emir Gümrükçüoğlu IPMU, University of Tokyo AEG, C. Lin, S. Mukohyama, JCAP 11 (2011) 030 [arxiv:1109.3845] AEG, C. Lin, S. Mukohyama, To appear
More informationMassive gravity and cosmology
Massive gravity and cosmology Shinji Mukohyama (Kavli IPMU, U of Tokyo) Based on collaboration with Antonio DeFelice, Emir Gumrukcuoglu, Kurt Hinterbichler, Chunshan Lin, Mark Trodden Why alternative gravity
More informationMASAHIDE YAMAGUCHI. Perturbations of Cosmological and Black Hole Solutions in Massive gravity and Bi-gravity. (Tokyo Institute of Technology)
Perturbations of Cosmological and Black Hole Solutions in Massive gravity and Bi-gravity MASAHIDE YAMAGUCHI (Tokyo Institute of Technology) 10/12/15@KICP, Exploring Theories of Modified Gravity arxiv:1509.02096,
More informationPerturbations of Cosmological and Black hole solutions
Perturbations of Cosmological and Black hole solutions in Bi-Gravity Daisuke Yoshida, Tokyo Institute of Technology Based on collaboration with Tsutomu Kobayashi, Masaru Siino, Masahide Yamaguchi (In progress)
More informationAspects of massive gravity
Aspects of massive gravity Sébastien Renaux-Petel CNRS - IAP Paris Rencontres de Moriond, 22.03.2015 Motivations for modifying General Relativity in the infrared Present acceleration of the Universe: {z
More informationOn the uniqueness of Einstein-Hilbert kinetic term (in massive (multi-)gravity)
On the uniqueness of Einstein-Hilbert kinetic term (in massive (multi-)gravity) Andrew J. Tolley Case Western Reserve University Based on: de Rham, Matas, Tolley, ``New Kinetic Terms for Massive Gravity
More informationClaudia de Rham July 30 th 2013
Claudia de Rham July 30 th 2013 GR has been a successful theory from mm length scales to Cosmological scales Then why Modify Gravity? Why Modify Gravity in the IR? Late time acceleration & CC problem First
More informationMassive and Newton-Cartan Gravity in Action
Massive and Newton-Cartan Gravity in Action Eric Bergshoeff Groningen University The Ninth Aegean Summer School on Einstein s Theory of Gravity and its Modifications: From Theory to Observations based
More informationMassive gravity and Caustics: A definitive covariant constraint analysis
Massive gravity and Caustics: A definitive covariant constraint analysis Cosmo 2014 - Chicago George Zahariade UC Davis August 29, 2014 1 / 18 Goals Motivation and goals de Rham-Gabadadze-Tolley massive
More informationHiguchi VS Vainshtein
Higuchi VS Vainshtein ArXiv: 1206.3852+ soon to appear. Matteo Fasiello and Andrew J. Tolley Case Western Reserve University Outline The Higuchi bound The Vainshtein mechanism Higuchi vs Vainshtein drgt
More informationarxiv: v1 [hep-th] 1 Oct 2008
Cascading Gravity and Degravitation Claudia de Rham Dept. of Physics & Astronomy, McMaster University, Hamilton ON, Canada Perimeter Institute for Theoretical Physics, Waterloo, ON, Canada arxiv:0810.069v1
More informationMassive gravity and cosmology
Massive gravity and cosmology Shinji Mukohyama Yukawa Institute for Theoretical Physics Kyoto University Based on collaborations with Katsuki Aoki, Antonio DeFelice, Garrett Goon, Emir Gumrukcuoglu, Lavinia
More informationMassive gravity and cosmology
Massive gravity and cosmology Shinji Mukohyama (YITP Kyoto) Based on collaboration with Antonio DeFelice, Garrett Goon, Emir Gumrukcuoglu, Lavinia Heisenberg, Kurt Hinterbichler, David Langlois, Chunshan
More informationHIGHER SPIN PROBLEM IN FIELD THEORY
HIGHER SPIN PROBLEM IN FIELD THEORY I.L. Buchbinder Tomsk I.L. Buchbinder (Tomsk) HIGHER SPIN PROBLEM IN FIELD THEORY Wroclaw, April, 2011 1 / 27 Aims Brief non-expert non-technical review of some old
More informationLorentz Center workshop Non-Linear Structure in the Modified Universe July 14 th Claudia de Rham
Lorentz Center workshop Non-Linear Structure in the Modified Universe July 14 th 2014 Claudia de Rham Modified Gravity Lorentz-Violating LV-Massive Gravity Ghost Condensate Horava- Lifshitz Cuscuton Extended
More informationNon-local Modifications of Gravity and Cosmic Acceleration
Non-local Modifications of Gravity and Cosmic Acceleration Valeri Vardanyan Cargese-2017 In collaboration with: Yashar Akrami Luca Amendola Alessandra Silvestri arxiv:1702.08908 Late time cosmology The
More informationGravitational waves, solitons, and causality in modified gravity
Gravitational waves, solitons, and causality in modified gravity Arthur Suvorov University of Melbourne December 14, 2017 1 of 14 General ideas of causality Causality as a hand wave Two events are causally
More informationBlack holes in massive gravity
Black holes in massive gravity Eugeny Babichev LPT, Orsay IAP PARIS, MARCH 14 2016 REVIEW: in collaboration with: R. Brito, M. Crisostomi, C. Deffayet, A. Fabbri,P. Pani, ARXIV:1503.07529 1512.04058 1406.6096
More informationHolographic Space Time
Holographic Space Time Tom Banks (work with W.Fischler) April 1, 2015 The Key Points General Relativity as Hydrodynamics of the Area Law - Jacobson The Covariant Entropy/Holographic Principle - t Hooft,
More informationNull Energy Condition violations in bimetric gravity
Null Energy Condition violations in bimetric gravity arxiv:1206.3814v2 [gr-qc] 27 Jun 2012 Valentina Baccetti, Prado Martin-Moruno, and Matt Visser School of Mathematics, Statistics, and Operations Research,
More informationVainshtein mechanism. Lecture 3
Vainshtein mechanism Lecture 3 Screening mechanism Screening mechanisms The fifth force should act only on large scales and it should be hidden on small scales This implies that these mechanisms should
More informationRecent developments in bimetric theory
Review: Updated March 31, 2016 Recent developments in bimetric theory arxiv:1512.00021v2 [hep-th] 30 Mar 2016 Angnis Schmidt-May, 1 Mikael von Strauss 2 1 Institut für Theoretische Physik, Eidgenössische
More informationMinimalism in Modified Gravity
Minimalism in Modified Gravity Shinji Mukohyama (YITP, Kyoto U) Based on collaborations with Katsuki Aoki, Nadia Bolis, Antonio De Felice, Tomohiro Fujita, Sachiko Kuroyanagi, Francois Larrouturou, Chunshan
More informationD. f(r) gravity. φ = 1 + f R (R). (48)
5 D. f(r) gravity f(r) gravity is the first modified gravity model proposed as an alternative explanation for the accelerated expansion of the Universe [9]. We write the gravitational action as S = d 4
More informationString theory triplets and higher-spin curvatures
String theory triplets and higher-spin curvatures Dario Francia Institute of Physics - Academy of Sciences of the Czech Republic SFT2010 YITP Kyoto October 19th, 2010 based on: D. F. J.Phys. Conf. Ser.
More informationMassive gravity meets simulations?
Massive gravity meets simulations? Kazuya Koyama University of Portsmouth Non-linear massive gravity theory (de Rham, Gadadadze & Tolley 10) Two key features Self-acceleration A graviton mass accounts
More informationThe Klein-Gordon Equation Meets the Cauchy Horizon
Enrico Fermi Institute and Department of Physics University of Chicago University of Mississippi May 10, 2005 Relativistic Wave Equations At the present time, our best theory for describing nature is Quantum
More informationA loop quantum multiverse?
Space-time structure p. 1 A loop quantum multiverse? Martin Bojowald The Pennsylvania State University Institute for Gravitation and the Cosmos University Park, PA arxiv:1212.5150 Space-time structure
More informationStable violation of the null energy condition and non-standard cosmologies
Paolo Creminelli (ICTP, Trieste) Stable violation of the null energy condition and non-standard cosmologies hep-th/0606090 with M. Luty, A. Nicolis and L. Senatore What is the NEC? Energy conditions: Singularity
More informationQUINTESSENTIAL INFLATION
QUINTESSENTIAL INFLATION Relic gravity waves M. SAMI Centre for Theoretical Physics Jamia Millia University New Delhi GC-2018 BRIEF OVER VIEW Acceleration Generic feature of cosmic history Late time acceleration:
More informationLecture 9: RR-sector and D-branes
Lecture 9: RR-sector and D-branes José D. Edelstein University of Santiago de Compostela STRING THEORY Santiago de Compostela, March 6, 2013 José D. Edelstein (USC) Lecture 9: RR-sector and D-branes 6-mar-2013
More informationGRAVITATION F10. Lecture Maxwell s Equations in Curved Space-Time 1.1. Recall that Maxwell equations in Lorentz covariant form are.
GRAVITATION F0 S. G. RAJEEV Lecture. Maxwell s Equations in Curved Space-Time.. Recall that Maxwell equations in Lorentz covariant form are. µ F µν = j ν, F µν = µ A ν ν A µ... They follow from the variational
More informationGalileon Cosmology ASTR448 final project. Yin Li December 2012
Galileon Cosmology ASTR448 final project Yin Li December 2012 Outline Theory Why modified gravity? Ostrogradski, Horndeski and scalar-tensor gravity; Galileon gravity as generalized DGP; Galileon in Minkowski
More informationNon-local infrared modifications of gravity and dark energy
Non-local infrared modifications of gravity and dark energy Michele Maggiore Los Cabos, Jan. 2014 based on M. Jaccard, MM and E. Mitsou, 1305.3034, PR D88 (2013) MM, arxiv: 1307.3898 S. Foffa, MM and E.
More informationNew Fundamental Wave Equation on Curved Space-Time and its Cosmological Applications
New Fundamental Wave Equation on Curved Space-Time and its Cosmological Applications Z.E. Musielak, J.L. Fry and T. Chang Department of Physics University of Texas at Arlington Flat Space-Time with Minkowski
More informationInflationary Paradigm in Modified Gravity
Inflationary Paradigm in Modified Gravity Lavinia Heisenberg (ETH-ITS) Institute for Theoretical Studies, Zürich Jul. 21th, Nordita, Stockholm/Sweden Theoretical modelling of the Universe General Relativity
More informationAspects of Spontaneous Lorentz Violation
Aspects of Spontaneous Lorentz Violation Robert Bluhm Colby College IUCSS School on CPT & Lorentz Violating SME, Indiana University, June 2012 Outline: I. Review & Motivations II. Spontaneous Lorentz Violation
More informationarxiv:hep-th/ v3 28 Dec 1996
HEP-TH/9509142, UPR-660T CONSISTENT SPIN-TWO COUPLING AND QUADRATIC GRAVITATION AHMED HINDAWI, BURT A. OVRUT, AND DANIEL WALDRAM Department of Physics, University of Pennsylvania Philadelphia, PA 19104-6396,
More informationMassive gravitons in arbitrary spacetimes
Massive gravitons in arbitrary spacetimes Mikhail S. Volkov LMPT, University of Tours, FRANCE Kyoto, YITP, Gravity and Cosmology Workshop, 6-th February 2018 C.Mazuet and M.S.V., Phys.Rev. D96, 124023
More informationSuper Yang-Mills Theory in 10+2 dims. Another Step Toward M-theory
1 Super Yang-Mills Theory in 10+2 dims. Another Step Toward M-theory Itzhak Bars University of Southern California Talk at 4 th Sakharov Conference, May 2009 http://physics.usc.edu/~bars/homepage/moscow2009_bars.pdf
More informationConstructive Gravity
Constructive Gravity A New Approach to Modified Gravity Theories Marcus C. Werner, Kyoto University Gravity and Cosmology 2018 YITP Long Term Workshop, 27 February 2018 Constructive gravity Standard approach
More informationString Theory and The Velo-Zwanziger Problem
String Theory and The Velo-Zwanziger Problem Rakibur Rahman Scuola Normale Superiore & INFN, Pisa February 10, 2011 DAMTP, University of Cambridge M. Porrati A. Sagnotti M. Porrati, RR and A. Sagnotti,
More informationDark energy & Modified gravity in scalar-tensor theories. David Langlois (APC, Paris)
Dark energy & Modified gravity in scalar-tensor theories David Langlois (APC, Paris) Introduction So far, GR seems compatible with all observations. Several motivations for exploring modified gravity Quantum
More informationDark Energy Theory. Mark Trodden University of Pennsylvania
Mark Trodden University of Pennsylvania 2015: the Spacetime Odyssey Continues Nordita, Stockholm, June 2, 2015 Overview Motivations - background, and the problem of cosmic acceleration Some possible approaches:
More informationCosmology with moving bimetric fluids
Prepared for submission to JCAP Cosmology with moving bimetric fluids arxiv:1608.06493v2 [gr-qc] 18 Nov 2016 Carlos García-García, Antonio L. Maroto, Prado Martín-Moruno Departamento de Física Teórica
More informationA brief introduction to modified theories of gravity
(Vinc)Enzo Vitagliano CENTRA, Lisboa May, 14th 2015 IV Amazonian Workshop on Black Holes and Analogue Models of Gravity Belém do Pará The General Theory of Relativity dynamics of the Universe behavior
More information"Topologically Massive" theories in and beyond 3D
"Topologically Massive" theories in and beyond 3D Yihao Yin (University of Groningen) In collaboration with E.A. Bergshoeff, M. Kovacevic, J. Rosseel, P.K. Townsend, etc. ( arxiv: 1109.0382 & 1207.0192
More informationCosmology, Scalar Fields and Hydrodynamics
Cosmology, Scalar Fields and Hydrodynamics Alexander Vikman (CERN) THIS TALK IS BASED ON WORK IN PROGRESS AND Imperfect Dark Energy from Kinetic Gravity Braiding arxiv:1008.0048 [hep-th], JCAP 1010:026,
More informationCosmological and astrophysical applications of vector-tensor theories
Cosmological and astrophysical applications of vector-tensor theories Shinji Tsujikawa (Tokyo University of Science) Collaboration with A.De Felice, L.Heisenberg, R.Kase, M.Minamitsuji, S.Mukohyama, S.
More informationManifestly diffeomorphism invariant classical Exact Renormalization Group
Manifestly diffeomorphism invariant classical Exact Renormalization Group Anthony W. H. Preston University of Southampton Supervised by Prof. Tim R. Morris Talk prepared for Asymptotic Safety seminar,
More informationMinimal theory of massive gravity
Minimal theory of massive gravity Antonio De Felice Yukawa Institute for Theoretical Physics, YITP, Kyoto U. 2-nd APCTP-TUS Workshop Tokyo, Aug 4, 2015 [with prof. Mukohyama] Introduction drgt theory:
More informationGauge coupling unification without leptoquarks Mikhail Shaposhnikov
Gauge coupling unification without leptoquarks Mikhail Shaposhnikov March 9, 2017 Work with Georgios Karananas, 1703.02964 Heidelberg, March 9, 2017 p. 1 Outline Motivation Gauge coupling unification without
More informationNon-relativistic holography
University of Amsterdam AdS/CMT, Imperial College, January 2011 Why non-relativistic holography? Gauge/gravity dualities have become an important new tool in extracting strong coupling physics. The best
More informationHAMILTONIAN FORMULATION OF f (Riemann) THEORIES OF GRAVITY
ABSTRACT We present a canonical formulation of gravity theories whose Lagrangian is an arbitrary function of the Riemann tensor, which, for example, arises in the low-energy limit of superstring theories.
More informationChapter 2 General Relativity and Black Holes
Chapter 2 General Relativity and Black Holes In this book, black holes frequently appear, so we will describe the simplest black hole, the Schwarzschild black hole and its physics. Roughly speaking, a
More informationPhysics Letters B 711 (2012) Contents lists available at SciVerse ScienceDirect. Physics Letters B.
Physics Letters B 711 01) 190 195 Contents lists available at SciVerse ScienceDirect Physics Letters B www.elsevier.com/locate/physletb Ghost free massive gravity in the Stücelberg language Claudia de
More informationQuantum Fields in Curved Spacetime
Quantum Fields in Curved Spacetime Lecture 3 Finn Larsen Michigan Center for Theoretical Physics Yerevan, August 22, 2016. Recap AdS 3 is an instructive application of quantum fields in curved space. The
More informationString Theory. Quantum Mechanics and Gravity: Cliff Burgess, McGill. The start of a beautiful relationship?
Quantum Mechanics and Gravity: The start of a beautiful relationship? Cliff Burgess, McGill Outline The 20 th Century Crisis Quantum Mechanics vs Relativity A Theoretical Balancing Act Possible Problems?
More informationScale-invariance from spontaneously broken conformal invariance
Scale-invariance from spontaneously broken conformal invariance Austin Joyce Center for Particle Cosmology University of Pennsylvania Hinterbichler, Khoury arxiv:1106.1428 Hinterbichler, AJ, Khoury arxiv:1202.6056
More informationJGRG 26 Conference, Osaka, Japan 24 October Frederic P. Schuller. Constructive gravity. Institute for Quantum Gravity Erlangen, Germany
JGRG 26 Conference, Osaka, Japan 24 October 2016 Constructive gravity Frederic P. Schuller Institute for Quantum Gravity Erlangen, Germany S matter ) S gravity JGRG 26 Conference, Osaka, Japan 24 October
More informationQuantum gravity, probabilities and general boundaries
Quantum gravity, probabilities and general boundaries Robert Oeckl Instituto de Matemáticas UNAM, Morelia International Loop Quantum Gravity Seminar 17 October 2006 Outline 1 Interpretational problems
More informationGravitational Waves and New Perspectives for Quantum Gravity
Gravitational Waves and New Perspectives for Quantum Gravity Ilya L. Shapiro Universidade Federal de Juiz de Fora, Minas Gerais, Brazil Supported by: CAPES, CNPq, FAPEMIG, ICTP Challenges for New Physics
More informationTesting the equivalence principle
19/07/2011 ACFC Testing the equivalence principle the link between constants, gravitation and cosmology Jean-Philippe UZAN Outline - Some words on fundamental constants - Links between constants and gravity
More informationEmergent space-time and gravity in the IIB matrix model
Emergent space-time and gravity in the IIB matrix model Harold Steinacker Department of physics Veli Losinj, may 2013 Geometry and physics without space-time continuum aim: (toy-?) model for quantum theory
More informationGravitation: Gravitation
An Introduction to General Relativity Center for Relativistic Astrophysics School of Physics Georgia Institute of Technology Notes based on textbook: Spacetime and Geometry by S.M. Carroll Spring 2013
More informationOut of equilibrium dynamics and Robinson-Trautman spacetimes. Kostas Skenderis
Out of equilibrium dynamics and STAG CH RESEARCH ER C TE CENTER NINTH CRETE REGIONAL MEETING IN STRING THEORY In memoriam: Ioannis Bakas Kolymbari, July 13, 2017 Out of equilibrium dynamics and Outline
More informationStatus of Hořava Gravity
Status of Institut d Astrophysique de Paris based on DV & T. P. Sotiriou, PRD 85, 064003 (2012) [arxiv:1112.3385 [hep-th]] DV & T. P. Sotiriou, JPCS 453, 012022 (2013) [arxiv:1212.4402 [hep-th]] DV, arxiv:1502.06607
More informationBlack Holes in Higher-Derivative Gravity. Classical and Quantum Black Holes
Black Holes in Higher-Derivative Gravity Classical and Quantum Black Holes LMPT, Tours May 30th, 2016 Work with Hong Lü, Alun Perkins, Kelly Stelle Phys. Rev. Lett. 114 (2015) 17, 171601 Introduction Black
More informationString Theory and Nonrelativistic Gravity
String Theory and Nonrelativistic Gravity Eric Bergshoeff Groningen University work done in collaboration with Ceyda Şimşek, Jaume Gomis, Kevin Grosvenor and Ziqi Yan A topical conference on elementary
More informationsquare kilometer array: a powerful tool to test theories of gravity and cosmological models
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/
More informationInflationary Massive Gravity
New perspectives on cosmology APCTP, 15 Feb., 017 Inflationary Massive Gravity Misao Sasaki Yukawa Institute for Theoretical Physics, Kyoto University C. Lin & MS, PLB 75, 84 (016) [arxiv:1504.01373 ]
More informationCosmology meets Quantum Gravity?
Cosmology meets Quantum Gravity? Sergey Sibiryakov Benasque, 08/08/14 plethora of inflationary models vs. limited experimental information plethora of inflationary models vs. limited experimental information
More informationLorentz-covariant spectrum of single-particle states and their field theory Physics 230A, Spring 2007, Hitoshi Murayama
Lorentz-covariant spectrum of single-particle states and their field theory Physics 30A, Spring 007, Hitoshi Murayama 1 Poincaré Symmetry In order to understand the number of degrees of freedom we need
More informationCausality, hyperbolicity, and shock formation in Lovelock theories
Causality, hyperbolicity, and shock formation in Lovelock theories Harvey Reall DAMTP, Cambridge University HSR, N. Tanahashi and B. Way, arxiv:1406.3379, 1409.3874 G. Papallo, HSR arxiv:1508.05303 Lovelock
More informationEn búsqueda del mundo cuántico de la gravedad
En búsqueda del mundo cuántico de la gravedad Escuela de Verano 2015 Gustavo Niz Grupo de Gravitación y Física Matemática Grupo de Gravitación y Física Matemática Hoy y Viernes Mayor información Quantum
More informationThe nonlinear dynamical stability of infrared modifications of gravity
The nonlinear dynamical stability of infrared modifications of gravity Aug 2014 In collaboration with Richard Brito, Vitor Cardoso and Matthew Johnson Why Study Modifications to Gravity? General relativity
More informationGreen s function of the Vector fields on DeSitter Background
Green s function of the Vector fields on DeSitter Background Gaurav Narain The Institute for Fundamental Study (IF) March 10, 2015 Talk Based On Green s function of the Vector fields on DeSitter Background,
More informationTopics on Galileons and generalized Galileons. Pacific 2016, Moorea, Sept the 13th. 1. What are scalar Galileons? 2. What are they useful for?
Topics on Galileons and generalized Galileons Pacific 2016, Moorea, Sept the 13th 1. What are scalar Galileons? Cédric Deffayet (IAP and IHÉS, CNRS Paris Bures sur Yvette) 2. What are they useful for?
More informationCosmology in generalized Proca theories
3-rd Korea-Japan workshop on dark energy, April, 2016 Cosmology in generalized Proca theories Shinji Tsujikawa (Tokyo University of Science) Collaboration with A.De Felice, L.Heisenberg, R.Kase, S.Mukohyama,
More informationHolography and Unitarity in Gravitational Physics
Holography and Unitarity in Gravitational Physics Don Marolf 01/13/09 UCSB ILQG Seminar arxiv: 0808.2842 & 0808.2845 This talk is about: Diffeomorphism Invariance and observables in quantum gravity The
More informationNo unitary theory of PM spin two and gravity
AEI-2014-027 No unitary theory of PM spin two and gravity arxiv:1406.2335v1 [hep-th] 9 Jun 2014 Euihun JOUNG, a Wenliang LI a and Massimo TARONNA b,c a AstroParticule et Cosmologie 1 10 rue Alice Domon
More informationNon-SUSY BSM: Lecture 1/2
Non-SUSY BSM: Lecture 1/2 Generalities Benasque September 26, 2013 Mariano Quirós ICREA/IFAE Mariano Quirós (ICREA/IFAE) Non-SUSY BSM: Lecture 1/2 1 / 31 Introduction Introduction There are a number of
More information752 Final. April 16, Fadeev Popov Ghosts and Non-Abelian Gauge Fields. Tim Wendler BYU Physics and Astronomy. The standard model Lagrangian
752 Final April 16, 2010 Tim Wendler BYU Physics and Astronomy Fadeev Popov Ghosts and Non-Abelian Gauge Fields The standard model Lagrangian L SM = L Y M + L W D + L Y u + L H The rst term, the Yang Mills
More informationExtensions of Lorentzian spacetime geometry
Extensions of Lorentzian spacetime geometry From Finsler to Cartan and vice versa Manuel Hohmann Teoreetilise Füüsika Labor Füüsika Instituut Tartu Ülikool LQP33 Workshop 15. November 2013 Manuel Hohmann
More informationTwistor Strings, Gauge Theory and Gravity. Abou Zeid, Hull and Mason hep-th/
Twistor Strings, Gauge Theory and Gravity Abou Zeid, Hull and Mason hep-th/0606272 Amplitudes for YM, Gravity have elegant twistor space structure: Twistor Geometry Amplitudes for YM, Gravity have elegant
More informationProblem Set #4: 4.1, 4.3, 4.5 (Due Monday Nov. 18th) f = m i a (4.1) f = m g Φ (4.2) a = Φ. (4.4)
Chapter 4 Gravitation Problem Set #4: 4.1, 4.3, 4.5 (Due Monday Nov. 18th) 4.1 Equivalence Principle The Newton s second law states that f = m i a (4.1) where m i is the inertial mass. The Newton s law
More informationBell s Theorem. Ben Dribus. June 8, Louisiana State University
Bell s Theorem Ben Dribus Louisiana State University June 8, 2012 Introduction. Quantum Theory makes predictions that challenge intuitive notions of physical reality. Einstein and others were sufficiently
More informationA model of the basic interactions between elementary particles is defined by the following three ingredients:
I. THE STANDARD MODEL A model of the basic interactions between elementary particles is defined by the following three ingredients:. The symmetries of the Lagrangian; 2. The representations of fermions
More informationSolutions to gauge hierarchy problem. SS 10, Uli Haisch
Solutions to gauge hierarchy problem SS 10, Uli Haisch 1 Quantum instability of Higgs mass So far we considered only at RGE of Higgs quartic coupling (dimensionless parameter). Higgs mass has a totally
More informationAn all-scale exploration of alternative theories of gravity. Thomas P. Sotiriou SISSA - International School for Advanced Studies, Trieste
An all-scale exploration of alternative theories of gravity Thomas P. Sotiriou SISSA - International School for Advanced Studies, Trieste General Outline Beyond GR: motivation and pitfalls Alternative
More informationPRINCIPLES OF PHYSICS. \Hp. Ni Jun TSINGHUA. Physics. From Quantum Field Theory. to Classical Mechanics. World Scientific. Vol.2. Report and Review in
LONDON BEIJING HONG TSINGHUA Report and Review in Physics Vol2 PRINCIPLES OF PHYSICS From Quantum Field Theory to Classical Mechanics Ni Jun Tsinghua University, China NEW JERSEY \Hp SINGAPORE World Scientific
More informationExact solutions in supergravity
Exact solutions in supergravity James T. Liu 25 July 2005 Lecture 1: Introduction and overview of supergravity Lecture 2: Conditions for unbroken supersymmetry Lecture 3: BPS black holes and branes Lecture
More informationMulti-disformal invariance of nonlinear primordial perturbations
Multi-disformal invariance of nonlinear primordial perturbations Yuki Watanabe Natl. Inst. Tech., Gunma Coll.) with Atsushi Naruko and Misao Sasaki accepted in EPL [arxiv:1504.00672] 2nd RESCEU-APCosPA
More informationLife with More Than 4: Extra Dimensions
Life with More Than 4: Extra Dimensions Andrew Larkoski 4/15/09 Andrew Larkoski SASS 5 Outline A Simple Example: The 2D Infinite Square Well Describing Arbitrary Dimensional Spacetime Motivations for Extra
More information