Dark energy and nonlocal gravity

Size: px
Start display at page:

Download "Dark energy and nonlocal gravity"

Transcription

1 Dark energy and nonlocal gravity Michele Maggiore Vacuum 2015, Barcelona

2 based on Jaccard, MM, Mitsou, PRD 2013, MM, PRD 2014, Foffa, MM, Mitsou, PLB 2014, Foffa, MM, Mitsou, IJMPA 2014, Kehagias and MM, JHEP 2014, MM and Mancarella, PRD 2014, Dirian, Foffa, Khosravi, Kunz, MM, JCAP 2014, Dirian and Mitsou, JCAP 2014, Dirian, Foffa, Kunz, MM, Pettorino, JCAP 2015, MM Dirian, Foffa, Kunz, MM, Pettorino, Cusin, Foffa, Maggiore, in preparation in preparation cosmological applications (Yves's talk) / theoretical aspects (this talk)

3 the general idea: modify GR in the infrared using non-local terms non-locality emerges from fundamental local theories in many situations classically, when separating long and short wavelength and integrating out the short wave-length (e.g cosmological perturbation theory) in QFT, when computing the effective action that includes the effect of radiative corrections of massless or light particles.

4 a natural way of modifying GR in the IR is by introducing a mass scale (e.g. massive gravity, bigravity,...) we will introduce a mass scale as the coefficient of a nonlocal term phenomenological approach. Identify a non-local modification of GR that works well attempt at a more fundamental understanding IR running and strong coupling in R 2 theories strong IR effects from the anomaly-induced effective action

5 a locality / gauge-invariance duality for massive gauge fields Proca theory for massive photons S = R d 4 x 1 4 F µ F µ 1 2 m2 A µ A µ j µ A µ F µ m 2 A = j! n m A =0 ( m 2 )A µ =0 non-local formulation (Dvali 2006) Stueckelberg trick: A µ! A µ + 1 µ' we add one field and we gain a gauge symmetry A µ! A µ, '! ' + m

6 S = R d 4 x 1 4 F µ F µ 1 2 m2 A µ A µ 1 µ'@ µ ' m A µ ' j µ A µ F µ = m 2 A + ' + j, ' + µ A µ =0. If we choose the unitary gauge φ=0 we get back to the original formulation of Proca theory (and loose the gauge sym because of gauge fixing). Instead, keep the gauge sym explicit and integrate out φ using its own equation of motion: '(x) = m 1 (@ µ A µ )

7 Substituting in the eq of motion for A ν : or 1 m 2 ( m 2 )A = we have explicit gauge invariance for the massive theory, at the price µ F µ = j 1 µ A µ + j a sort of duality between explicit gauge-invariance and explicit µ A µ =0 we can fix the gauge and the non-local term disappears (and we are back to Proca eqs.) with hindsight, the Stueckelberg trick was not needed

8 massive photon: can be described replacing (Dvali 2006) for gravity, a first guess for a massive deformation of GR could be however this is not correct since (Arkani-Hamed, Dimopoulos, Dvali and Gabadadze 2002) we lose energy-momentum conservation

9 to preserve energy-momentum conservation: G µ m 2 ( 1 G µ ) T =8 GT µ (Jaccard,MM, Mitsou, 2013) however, instabilities in the cosmological evolution (Foffa,MM, Mitsou, 2013) G µ m 2 (g µ 1 R) T =8 GT µ (MM 2013) stable cosmological evolution! a related model: S NL = 1 Z 16 G d 4 x p g apple R m 2 R 1 2 R (MM and M.Mancarella, 2014)

10 At the phenomenological level, these two non-local models work very well: no vdvz discontiuity, solar system tests OK generates dynamically a dark energy cosmological perturbations work well passes tests of structure formation comparison with CMB,SNe,BAO with modified Boltzmann code ok higher value of H0! see Yves' talk They are the only existing models, with the same number of parameters as ΛCDM, which are competitive with ΛCDM from the point of view of fitting the data

11 Where such non-locality comes from? we will explore two related ideas that could lead to strong IR effects in gravity MM IR running of coupling constants in R 2 gravity IR effects from the anomaly-induced effective action in Einstein gravity

12 Running coupling constants in R 2 theory in QFT, loops involving massless or light particles give nonlocal terms e.g. in QED S e = 1 4 R d 4 xf µ 1 e 2 ( ) F µ 1 e 2 ( ) = 1 e 2 (µ) 0 log µ 2

13 R 2 gravity S = Z d 4 x p g apple m 2 Pl 2 R a 1C 2 + a 2 R 2 + a 3 E schematically: L m 2 Pl(h@ 2 h + h@h@h +...) a (2h) 2 + h(2h) in an effective action approach, the dof are read from the Einstein-Hilbert term after canonical normalization: L h@ 2 h + 1 h@h@h +... m Pl a m 2 Pl apple (2h) m Pl h(2h)

14 L 2 h + 1 h@h@h +... m Pl a m 2 Pl apple (2h) m Pl h(2h) standard lore: the higher-derivative terms give corrections ae 2 /m 2 Pl, irrelevant in the IR however, in QFT, a 2 =a 2 (E) runs with energy. can it become large in the IR? can it develop a IR singularity a(e) / E 4? Then in the IR a 2 R 2! Ra 2 (2)R / R R

15 running due to loops of massles (or light) scalar, spinor and vector field in a fixed curved background: well understood (e.g. Birrel-Davies 1982) S 1 loop NL = graviton loops 1 2(4 ) 2 Z d 4 xg 1/2 apple R log µ 2 + R µ log R + µ 2 R µ log R µ µ 2 R µ in GR, the one-loop divergences vanish on-shell, and can be set to zero with a redefinition of the metric ('t Hooft-Veltman 1974) off-shell, the beta functions depends on the choise of gauge fixing (Kallosh-Tarasov-Tyutin 1978) In GR, there is no sense in which we can compute the physical running of the coupling associated to the R 2 term!

16 Stelle theory: consider again S = Z d 4 x p g apple m 2 Pl 2 R a 1C 2 + a 2 R 2 + a 3 E but now the R 2 terms are not treated in an effective action approach, but as a full UV completion L m 2 Pl(h@ 2 h + h@h@h +...) a (2h) 2 + h(2h) G(k) 1 m 2 Pl k2 + ak 4 the theory is renormalizable! (Stelle 1977)

17 however: the spectrum of the theory read from the full propagator is massless spin-2 graviton massive spin-2 ghost, m 2 = m Pl2 /(2a 1 ) massive spin 0, m 2 = -m Pl2 /(12a 2 ) because of the ghost, it is not a consistent theory the beta functions of a 1,a 2 are well-defined and gauge-inv Fradkin-Tseytlin 1982, Avramidi-Barvinski 1985 the limit a 1,a 2! 0 of the beta functions is singular, since the structure of the divergences changes (even for graphs with sub-planckian external momenta! nice example of IR/UV mixing)

18 take-home lessons: in GR the beta functions associated to R 2 and C 2 are not well defined. in a theory with improved UV behavior, as Stelle theory, they are well defined. However, we cannot take literally this result, because the theory has a ghost (and furthermore the beta functions have been computed only at E >> m Pl ) The result depends on the UV completion. In a fundamental UV complete theory of quantum gravity, we expect that the beta functions will be well defined depending on the sign of the beta function, there will be basically two options, a 2 (E) growing or decreasing in the IR we explore the scenario where a 2 (E) grows (when it is is positive)

19 consider the scenario where the beta function of a 2 (E) corresponds to asymptotic freedom in the UV: a 2 (E) g 2 (E), g 2 (E) = g 2 (µ) 1+g 2 (µ) 0 log(e/µ) 0 > 0 as in QCD, this generates dynamically a IR scale, RR = µe 1/[ 0g 2 (µ)] (dimensional transmutation) in the IR the form factor a 2 ( ) will be non-trivial functions of /Λ RR. Can we get a 2 ( )=(Λ 2 RR/ ) 2? generally speaking, power-like behavior can emerge from resummation of leading logs 1X n=0 ( ) n n! log 2 RR n = 2 RR

20 a more concrete argument from analogy with QCD? in QCD a term m 2 2 Z d 4 xf a µ apple 1 D 2 ab Fµ b in the effective action is know to reproduce the non-perturbative behavior of the gluon propagator derived from OPE and lattice simulations e.g. review by Boucaud et al is a gauge-inv and non-local mass term for the gluon writing g µ = e 2 (x) µ R = 6e 2 ( µ ) = 6 + O( 2 ) m 2 R 1 2 R = 36m O( 3 ) is a diff-inv and non-local mass term for the conformal mode!

21 this gives a new perspective on the naturalness problem for the cosmological constant: 1. the scale Λ RR emerges from dimensional transmutation, similarly to Λ QCD. There is no issue of naturalness for such a quantity, which is determined by the logarithmic running of a dimensionless coupling constant

22 2. numerical value of the DE scale the action in the IR is we can rewrite it as S ' Z d 4 x p S ' m2 Pl 2 m2 Pl 2 Z Z g apple m 2 Pl 2 R 4 RRR 1 2 R d 4 x p d 4 x p g g apple R apple R 2 4 RR m 2 Pl R 1 2 R m 2 R 1 2 R cosmology requires m ' 2 RR m Pl m H 0! RR mev we do not need to introduce a particle with astonishingly small mass m H ev, as in massive gravity m ~10-32 ev is just a derived quantity. The fundamental scale is Λ RR

23 Strong IR effects from conformal-mode dynamics? In pure Einstein gravity + massless matter, higher-derivative terms are generated by the conformal anomaly in D=2, this gives the Polyakov action ht µ µ i = N 24 R! S anom = N 96 Z d 2 x p gr 1 2 R writing g µ (x) =e 2 (x) ḡ µ (x) we get S anom = N 24 Z d 2 x p ḡ ( + R ) the anomaly gives dynamics to the conformal mode

24 in 4D ht µ µ i = bc 2 + b 0 E 2 3 2R + b 00 2R S anom = 1 8 Z d 4 x p g E 23 2R 4 1 appleb 0 E 23 2R 2bC 2 4 = R µ r µ r 2 3 R (rµ R)r µ restricting to the conformal mode S anom = R Q2 16 d 4 x ( ) 2 2 Q 2 = (N S N F + 62N V 28) + Q 2 grav

25 In the classical theory σ is a constrained variable. At the quantum level it acquires dynamics because of the conformal anomaly 4D-quantum gravity in the IR is dominated by the conformal mode, because of the 1/k 4 propagator Antoniadis and Mottola 1992 Antoniadis, Mazur and Mottola 2007 fluctuations in σ become large in the IR ( ) 2! G(x, x 0 )= 1 2Q 2 log µ 2 (x x 0 ) 2

26 situation similar to the BKT transition in D=2 in D=2, G(k) =1/k 2! G(x) / log x 2 Antoniadis, Mazur and Mottola 2007 vortex solutions S E = 1 2 Q2 q 2 ln L a (x) =q ln x x 0 F = 1 2 Q2 q 2 4 ln L a if if Q 2 > 8/q Q 2 < 8/q the free energy diverges as we remove the cutoffs and these configurations are irrelevant they dominate this is exactly what happens in the XY model in D=2! BTK phase transition and generation of a mass gap

27 Thus, once again, we expect a dynamical generation of a mass gap for the conformal mode! Recalling that m 2 R 1 R = 36m O( 3 ) 2 diff invariance requires the non-local term with the mass term: G(x) = 8 2 Q 2 Z d 4 k 1 (2 ) 4 k 4 + µ 4 e ikx / log x µx 1 1/(µx) 3 µx 1 physical picture: the log growth of the propagator derived from the anomaly-induced effective action is a sign of a IR instability the generation of a mass gap is the response of the vacuum to this instability

28 Conclusions a term R2 2 R could in principle be generated by (possibly related) non-perturbative IR effects running of an asymptotically free R 2 coupling large-distance fluctuations of the conformal mode In both cases the mass scale associated to dark energy would be generated dynamically, similarly to QCD, or to the generation of a mass gap in strongly-coupled theories

29 Thank you!

30 Absence of vdvz discontinuity and of a strong coupling regime write the eqs of motion of the non-local theory in spherical symmetry: for mr <<1: low-mass expansion A. Kehagias and MM 2014 ds 2 = A(r)dt 2 + B(r)dr 2 + r 2 (d 2 +sin 2 d 2 ) for r>>r S : Newtonian limit (perturbation over Minowski) match the solutions for r S << r << m -1 (this fixes all coefficients)

31 result: for r>>r s for r s <<r<< m -1 : m! 0 A(r) = 1 the limit is smooth! r S r B(r) = 1+ r S r A(r) ' 1 r S r apple 1+ 1 (1 cos mr) 3 apple 1 1 (1 cos mr mr sin mr) 3 1+ m2 r 2 6 By comparison, in massive gravity the same computation gives A(r) =1 4 3 vdvz discontinuity r S r 1 r S 12m 4 r 5 breakdown of linearity below r V =(r s /m^4) 1/5

Non-local infrared modifications of gravity and dark energy

Non-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 information

Nonlocal gravity and comparison with cosmological datasets

Nonlocal gravity and comparison with cosmological datasets Nonlocal gravity and comparison with cosmological datasets Michele Maggiore Cosmology on Safari, Jan. 2015 based on Jaccard, MM, Mitsou, PRD 2013, 1305.3034 MM, PRD 2014, 1307.3898 Foffa, MM, Mitsou, PLB

More information

Nonlocal gravity. Conceptual aspects and cosmological consequences

Nonlocal gravity. Conceptual aspects and cosmological consequences Nonlocal gravity. Conceptual aspects and cosmological consequences Michele Maggiore Sifnos, Sept. 18-23, 2017 based on Jaccard, MM, Mitsou, PRD 2013, 1305.3034 MM, PRD 2014, 1307.3898 Foffa, MM, Mitsou,

More information

Nonlocal gravity. Conceptual aspects and cosmological consequences

Nonlocal gravity. Conceptual aspects and cosmological consequences Nonlocal gravity. Conceptual aspects and cosmological consequences Michele Maggiore Moriond 2018 based on recent works with Enis Belgacem, Giulia Cusin, Yves Dirian, Stefano Foffa, Martin Kunz, Michele

More information

Quantum Gravity and the Renormalization Group

Quantum Gravity and the Renormalization Group Nicolai Christiansen (ITP Heidelberg) Schladming Winter School 2013 Quantum Gravity and the Renormalization Group Partially based on: arxiv:1209.4038 [hep-th] (NC,Litim,Pawlowski,Rodigast) and work in

More information

Aspects of massive gravity

Aspects 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 information

Non-local Modifications of Gravity and Cosmic Acceleration

Non-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 information

Gravitational Waves. GR: 2 polarizations

Gravitational 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 information

Asymptotically safe Quantum Gravity. Nonperturbative renormalizability and fractal space-times

Asymptotically safe Quantum Gravity. Nonperturbative renormalizability and fractal space-times p. 1/2 Asymptotically safe Quantum Gravity Nonperturbative renormalizability and fractal space-times Frank Saueressig Institute for Theoretical Physics & Spinoza Institute Utrecht University Rapporteur

More information

Introduction to the Vainshtein mechanism

Introduction 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 information

A 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 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 information

Gravity vs Yang-Mills theory. Kirill Krasnov (Nottingham)

Gravity vs Yang-Mills theory. Kirill Krasnov (Nottingham) Gravity vs Yang-Mills theory Kirill Krasnov (Nottingham) This is a meeting about Planck scale The problem of quantum gravity Many models for physics at Planck scale This talk: attempt at re-evaluation

More information

New Model of massive spin-2 particle

New 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 information

Gravitational Waves and New Perspectives for Quantum Gravity

Gravitational 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 information

On the uniqueness of Einstein-Hilbert kinetic term (in massive (multi-)gravity)

On 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 information

Dilaton and IR-Driven Inflation

Dilaton and IR-Driven Inflation Dilaton and IR-Driven Inflation Chong-Sun Chu National Center for Theoretical Science NCTS and National Tsing-Hua University, Taiwan Third KIAS-NCTS Joint Workshop High 1 Feb 1, 2016 1506.02848 in collaboration

More information

Towards a manifestly diffeomorphism invariant Exact Renormalization Group

Towards a manifestly diffeomorphism invariant Exact Renormalization Group Towards a manifestly diffeomorphism invariant Exact Renormalization Group Anthony W. H. Preston University of Southampton Supervised by Prof. Tim R. Morris Talk prepared for UK QFT-V, University of Nottingham,

More information

arxiv: v1 [hep-th] 1 Oct 2008

arxiv: 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 information

Status of Hořava Gravity

Status 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 information

arxiv: v3 [hep-th] 30 May 2018

arxiv: v3 [hep-th] 30 May 2018 arxiv:1010.0246v3 [hep-th] 30 May 2018 Graviton mass and cosmological constant: a toy model Dimitrios Metaxas Department of Physics, National Technical University of Athens, Zografou Campus, 15780 Athens,

More information

Scale symmetry a link from quantum gravity to cosmology

Scale symmetry a link from quantum gravity to cosmology Scale symmetry a link from quantum gravity to cosmology scale symmetry fluctuations induce running couplings violation of scale symmetry well known in QCD or standard model Fixed Points Quantum scale symmetry

More information

Manifestly diffeomorphism invariant classical Exact Renormalization Group

Manifestly 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 information

The Non-commutative S matrix

The Non-commutative S matrix The Suvrat Raju Harish-Chandra Research Institute 9 Dec 2008 (work in progress) CONTEMPORARY HISTORY In the past few years, S-matrix techniques have seen a revival. (Bern et al., Britto et al., Arkani-Hamed

More information

Duality and Holography

Duality and Holography Duality and Holography? Joseph Polchinski UC Davis, 5/16/11 Which of these interactions doesn t belong? a) Electromagnetism b) Weak nuclear c) Strong nuclear d) a) Electromagnetism b) Weak nuclear c) Strong

More information

Nonlinear massive gravity and Cosmology

Nonlinear 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 information

!onformali" Los# J.-W. Lee D. T. Son M. Stephanov D.B.K. arxiv: Phys.Rev.D80:125005,2009

!onformali Los# J.-W. Lee D. T. Son M. Stephanov D.B.K. arxiv: Phys.Rev.D80:125005,2009 !onformali" Los# J.-W. Lee D. T. Son M. Stephanov D.B.K arxiv:0905.4752 Phys.Rev.D80:125005,2009 Motivation: QCD at LARGE N c and N f Colors Flavors Motivation: QCD at LARGE N c and N f Colors Flavors

More information

The nonlinear dynamical stability of infrared modifications of gravity

The 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 information

Claudia de Rham July 30 th 2013

Claudia 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 information

P-ADIC STRINGS AT FINITE TEMPERATURE

P-ADIC STRINGS AT FINITE TEMPERATURE P-ADIC STRINGS AT FINITE TEMPERATURE Jose A. R. Cembranos Work in collaboration with Joseph I. Kapusta and Thirthabir Biswas T. Biswas, J. Cembranos, J. Kapusta, PRL104:021601 (2010) T. Biswas, J. Cembranos,

More information

Lorentz 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 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 information

Scattering Amplitudes

Scattering Amplitudes Scattering Amplitudes LECTURE 1 Jaroslav Trnka Center for Quantum Mathematics and Physics (QMAP), UC Davis ICTP Summer School, June 2017 Particle experiments: our probe to fundamental laws of Nature Theorist

More information

D. f(r) gravity. φ = 1 + f R (R). (48)

D. 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 information

MASAHIDE YAMAGUCHI. Perturbations of Cosmological and Black Hole Solutions in Massive gravity and Bi-gravity. (Tokyo Institute of Technology)

MASAHIDE 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 information

The effective field theory of general relativity and running couplings

The effective field theory of general relativity and running couplings The effective field theory of general relativity and running couplings 1) GR as an EFT 2) Gravitational corrections to gauge coupling running? 3) Can we define a good running G in the perturbative region?

More information

Local RG, Quantum RG, and Holographic RG. Yu Nakayama Special thanks to Sung-Sik Lee and Elias Kiritsis

Local RG, Quantum RG, and Holographic RG. Yu Nakayama Special thanks to Sung-Sik Lee and Elias Kiritsis Local RG, Quantum RG, and Holographic RG Yu Nakayama Special thanks to Sung-Sik Lee and Elias Kiritsis Local renormalization group The main idea dates back to Osborn NPB 363 (1991) See also my recent review

More information

Analyzing WMAP Observation by Quantum Gravity

Analyzing WMAP Observation by Quantum Gravity COSMO 07 Conference 21-25 August, 2007 Analyzing WMAP Observation by Quantum Gravity Ken-ji Hamada (KEK) with Shinichi Horata, Naoshi Sugiyama, and Tetsuyuki Yukawa arxiv:0705.3490[astro-ph], Phys. Rev.

More information

Cosmological perturbations in nonlinear massive gravity

Cosmological 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 information

Holography with Shape Dynamics

Holography with Shape Dynamics . 1/ 11 Holography with Henrique Gomes Physics, University of California, Davis July 6, 2012 In collaboration with Tim Koslowski Outline 1 Holographic dulaities 2 . 2/ 11 Holographic dulaities Ideas behind

More information

Anisotropic Interior Solutions in Hořava Gravity and Einstein-Æther Theory

Anisotropic Interior Solutions in Hořava Gravity and Einstein-Æther Theory Anisotropic Interior Solutions in and Einstein-Æther Theory CENTRA, Instituto Superior Técnico based on DV and S. Carloni, arxiv:1706.06608 [gr-qc] Gravity and Cosmology 2018 Yukawa Institute for Theoretical

More information

One Loop Tests of Higher Spin AdS/CFT

One Loop Tests of Higher Spin AdS/CFT One Loop Tests of Higher Spin AdS/CFT Simone Giombi UNC-Chapel Hill, Jan. 30 2014 Based on 1308.2337 with I. Klebanov and 1401.0825 with I. Klebanov and B. Safdi Massless higher spins Consistent interactions

More information

Quantum Fields in Curved Spacetime

Quantum 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 information

CFTs with O(N) and Sp(N) Symmetry and Higher Spins in (A)dS Space

CFTs with O(N) and Sp(N) Symmetry and Higher Spins in (A)dS Space CFTs with O(N) and Sp(N) Symmetry and Higher Spins in (A)dS Space Igor Klebanov Talk at New England Strings Meeting Brown University November 6, 2015 Based mainly on L. Fei, S. Giombi, IK, arxiv:1404.1094

More information

Stable violation of the null energy condition and non-standard cosmologies

Stable 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 information

Quantum corpuscular corrections to the Newtonian potential

Quantum corpuscular corrections to the Newtonian potential Quantum corpuscular corrections to the Newtonian potential Based on arxiv:1702.05918, to appear in PRD Andrea Giugno Arnold Sommerfeld Center, Ludwig Maximilians Universität, Theresienstraße 37, 80333,

More information

Dimensional Reduction in the Renormalisation Group:

Dimensional Reduction in the Renormalisation Group: Dimensional Reduction in the Renormalisation Group: From Scalar Fields to Quantum Einstein Gravity Natália Alkofer Advisor: Daniel Litim Co-advisor: Bernd-Jochen Schaefer 11/01/12 PhD Seminar 1 Outline

More information

Massive gravity and cosmology

Massive 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 information

Universal Dynamics from the Conformal Bootstrap

Universal Dynamics from the Conformal Bootstrap Universal Dynamics from the Conformal Bootstrap Liam Fitzpatrick Stanford University! in collaboration with Kaplan, Poland, Simmons-Duffin, and Walters Conformal Symmetry Conformal = coordinate transformations

More information

Massive gravity and cosmology

Massive 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 information

German physicist stops Universe

German physicist stops Universe Big bang or freeze? NATURE NEWS Cosmologist claims Universe may not be expanding Particles' changing masses could explain why distant galaxies appear to be rushing away. Jon Cartwright 16 July 2013 German

More information

Why we need quantum gravity and why we don t have it

Why we need quantum gravity and why we don t have it Why we need quantum gravity and why we don t have it Steve Carlip UC Davis Quantum Gravity: Physics and Philosophy IHES, Bures-sur-Yvette October 2017 The first appearance of quantum gravity Einstein 1916:

More information

Introduction to Quantum Chromodynamics (QCD)

Introduction to Quantum Chromodynamics (QCD) Introduction to Quantum Chromodynamics (QCD) Jianwei Qiu Theory Center, Jefferson Lab May 29 June 15, 2018 Lecture One The plan for my four lectures q The Goal: To understand the strong interaction dynamics

More information

«Massive Gravity» (some of its open problems)

«Massive Gravity» (some of its open problems) A short review on Cédric Deffayet (APC, Paris) «Massive Gravity» (some of its open problems) 1. Pauli-Fierz (PF) theory 2. Non linear PF theory 3. DGP Model Journée ANR Math-GR Méthodes Mathématiques pour

More information

SM, EWSB & Higgs. MITP Summer School 2017 Joint Challenges for Cosmology and Colliders. Homework & Exercises

SM, EWSB & Higgs. MITP Summer School 2017 Joint Challenges for Cosmology and Colliders. Homework & Exercises SM, EWSB & Higgs MITP Summer School 017 Joint Challenges for Cosmology and Colliders Homework & Exercises Ch!"ophe Grojean Ch!"ophe Grojean DESY (Hamburg) Humboldt University (Berlin) ( christophe.grojean@desy.de

More information

Introduction to String Theory ETH Zurich, HS11. 9 String Backgrounds

Introduction to String Theory ETH Zurich, HS11. 9 String Backgrounds Introduction to String Theory ETH Zurich, HS11 Chapter 9 Prof. N. Beisert 9 String Backgrounds Have seen that string spectrum contains graviton. Graviton interacts according to laws of General Relativity.

More information

Black holes in massive gravity

Black 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 information

Massive Photon and Cosmology

Massive Photon and Cosmology Massive Photon and Cosmology Phillial Oh Sungkyunkwan University KIAS 2014. 6. Contents I. Introduction II. Massive QED and Cosmology III. Massive Dark Photon and Cosmology IV. Conslusions Massive Photon:

More information

Quantum Field Theory 2 nd Edition

Quantum Field Theory 2 nd Edition Quantum Field Theory 2 nd Edition FRANZ MANDL and GRAHAM SHAW School of Physics & Astromony, The University of Manchester, Manchester, UK WILEY A John Wiley and Sons, Ltd., Publication Contents Preface

More information

Holographic self-tuning of the cosmological constant

Holographic self-tuning of the cosmological constant Holographic self-tuning of the cosmological constant Francesco Nitti Laboratoire APC, U. Paris Diderot IX Aegean Summer School Sifnos, 19-09-2017 work with Elias Kiritsis and Christos Charmousis, 1704.05075

More information

Zhong-Zhi Xianyu (CMSA Harvard) Tsinghua June 30, 2016

Zhong-Zhi Xianyu (CMSA Harvard) Tsinghua June 30, 2016 Zhong-Zhi Xianyu (CMSA Harvard) Tsinghua June 30, 2016 We are directly observing the history of the universe as we look deeply into the sky. JUN 30, 2016 ZZXianyu (CMSA) 2 At ~10 4 yrs the universe becomes

More information

Bimetric Massive Gravity

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 information

ds/cft Contents Lecturer: Prof. Juan Maldacena Transcriber: Alexander Chen August 7, Lecture Lecture 2 5

ds/cft Contents Lecturer: Prof. Juan Maldacena Transcriber: Alexander Chen August 7, Lecture Lecture 2 5 ds/cft Lecturer: Prof. Juan Maldacena Transcriber: Alexander Chen August 7, 2011 Contents 1 Lecture 1 2 2 Lecture 2 5 1 ds/cft Lecture 1 1 Lecture 1 We will first review calculation of quantum field theory

More information

Special Relativity from Soft Gravitons

Special Relativity from Soft Gravitons Special Relativity from Soft Gravitons Mark Hertzberg, Tufts University CosPA, December 14, 2017 with McCullen Sandora, PRD 96 084048 (1704.05071) Can the laws of special relativity be violated in principle?

More information

de Sitter Inv. & Quantum Gravity (arxiv: , , , ) S. P. Miao (Utrecht) N. C. Tsamis (Crete) R. P.

de Sitter Inv. & Quantum Gravity (arxiv: , , , ) S. P. Miao (Utrecht) N. C. Tsamis (Crete) R. P. de Sitter Inv. & Quantum Gravity (arxiv:0907.4930, 1002.4037, 1106.0925, 1107.4733) S. P. Miao (Utrecht) N. C. Tsamis (Crete) R. P. Woodard (Florida) Primordial Inflation was nearly de Sitter with small

More information

Holographic self-tuning of the cosmological constant

Holographic self-tuning of the cosmological constant Holographic self-tuning of the cosmological constant Francesco Nitti Laboratoire APC, U. Paris Diderot IX Crete Regional Meeting in String Theory Kolymbari, 10-07-2017 work with Elias Kiritsis and Christos

More information

Recovering General Relativity from Hořava Theory

Recovering General Relativity from Hořava Theory Recovering General Relativity from Hořava Theory Jorge Bellorín Department of Physics, Universidad Simón Bolívar, Venezuela Quantum Gravity at the Southern Cone Sao Paulo, Sep 10-14th, 2013 In collaboration

More information

Symmetries Then and Now

Symmetries Then and Now Symmetries Then and Now Nathan Seiberg, IAS 40 th Anniversary conference Laboratoire de Physique Théorique Global symmetries are useful If unbroken Multiplets Selection rules If broken Goldstone bosons

More information

Asymptotic safety of gravity and the Higgs boson mass. Mikhail Shaposhnikov Quarks 2010, Kolomna, June 6-12, 2010

Asymptotic safety of gravity and the Higgs boson mass. Mikhail Shaposhnikov Quarks 2010, Kolomna, June 6-12, 2010 Asymptotic safety of gravity and the Higgs boson mass Mikhail Shaposhnikov Quarks 2010, Kolomna, June 6-12, 2010 Based on: C. Wetterich, M. S., Phys. Lett. B683 (2010) 196 Quarks-2010, June 8, 2010 p.

More information

Loop Quantum Gravity a general-covariant lattice gauge theory. Francesca Vidotto UNIVERSITY OF THE BASQUE COUNTRY

Loop Quantum Gravity a general-covariant lattice gauge theory. Francesca Vidotto UNIVERSITY OF THE BASQUE COUNTRY a general-covariant lattice gauge theory UNIVERSITY OF THE BASQUE COUNTRY Bad Honnef - August 2 nd, 2018 THE GRAVITATIONAL FIELD GENERAL RELATIVITY: background independence! U(1) SU(2) SU(3) SL(2,C) l

More information

Effective Field Theory

Effective Field Theory Effective Field Theory Iain Stewart MIT The 19 th Taiwan Spring School on Particles and Fields April, 2006 Physics compartmentalized Quantum Field Theory String Theory? General Relativity short distance

More information

Chern-Simons Theories and AdS/CFT

Chern-Simons Theories and AdS/CFT Chern-Simons Theories and AdS/CFT Igor Klebanov PCTS and Department of Physics Talk at the AdS/CMT Mini-program KITP, July 2009 Introduction Recent progress has led to realization that coincident membranes

More information

Minimalism in Modified Gravity

Minimalism 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 information

Modified Gravity and Dark Matter

Modified Gravity and Dark Matter Modified Gravity and Dark Matter Jose A. R. Cembranos University Complutense of Madrid, Spain J. Cembranos, PRL102:141301 (2009) Modifications of Gravity We do not know any consistent renormalizable Quantum

More information

Lecture notes Particle Physics II. Quantum Chromo Dynamics. 7. Soft and Collinear Singularities. Michiel Botje Nikhef, Science Park, Amsterdam

Lecture notes Particle Physics II. Quantum Chromo Dynamics. 7. Soft and Collinear Singularities. Michiel Botje Nikhef, Science Park, Amsterdam Lecture notes Particle Physics II Quantum Chromo Dynamics 7. Soft and Collinear Singularities Michiel Botje Nikhef, Science Park, Amsterdam December 2, 2013 Can perturbative QCD predict anything? We have

More information

Conformal factor dynamics in the 1=N. expansion. E. Elizalde. Department ofphysics, Faculty of Science, Hiroshima University. and. S.D.

Conformal factor dynamics in the 1=N. expansion. E. Elizalde. Department ofphysics, Faculty of Science, Hiroshima University. and. S.D. Conformal factor dynamics in the =N expansion E. Elizalde Department ofphysics, Faculty of Science, Hiroshima University Higashi-Hiroshima 74, Japan and S.D. Odintsov Department ECM, Faculty ofphysics,

More information

Beyond Einstein: gravitational waves from extended gravities

Beyond Einstein: gravitational waves from extended gravities Beyond Einstein: gravitational waves from extended gravities Salvatore Capozziello Università di Napoli Federico II and INFN sez. di Napoli in collaboration with Mariafelicia De Laurentis Institute for

More information

Chris Verhaaren Joint Theory Seminar 31 October With Zackaria Chacko, Rashmish Mishra, and Simon Riquelme

Chris Verhaaren Joint Theory Seminar 31 October With Zackaria Chacko, Rashmish Mishra, and Simon Riquelme Chris Verhaaren Joint Theory Seminar 31 October 2016 With Zackaria Chacko, Rashmish Mishra, and Simon Riquelme It s Halloween A time for exhibiting what some find frightening And seeing that it s not so

More information

Cosmology meets Quantum Gravity?

Cosmology 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 information

Themodynamics at strong coupling from Holographic QCD

Themodynamics at strong coupling from Holographic QCD Themodynamics at strong coupling from Holographic QCD p. 1 Themodynamics at strong coupling from Holographic QCD Francesco Nitti APC, U. Paris VII Excited QCD Les Houches, February 23 2011 Work with E.

More information

Gauge Theories of the Standard Model

Gauge Theories of the Standard Model Gauge Theories of the Standard Model Professors: Domènec Espriu (50%, coordinador) Jorge Casalderrey (25%) Federico Mescia (25%) Time Schedule: Mon, Tue, Wed: 11:50 13:10 According to our current state

More information

MITOCW watch?v=nw4vp_upvme

MITOCW watch?v=nw4vp_upvme MITOCW watch?v=nw4vp_upvme The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free. To

More information

Topologically Massive Gravity and AdS/CFT

Topologically Massive Gravity and AdS/CFT Topologically Massive Gravity and AdS/CFT Institute for Theoretical Physics University of Amsterdam The Planck Scale, XXV Max Born Symposium Wroclaw, 30 June 2009 Introduction Three dimensional gravity

More information

Green s function of the Vector fields on DeSitter Background

Green 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 information

The cosmological constant puzzle

The cosmological constant puzzle The cosmological constant puzzle Steven Bass Cosmological constant puzzle: Accelerating Universe: believed to be driven by energy of nothing (vacuum) Vacuum energy density (cosmological constant or dark

More information

Critical exponents in quantum Einstein gravity

Critical exponents in quantum Einstein gravity Critical exponents in quantum Einstein gravity Sándor Nagy Department of Theoretical physics, University of Debrecen MTA-DE Particle Physics Research Group, Debrecen Leibnitz, 28 June Critical exponents

More information

Complex entangled states of quantum matter, not adiabatically connected to independent particle states. Compressible quantum matter

Complex entangled states of quantum matter, not adiabatically connected to independent particle states. Compressible quantum matter Complex entangled states of quantum matter, not adiabatically connected to independent particle states Gapped quantum matter Z2 Spin liquids, quantum Hall states Conformal quantum matter Graphene, ultracold

More information

Lorentz violations: from quantum gravity to black holes. Thomas P. Sotiriou

Lorentz violations: from quantum gravity to black holes. Thomas P. Sotiriou Lorentz violations: from quantum gravity to black holes Thomas P. Sotiriou Motivation Test Lorentz symmetry Motivation Old problem: Can we make gravity renormalizable? Possible solution: Add higher-order

More information

Effective Field Theory in Cosmology

Effective Field Theory in Cosmology C.P. Burgess Effective Field Theory in Cosmology Clues for cosmology from fundamental physics Outline Motivation and Overview Effective field theories throughout physics Decoupling and naturalness issues

More information

Inflation in Flatland

Inflation in Flatland Inflation in Flatland Austin Joyce Center for Theoretical Physics Columbia University Kurt Hinterbichler, AJ, Justin Khoury, 1609.09497 Theoretical advances in particle cosmology, University of Chicago,

More information

The Role Of Magnetic Monopoles In Quark Confinement (Field Decomposition Approach)

The Role Of Magnetic Monopoles In Quark Confinement (Field Decomposition Approach) The Role Of Magnetic Monopoles In Quark Confinement (Field Decomposition Approach) IPM school and workshop on recent developments in Particle Physics (IPP11) 2011, Tehran, Iran Sedigheh Deldar, University

More information

Sphere Partition Functions, Topology, the Zamolodchikov Metric

Sphere Partition Functions, Topology, the Zamolodchikov Metric Sphere Partition Functions, Topology, the Zamolodchikov Metric, and Extremal Correlators Weizmann Institute of Science Efrat Gerchkovitz, Jaume Gomis, ZK [1405.7271] Jaume Gomis, Po-Shen Hsin, ZK, Adam

More information

MCRG Flow for the Nonlinear Sigma Model

MCRG Flow for the Nonlinear Sigma Model Raphael Flore,, Björn Wellegehausen, Andreas Wipf 23.03.2012 So you want to quantize gravity... RG Approach to QFT all information stored in correlation functions φ(x 0 )... φ(x n ) = N Dφ φ(x 0 )... φ(x

More information

Constraints on Inflationary Correlators From Conformal Invariance. Sandip Trivedi Tata Institute of Fundamental Research, Mumbai.

Constraints on Inflationary Correlators From Conformal Invariance. Sandip Trivedi Tata Institute of Fundamental Research, Mumbai. Constraints on Inflationary Correlators From Conformal Invariance Sandip Trivedi Tata Institute of Fundamental Research, Mumbai. Based on: 1) I. Mata, S. Raju and SPT, JHEP 1307 (2013) 015 2) A. Ghosh,

More information

A Modern View of Quantum Gravity. John F. Donoghue at Universität Wien October 13, 2015

A Modern View of Quantum Gravity. John F. Donoghue at Universität Wien October 13, 2015 A Modern View of Quantum Gravity John F. Donoghue at Universität Wien October 13, 2015 Goal: We have made progress! 1) Bad quotes good quotes 2) The Effective Field Theory revolution 3) A minimal primer

More information

Theory of Elementary Particles homework VIII (June 04)

Theory of Elementary Particles homework VIII (June 04) Theory of Elementary Particles homework VIII June 4) At the head of your report, please write your name, student ID number and a list of problems that you worked on in a report like II-1, II-3, IV- ).

More information

Mathematical and Physical Foundations of Extended Gravity (II)

Mathematical and Physical Foundations of Extended Gravity (II) Mathematical and Physical Foundations of Extended Gravity (II) -The Gravitational Waves era- Salvatore Capozziello Università di Napoli Federico II INFN sez. di Napoli SIGRAV Open Fundamental Issues! What

More information

Black Hole Production in Planckian Scattering*

Black Hole Production in Planckian Scattering* Black Hole Production in Planckian Scattering* Kyungsik Kang and Horatiu Nastase Department of Physics, Brown University, Providence, RI 02912, USA Gauge/gravity duality correspondence suggests to a new

More information

Hamiltonian approach to Yang- Mills Theories in 2+1 Dimensions: Glueball and Meson Mass Spectra

Hamiltonian approach to Yang- Mills Theories in 2+1 Dimensions: Glueball and Meson Mass Spectra Hamiltonian approach to Yang- Mills Theories in 2+1 Dimensions: Glueball and Meson Mass Spectra Aleksandr Yelnikov Virginia Tech based on hep-th/0512200 hep-th/0604060 with Rob Leigh and Djordje Minic

More information

Quantum Field Theory. and the Standard Model. !H Cambridge UNIVERSITY PRESS MATTHEW D. SCHWARTZ. Harvard University

Quantum Field Theory. and the Standard Model. !H Cambridge UNIVERSITY PRESS MATTHEW D. SCHWARTZ. Harvard University Quantum Field Theory and the Standard Model MATTHEW D. Harvard University SCHWARTZ!H Cambridge UNIVERSITY PRESS t Contents v Preface page xv Part I Field theory 1 1 Microscopic theory of radiation 3 1.1

More information

8.821 F2008 Lecture 05

8.821 F2008 Lecture 05 8.821 F2008 Lecture 05 Lecturer: McGreevy Scribe: Evangelos Sfakianakis September 22, 2008 Today 1. Finish hindsight derivation 2. What holds up the throat? 3. Initial checks (counting of states) 4. next

More information

Analog Duality. Sabine Hossenfelder. Nordita. Sabine Hossenfelder, Nordita Analog Duality 1/29

Analog Duality. Sabine Hossenfelder. Nordita. Sabine Hossenfelder, Nordita Analog Duality 1/29 Analog Duality Sabine Hossenfelder Nordita Sabine Hossenfelder, Nordita Analog Duality 1/29 Dualities A duality, in the broadest sense, identifies two theories with each other. A duality is especially

More information