Cosmological (non)-constant Problem: The case for TeV scale quantum gravity
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1 Theoretical High Energy Physics seminar University of Toronto, April 20, 2015 Cosmological (non)-constant Problem: The case for TeV scale quantum gravity Niayesh Afshordi
2 Punchline! Quantum Gravity is already in the Infrared! CC problem (in its various forms) is possibly the single most significant theoretical clue as to how to modify UV and IR physics
3 Hierarchy problem(s) neutrino mass Higgs, Electroweak GUT Planck dark energy LHC 10 3 ev ev ev DE 4 m 2? H 2
4 Hierarchy problem(s) old cosmological constant (CC) problem neutrino mass Higgs, Electroweak GUT Planck dark energy LHC 10 3 ev ev ev DE 4 m 2? H 2
5 Hierarchy problem(s) old cosmological constant (CC) problem Higgs hierarchy problem neutrino mass Higgs, Electroweak GUT Planck dark energy LHC 10 3 ev ev ev DE 4 m 2? H 2
6 Hierarchy problem(s) old cosmological constant (CC) problem Higgs hierarchy problem CnC problem neutrino mass Higgs, Electroweak GUT Planck dark energy LHC 10 3 ev ev ev DE 4 m 2? H 2
7 Can modifying gravity solve the old CC problem? (Narimani, NA & Scott 2014)
8 Can modifying gravity solve the old CC problem? not quite yet! (Narimani, NA & Scott 2014)
9 Outline Prelude: Cosmological Hierarchy Problems Cosmological non-constant (CnC) Problem (TeV scale QG!) Argument 1: Poisson Phase Space Argument 2: Kallen-Lehmann representation Argument 3: Holographic entropy bound Epilogue: The folly of the Effective Field Theory Firewalls!
10 Does Quantum Gravity matter in the IR? Quantum Fluctuations do fluctuate! ht µ i =06) ht µ T i =0 What is the analog of CC for the covariance of stress fluctuations? Can these fluctuations have an observable gravitational signature on large scales? with Elliot Nelson (Penn-State PI),
11 Vacuum Fluctuations in Linear Gravity Linearized Perturbations around FRW space-time Einstein constraint sector: scalars in longitudinal gauge and vectors
12 CnC: the upshot!
13 CnC: the upshot! Random stress fluctuations at cut-off scale Λ
14 CnC: the upshot! Random stress fluctuations at cut-off scale Λ Poisson eq. for anisotropic stress
15 CnC: the upshot! Random stress fluctuations at cut-off scale Λ Poisson eq. for anisotropic stress Variance of Metric perturbations grows as distance
16 CnC: the upshot! Random stress fluctuations at cut-off scale Λ Poisson eq. for anisotropic stress Variance of Metric perturbations grows as distance A UV/IR Heisenberg uncertainty relation IR = 5 UV M 4 p
17 CnC: the upshot! Random stress fluctuations at cut-off scale Λ Poisson eq. for anisotropic stress Variance of Metric perturbations grows as distance A UV/IR Heisenberg uncertainty relation IR = 5 UV M 4 p Cosmology limits the UV scale
18 Outline Prelude: Cosmological Hierarchy Problems Cosmological non-constant (CnC) Problem (TeV scale QG!) Argument 1: Poisson Phase Space Argument 2: Kallen-Lehmann representation Argument 3: Holographic entropy bound Epilogue: The folly of the Effective Field Theory Firewalls!
19 What is a cosmological non-constant?
20 What is a cosmological non-constant? Vacuum fluctuations should be finite, Lorentz invariant, and conserved (i.e. satisfy Ward identities)
21 What is a cosmological non-constant? Vacuum fluctuations should be finite, Lorentz invariant, and conserved (i.e. satisfy Ward identities) UV fluctuations should be un-correlated in the IR
22 What is a cosmological non-constant? Vacuum fluctuations should be finite, Lorentz invariant, and conserved (i.e. satisfy Ward identities) UV fluctuations should be un-correlated in the IR Imagine particles of mass m, uniformly sprinkled in the phase space with density <f 0 >
23 What is a cosmological non-constant? Vacuum fluctuations should be finite, Lorentz invariant, and conserved (i.e. satisfy Ward identities) UV fluctuations should be un-correlated in the IR Imagine particles of mass m, uniformly sprinkled in the phase space with density <f 0 > We shall see that this structure occurs in generic quantum field theories.
24 Gravity of Poisson vacuum Solving Einstein equations, we find the spectrum of or metric perturbations: 2 ' m 5 hf0 i 50 TeV 1/2 spectrum of CMB anisotropies (Integrated Sachs- Wolfe, or ISW effect): 2 ' m5 hf 0 i Mpk 4 k/a Mpc 1 1 (t0 = 13.7 billion years)
25 power spectrum of CMB
26 power spectrum of CMB m < 14 TeV! (<f0>~1)
27 Outline Prelude: Cosmological Hierarchy Problems Cosmological non-constant (CnC) Problem (TeV scale QG!) Argument 1: Poisson Phase Space Argument 2: Kallen-Lehmann representation Argument 3: Holographic entropy bound Epilogue: The folly of the Effective Field Theory Firewalls!
28 Kallen-Lehmann spectral representation Most general expectation for stress correlators from Unitarity +Lorentz symmetry ρ s must positive. Cosmological constraints will roughly translate to Z dµ p µ 2 (µ). (10 TeV 1PeV) 5 Metric fluctuations are high frequency but blow up at long wavelength > Observables??
29 I: An offset in Hubble law Particle action To 2nd order in φ Effective Newtonian potenial An offset in the Hubble law v ' Hr 1 32 HM 4 p Z dµ p µ 2 (µ) Planck cluster ksz monopole
30 I: An offset in Hubble law Particle action To 2nd order in φ Effective Newtonian potenial An offset in the Hubble law v ' Hr 1 32 HM 4 p Z dµ p µ 2 (µ) Planck cluster ksz monopole
31 II: CMB anisotropies For a weakly coupled scalar field s 2 (µ) = For large scale, real-space correlations, one can deform the contour to get 2,e (µ) = m 2 This is identical to Poisson model, with µ m p ( µ) µ apple µ m2 µ + m 4 (µ 4m 2 )
32 II: CMB anisotropies For a weakly coupled scalar field s 2 (µ) = For large scale, real-space correlations, one can deform the contour to get 2,e (µ) = m 2 This is identical to Poisson model, with µ m p ( µ) µ apple µ m2 µ + m 4 (µ 4m 2 )
33 Outline Prelude: Cosmological Hierarchy Problems Cosmological non-constant (CnC) Problem (TeV scale QG!) Argument 1: Poisson Phase Space Argument 2: Kallen-Lehmann representation Argument 3: Holographic entropy bound Epilogue: The folly of the Effective Field Theory Firewalls!
34 Interaction entropy Imagine a system with Hamiltonian H o, in its ground state, and zero energy Now, turn on H int ;To 1st order, new eigenstates are Time-Averaged density matrix: Entropy of a 2-state system Fine structure constant
35 A Holographic Bound! Gravitational fine structure constant Number of qubits in a Dirac field Holographic Bound An IR cut-off for gravity
36 Cosmological Non-Constant (CnC) problem
37 Cosmological Non-Constant (CnC) problem Vacuum energy-momentum fluctuations can also source gravity
38 Cosmological Non-Constant (CnC) problem Vacuum energy-momentum fluctuations can also source gravity They change the gravitational constraint sector in the IR, thru equal-time correlators
39 Cosmological Non-Constant (CnC) problem Vacuum energy-momentum fluctuations can also source gravity They change the gravitational constraint sector in the IR, thru equal-time correlators Heisenberg Uncertainty principle for UV/IR observables
40 Cosmological Non-Constant (CnC) problem Vacuum energy-momentum fluctuations can also source gravity They change the gravitational constraint sector in the IR, thru equal-time correlators Heisenberg Uncertainty principle for UV/IR observables CnC problem is more severe than the old CC problem, due to the positivity of the spectral functions or entropy, i.e. fine-tuning doesn t work
41 Cosmological Non-Constant (CnC) problem Vacuum energy-momentum fluctuations can also source gravity They change the gravitational constraint sector in the IR, thru equal-time correlators Heisenberg Uncertainty principle for UV/IR observables CnC problem is more severe than the old CC problem, due to the positivity of the spectral functions or entropy, i.e. fine-tuning doesn t work What about Effective Field Theory?
42 Outline Prelude: Cosmological Hierarchy Problems Cosmological non-constant (CnC) Problem (TeV scale QG!) Argument 1: Poisson Phase Space Argument 2: Kallen-Lehmann representation Argument 3: Holographic entropy bound Epilogue: The folly of the Effective Field Theory Firewalls!
43 On the folly of EFT
44 On the folly of EFT When it comes to gravity, EFT doesn t have a good track record!
45 On the folly of EFT When it comes to gravity, EFT doesn t have a good track record! CC problem
46 On the folly of EFT When it comes to gravity, EFT doesn t have a good track record! CC problem CnC problem
47 On the folly of EFT When it comes to gravity, EFT doesn t have a good track record! CC problem CnC problem and firewalls!
48 On the folly of EFT Gravitational Path Integral Naive Effective Action Ignores GR Constraints :-(
49 On the folly of EFT Low energy scattering CANNOT produce massive particles of mass Λ Effective Field Theory This is NOT the case for macroscopic systems Nearly all macroscopic systems have a fluid description in the IR; UV actions strongly coupled Separation of scales is not guaranteed, e.g. turbulent cascade, inverse cascade
50 Open Questions Should we take CnC problem seriously?! What about the early universe/inflation? Is there a gauge-invariant description of this effect? What happens beyond linear order? Nature of IR cut-off? massive gravity, Dark Energy? What will a 100 TeV collider see?
51 Final Thoughts
52 Final Thoughts CC problem: Possible to solve in a scientific framework; change how pressure gravitates
53 Final Thoughts CC problem: Possible to solve in a scientific framework; change how pressure gravitates CnC problem: Quantum Gravity effects must show up below 20 TeV-PeV scale
54 Final Thoughts CC problem: Possible to solve in a scientific framework; change how pressure gravitates CnC problem: Quantum Gravity effects must show up below 20 TeV-PeV scale Also motivated by solving the Higgs hierarchy problem, e.g. Large Extra Dimensions
55 Final Thoughts CC problem: Possible to solve in a scientific framework; change how pressure gravitates CnC problem: Quantum Gravity effects must show up below 20 TeV-PeV scale Also motivated by solving the Higgs hierarchy problem, e.g. Large Extra Dimensions A definite target for particle colliders (e.g. 100 TeV collider)
56 Final Thoughts CC problem: Possible to solve in a scientific framework; change how pressure gravitates CnC problem: Quantum Gravity effects must show up below 20 TeV-PeV scale Also motivated by solving the Higgs hierarchy problem, e.g. Large Extra Dimensions A definite target for particle colliders (e.g. 100 TeV collider) EFT: Just think outside the box!
57 why EFT fails at horizon Information paradox: unitary black hole evaporation, not consistent with local physics +smooth horizon (Hawking AMPS 2013) Quantum Tunnelling: exp(-se)x exp(entropy) ~ 1 Fuzzballs: (a la Mathur): classical horizon-less spacetimes, that account for BH entropy Dark Energy: pressure eq. with stellar BH firewalls, scale of dark energy (Presocd-Weinstein, NA, Balogh 2009)
58 How to form a Black Hole How to form a Firewall?!
59 Firewall entropy & Lorentz violation Assume space-time ends at stretched horizon Israel Junction condition+z 2 symmetry: membrane has vanishing surface density (c s ) integrated (surface) pressure: = Unruh Temperature/4 Entropy per unit area = 1/4 (Bekenstein-Hawking)! Saravani, NA, Mann 2012
60 Firewall entropy & Lorentz violation Assume space-time ends at stretched horizon Israel Junction condition+z 2 symmetry: membrane has vanishing surface density (c s ) integrated (surface) pressure: = Unruh Temperature/4 Entropy per unit area = 1/4 (Bekenstein-Hawking)! Saravani, NA, Mann 2012
61 Can we see firewalls?! If firewalls have a dense atmosphere, it could be opaque to photons but transparent to neutrinos similar to core-collapse supernovae A fraction of accreted energy into the firewall/bh horizon can be re-radiated as neutrinos
62 Possibly! (NA & Yazdi 2015) IceCube constraints on firewall neutrino spectrum Spectrum of High Energy Neutrinos dn/de ~ E -p Fraction of accreted energy re-radiated as neutrinos spectral index
63 What if Newton knew quantum field theory (and special relativity)?! 2 =4 G( ) + p/c 2 )
64 What if Newton knew quantum field theory (and special relativity)?! 2 =4 G( + p/c 2 )
65 How to do it covariantly? Let us propose (NA 2008): (8 G ) 1 G µ = T µ 1 The metric is now blind to vacuum energy In order to satisfy Bianchi identity: T µ = vac g µ + excitations (8 G ) 1 G µ = T µ 1 4 T g µ T g µ + T µ, T µ ;µ = 1 4 T, Further assume an incompressible fluid (or gravitational aether) T µ = p (u µ u g µ ) **Disclaimer: The field equations do not follow from an Action principle
66 Deviations from GR sourced by Pressure or Vorticity (Kamiab & NA, 2011) (Aslanbeigi, Robbers, Foster, Kohri & NA, 2011) (Narimani, NA & Scott, 2014) Neutron Star Structure (e.g. Adv LIGO) Cosmology (CMB, Big Bang Nucleosynthesis) Intrinsic Gravitomagnetic Effect (LAGEOS, GPB) Vacuum gravity identical to GR**
67 How does pressure gravitate? (Narimani, NA & Scott 2014)
68 What now? Original Gravitational Aether proposal (NA 2008) is ruled out at 3-4σ (still better than σ!) But, vacuum is smooth matter is lumpy Does that make a difference? ~ 1 mm The theory must have a cut-off/coarse-graining scale
69 neutron stars and aether Deviations from Einstein gravity are sourced by pressure Neutron Stars Aether EOS) it out Aether General Relativity Uncertainty in nuclear equation of states Kamiab & NA 2011 Can test with Gravitational Wave detection from NS-NS mergers
70 Cosmology (GN/GR = 0.75 or 1?) (Aslanbeigi, Robbers, Foster, Kohri, NA, 2011) 1.4 G N / GR General Relativity X Gravitational Aether X h b Cosmic Microwave Background Big Bang Nucleosynthesis
71 aether and black holes We can solve for the black hole spacetime in this theory ds 2 = 1 2m r [1 + 4 p 0 f(r)] 2 dt 2 1 p 0 is the aether pressure at infinity 2m r 1 dr 2 r 2 d 2 f(r) is an analytic function of r that diverges at r 2m & r UV-IR coupling thru aether pressure, p 0 Finite redshift at r=2m No Horizon(similar to Fuzzball models)
72 ... and dark energy! Let us propose that maximum redshift at horizon is set to Planck Temperature/Hawking Temperature by quantum gravity effects: p 0 = 1 m m 3 74 M 3 p DE,obs!! Aether pressure has the same sign and magnitude as Dark Energy for stellar mass black holes! Conjecture: Formation of stellar black holes causes cosmic acceleration Conjecture: Evolution of Astrophysical black holes leads to dynamical Dark Energy
73 ... and dark energy! Let us propose that maximum redshift at horizon is set to Planck Temperature/Hawking Temperature by quantum gravity effects: p 0 = 1 m m 3 74 M 3 p DE,obs!! Prescod-Weinstein, NA, Balogh 2009 Aether pressure has the same sign and magnitude as Dark Energy for stellar mass black holes! Conjecture: Formation of stellar black holes causes cosmic acceleration Conjecture: Evolution of Astrophysical black holes leads to dynamical Dark Energy Dark Energy equation of state Mean Black Hole Mass (M )
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75 A lesson from perihelion precession of Mercury
76 A lesson from perihelion precession of Mercury Newtonian Gravity has a symmetry between angular and radial coord s: r θ, Ωr = Ωθ
77 A lesson from perihelion precession of Mercury Newtonian Gravity has a symmetry between angular and radial coord s: r θ, Ωr = Ωθ Is this fundamental?
78 A lesson from perihelion precession of Mercury Newtonian Gravity has a symmetry between angular and radial coord s: r θ, Ωr = Ωθ Is this fundamental? No. It only emerges at low energies, but is broken at high energies perihelion precession of Mercury
79 A lesson from perihelion precession of Mercury Newtonian Gravity has a symmetry between angular and radial coord s: r θ, Ωr = Ωθ Is this fundamental? No. It only emerges at low energies, but is broken at high energies perihelion precession of Mercury Same could happen to Lorentz symmetry
80 A lesson from perihelion precession of Mercury Newtonian Gravity has a symmetry between angular and radial coord s: r θ, Ωr = Ωθ Is this fundamental? No. It only emerges at low energies, but is broken at high energies perihelion precession of Mercury Same could happen to Lorentz symmetry Cosmologist:Universe has already done this!
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