Condensed Cosmological constant & vacuum energy matter Cosmology G. Volovik COSLAB Particle Scientific Advisory Board Meeting, November 9, 2006 Particle physics
How condensed-matter experience allows us to treat the problems of vacuum energy & cosmological constant
* Universality classes of vacua & momentum-space topology Fermi surface & Fermi points
* Emergent relativity in vacua with Fermi points together with chiral fermions, gauge fields, spin, metric fields, etc.
* Applications: dark energy, vacuum energy, zero-point energy, cosmological constant * Conclusion: 01 vacuum energy is the natural candidate for dark energy Supernova luminosity distances observational Acoustic peak dark energy vs Galaxy clusters dark matter
paradox of vacuum energy
−123 εDE=0.7εcrit εDarkEnergy = 10 εVacuumEnergy ∗ εDM=0.3εcrit εDarkEnergy vacuum is too light ! εcrit
02 εMatter/εcrit receipt to cook Universe
Problems: εDark Energy = 70%
* Why is vacuum not extremely heavy? εDark Matter = 30%
* Why is vacuum gravitating? εVisible Matter = 0,4% it is easier to accept that is exactly zero, Λ where is all this matter ? than 123 orders of magnitude smaller
* Why is vacuum as heavy as (dark) matter ? −123 εDM = 2-3 εDM = 10 εzero point
What can Low-Temperature physics say on these problems?
Why low-T physics ?
03 high-energy physics and cosmology are ultra-low temperature physics
characteristic high-energy scale in our vacuum (analog of atomic scale in cond-mat) is Planck energy 19 32 EP ~10 GeV~10 K
highest energy in accelerators −16 16 Eew =10 EPlanck Eew ~1 TeV ~ 10 K
T of cosmic background radiation −32 TCMBR =10 EPlanck TCMBR ~ 1 K
we can use methods B. L. Hu of low temperature physics? New View on Quantum Gravity and the Origin of the Universe
gr-qc/0611058
05 Why no freezing at low T? at low T all gapped modes must be frozen out TCMBR ~ 1 K 1016 −∆/T − 19 32 e =10 =0 ∆~EP ~10 GeV~10 K 16 Tew ~ 1 TeV~10 K 10−123, 10−1016, 10−1032 another great challenge? gapless excitations are not frozen out who protects massless excitations? topology
gapless (massless) fermions live: near p-space topological defects no life without (Fermi surface, Fermi point, ...) topology ... & in cores of r-space topological defects (strings, domain walls, monopoles,...)
06 Nielsen 1976; Volovik 1986; Horava: PRL 95, 016405 (2005) Main lesson from superfluid 3He-A
Fermi points life exists because Fermi point is hedgehog in momentum space p protected by topology z p y
p x
Fermi point: hedgehog in momentum space
???
07 relativistic quantum fields and gravity emerging near Fermi point Atiyah-Bott-Shapiro construction: expansion of Hamiltonian near the node in terms of Dirac Γ-matrices k i 0 H = ei Γ .(pk − pk)
H = + c σ .p gµν(p - eA - e .W )(p - eA - e .W ) = 0 general deformation µ µ τ µ ν ν τ ν
effective spin effective metric effective effective SU(2) gauge p emergent gravity isotopic spin z field effective py effective electromagnetic electric charge field e = + 1 or −1
px all ingredients of Standard Model and gravity: chiral fermions, gauge fields & gravity emerge in low-energy corner together with spin & physical laws: hedgehog in p-space Lorentz & gauge invariance 08 Applications & problems
is gravity fundamental or emergent? in any case you may use quantum liquid as analog system
to study problems of cosmological constant? for example
How can you do that? "condensed matter physics could be Why quantum liquid? applied to problems in quantum vacuum" L. Smolin, Physics Today, Nov. 2006, 44
* Ground state of quantum condensed matter (say, superfluid) mimics quantum vacuum: quasiparticles (matter) are not scatterred by atoms: for them ground state is empty space (vacuum)
* We know both: effective theory & microscopic physics in some systems the effective gravity emerges
* We can estimate zero point energy using effective theory as we did for quantum vacuum
* We can calculate vacuum energy in exact microscopic theory not known for quantum vacuum and see the difference
let us do this programme "even hint that the cosmological-constant problem is solved in such theories" L. Smolin, Physics Today, Nov. 2006, 44 09 Universal results of consideration of vacuum energy in quantum liquids "Vacuum Energy: Myths and Reality" vacuum energy is never big Int. J. Mod. Phys. issue devoted to dark energy & dark matter thermodynamics of quantum liquids demonstrates gr-qc/0604062 how nullification of vacuum energy occurs without fine-tuning:
in perfect vacuum state microscopic degrees of freedom fully compensate zero-point energy of quantum fields
vacuum energy is zero before and after cosmological transition
vacuum energy is non-zero if vacuum is not perfect
thermodynamics allows to obtain response of vacuum energy to: matter, temperature, gravity, curvature, phase transition, etc.
vacuum energy is naturally of order of dark matter vacuum energy is natural candidate for observed dark energy
no paradox − no crisis in theoretical physics 10 Condensed Problem for future matter
CosmologyCOSLAB Particle The main remaining cosmological constant problem: Particle physics Dynamics of vacuum energy
How does vacuum energy adjust itself to evolving Universe ?
How does vacuum energy relax after cosmological phase transition ? . . .
dynamics of vacuum energy may require modification of Einstein equations
but there is nothing unnatural with this technical problem
so, let us do this problem !
11 Torsion & spinning strings, torsion instanton Screening - antiscreening (running coupling) Fermion zero modes on strings & walls Symmetry breaking (anisotropy of vacuum) Antigravitating (negative-mass) string Parity violation -- chiral fermions Gravitational Aharonov-Bohm effect Vacuum instability in strong fields Domain wall terminating on string Casimir force & quantum friction 3He network String terminating on domain wall Fermionic charge of vacuum Monopoles on string & Boojums Higgs fields & gauge bosons Witten superconducting string Momentum-space topology Soft core string, Q-balls cosmic physical Neutrino oscillations Z &W strings Chiral anomaly & axions Kibble mechanism Gap nodes skyrmions strings vacuum Spin & isospin Dark matter detector Low -T scaling Alice string CPT-violation Primordial magnetic field mixed state Pion string String theory, GUT Baryogenesis by textures Broken time reversal High Energy high-T & chiral & strings 1/2-vortex, vortex dynamics Cosmological & Inflation cosmology Physics super- Films: FQHE, Newton constants Branes conductivity Statistics & charge of Effective gravity low skyrmions & vortices Bi-metric & vacuum Condensed Edge states; spintronics 3He dimensional conformal gravity gravity Gravity Matter 1D fermions in vortex core Graviton, dilaton systems Critical fluctuations Spin connection Mixture of condensates Rotating vacuum black Phenome Bose QCD Plasma Vector & spinor condensates Ergoregion, Event horizon holes nology condensates Quantum phase transition Hawking radiation, Entropy Physics meron, skyrmion, 1/2 vortex General fermion zero modes quark Relativistic plasma hydrodynamics Vacuum instability nuclear Photon mass Relativistic matter Multi-fluid Superfluidity physics Vortex Coulomb random neutron disorder Magnetic superfluidity of neutron star plasma anisotropy stars Quark condensate Nuclei vs Hydrodynamics of Vortices Larkin- Imry-Ma Nambu--Jona-Lasinio 3He droplet phase rotating superfluid Glitches effect Vaks--Larkin Shell model Shear flow instability Shear flow transitions Color superfluidity Pair-correlations Magnetohydrodynamic instability Savvidi vacuum Collective modes quantum phase Turbulence of vortex lines Intrinsic orbital momentum of quark matter transitions & vortex front Quark confinement momentum-space topology Cosmological constant problem #6
How big is vacuum How big is response response to cosmological transition ? of liquid helium to A-B transition ?
parameters of vacuum: Planck energy, Planck length, parameter of liquid helium: Newton constant interatomic distance a −2 2 G=EPlanck =aPlanck 4 2 δG δa Eelectroweak ~ ~ ~ 10−64 δa ∆ ~ ~ 10−6 G a 4 a 2 EPlanck EF
practically no change
deep vacuum is extremely strong
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