Un-natural cosmology and observer selection. John Peacock ICCUB Barcelona 19 Jan 2017

Transcription

1 Un-natural cosmology and observer selection John Peacock ICCUB Barcelona 19 Jan 2017

2 Outline Defining natural-ness and fine tuning PPT viewpoint Bayesian framework List of cosmological problems Strange parameter coincidences The vacuum challenge Modelling and observing dark energy Searching for DE dynamics Modifying gravity The ensemble approach Physics of variable Λ Impact on the history of star formation Other issues involving observer bias

3 Natural-ness in PP All dimensionless parameters should be O(1) So all fundamental masses should derive from Planck scale (before running) Unless parameter = 0 is enforced by symmetry Tiny parameter from symmetry breaking Quantum corrections should not be >> observed value of any quantity (no fine-tuning) e.g. electron self-energy Higgs mass has un-natural quadratic correction

4 Un-natural aspects of cosmology Coincidences of value Baryon density» DM density Matter-radiation equality = recombination Coincidences of time ( why now? ) Vacuum density» matter density P(k) break scale» nonlinear scale The nature of the vacuum density ( Dark Energy )

5 The baryon-dm coincidence Unrelated quantities in the standard model. Baryon density set by CP violation (?): DM density set by freezeout (?): So overall

6 The radiation-recombination coincidence Recombination is when thermal photons can ionize H m-r equality when kt n γ» m p c 2 n B

7 Bayesian view of parameters P(p) represents state of knowledge about theory i.e. p has some definite (unknown) value Or perhaps genuine relative frequency of events within a multiverse? How to get a prior? If p can have either sign, reasonable to treat dp/dp as constant near p=0 (e.g. for Λ) But p=0 must not be special (e.g. Coleman-de Lucia bubble nucleation produces only negative curvature) Otherwise tend to use Jaynes dp/d ln p = const

8 Coincidences do happen Two independent parameters x, y with uniform prior over 0 to 1 x-y < in 5% of experiments So coincidence to an order of magnitude plausible in a Jaynes prior with range 40 powers of 10 e.g. Baryon-DM coincidence may be just that

9 Most important challenge to naturalness in cosmology comes from Dark Energy

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11 Possible explanations for Dark Energy (1) Denial (2) Cosmological constant (1917) (3) Vacuum energy (Nernst 1916, then 1960s) (4) Dynamical Dark Energy (1980s/1990s) - Empirical w = P / ρ c 2 ; fit w(a) = w 0 + w a (1-a) - Quintessence : use inflationary technology of w<0 from scalar fields

12 The zero-point energy of the vacuum Nernst (1916) New physics causes cutoff of high-energy modes. Common to set E max =E Planck : origin of discrepancy But this is just radiation with occupation no. = ½ Need relativistic cutoff procedure

13 Renormalized vacuum density for particle of mass m and cutoff scale M: (Koksma & Prokopec ) Real vacuum problem is that observed energy scale is at mev level, not TeV: discrepancy of 15 powers of 10, not 120 The bare Λ can absorb divergence Zeldovich 1968 Sakharov 1968 un-natural?

14 Dynamics: perhaps DE is declining towards a low value?

15 Quintessence Two equations of state for the vacuum: (1) Potential dominates: w = -1 (2) Kinetic term dominates: w = +1 ( ρ v a -6 ) Ratra & Peebles (1988): consider rolling scalar field with an arbitrary potential as dynamical vacuum energy$ - thus redshift away kinetic term: leaves frozen field that is indistinguishable from Λ

16 Tracker solutions: explaining ρ DE ~ ρ m Suppose ρ m a -α$ density matter Look for a solution with fixed ρ v /ρ m - not slow-roll, since need K V DE now Solution: with ρ v /ρ m = α/λ 2 time But tracks equally well in matter and radiation era, and is an attractor. Can only switch on w = -1 today if we fine-tune a feature in the potential

17 Is dark energy empirically different from Λ?

18 Sensitivity to the vacuum Vacuum affects H(z) via Friedmann equation: H 2 (z) = H 2 0 [ Ω M (1+z) 3 + Ω R (1+z) 4 + Ω V (1+z) 3 (1+w) + (1-Ω) (1+z) 2 ] matter radiation vacuum Alters D(z) via r = c dz / H(z) And growth via 2H dδ/dt term in growth equation Effects of w are: (1) Small (need D to 1% for w to 5%) Rule of 5 (2) Degenerate with changes in Ω m To measure w to a few %, we need independent data on Ω m and to be able to control systematics to ~ parts in 1000

19 Direct measures of D(z) z=0.6: WiggleZ ( ): 4% measure of D(z) from 130k z s z=0.57: BOSS ( ): 3% measure of D(z) from 264k z s. Near 1% from DR12 Consistent with standard cosmology also from SNe

20 The equation of state: constraints from CMB + D(z) Combined: Future probes need to achieve <1% accuracy in D(z)

21 Dark energy or modified gravity? Dark energy: inferred assuming H(z) comes from standard Friedmann equation. Focus on equation of state w = P / ρ c 2 (= -1?) assumes DE is a real substance - but is it? H 2 (z) = H 2 0 [ (1-Ω) (1+z) 2 + Ω M (1+z) 3 + Ω R (1+z) 4 + Ω DE (1+z) 3 (1+w) ] Curvature matter radiation extra term from non-einstein??

22 Phenomenology of modified gravity Adopt longitudinal gauge (in effect gauge-invariant) In MG, potentials can differ ( slip : affects lensing), plus Poisson equation is modified. No standard notation. Good refs are Skordis ( ) or Daniel et al. ( ). Assume modifications negligible at high z, since no DE then: Combine to affect growth of fluctuations

23 Mock 2dFGRS from Hubble volume real space Eke, Frenk, Cole, Baugh + 2dFGRS 2003

24 Mock 2dFGRS from Hubble volume z-space Eke, Frenk, Cole, Baugh + 2dFGRS 2003

25 Growth rate: consistent with Einstein

26 Complementary data: gravitational lensing Image distortion depends on Geometry: angular diameter distance (Dark Energy) Dynamics: growth of structure (Modified Gravity) Potentially most accurate probe, but effect is small: ~1% extra image ellipticity needs to be measured precisely

27 Overall MG consistency ( )

28 or inconsistency? ( )

29 So for now we need to make sense of cosmology with standard gravity and physical DE

30 Two problems for all explanations of DE Still have to solve the classical vacuum energy problem matter density future is vacuum dominated The why now problem vacuum now time

31 The answer to why now must be anthropic One-universe anthropic Life (structure) only after matterradiation equality But life possible before and after Λ domination Many-universe anthropic Postulate ensemble of universes with different Λ (at least) e.g. bubbles predicted in some inflation models Predates landscape, but requires new physics for variable Λ$ Ask if structure formation can differ between universes

32 The biggest question in cosmology: is there more than one universe?

33 Weinberg s prediction

34 Λ suppresses growth of structure

35 Shutdown of DM halo growth Fraction of DM density per d ln M Vacuum domination means growth of DM haloes is switching off: fixed population in the far future (redshift z = -1) Freezeout below galaxy masses if Λ were much larger

36 Weinberg detail I: where are the stars? Eke et al PIGG groups optimal halo: ~ M sun

37 Weinberg detail II: how to get a variable Λ? V(ϕ) δϕ V=0 Simplest idea: linear potential (Linde, Vilenkin, Garriga) with quantum fluctuations + inflationary multiverse Not dependent on string landscape ϕ Note negative Λ equally likely

38 Weinberg detail III: Bayesian mediocrity Assume you are a randomly-selected member of all observers ever generated in the multiverse Bayes: P( Λ observer ) P prior (Λ) N gal (Λ) Take prior on vacuum energy constant over small range around zero (not a special value) Number of galaxies depends on fraction of universe collapsed into mass near that of Milky Way

39 Efstathiou 1995 Fixed T = 2.73 K uncertain Ω m h 2 OK if we want to predict Λ in our universe = Ω v = 1 - Ω m

40 Predicting the CMB temperature JP 2007: avoid biology by predicting posterior for Λ and T at formation compare with data for Sun (simplest ensemble in which only Λ varies)

41 Positivity of ρ vac? T max = JAP 2007 For negative Λ, most structure forms after turnround P(Λ>0): 0.25 (T max =10) 0.03 (T max =30) Mild preference for a recollapsing universe P( Λ <obs value): 0.1 (T max =10) 0.02 (T max =30)

42 Is this really the right explanation for Λ? (many feel it is no explanation at all)

43 Evidence: the P(k) coincidence Variance in density Nonlinear evolution is close to destroying all information below the break Reasonable: flat portion must be nonlinear to get full collapse But growth has almost saturated: much larger Λ would prevent nonlinearities scale

44 The impact of DE on Galaxy Formation DE % Is the turndown in star-formation rate connected to DE? How would things look if Λ were larger?

45 Just-so halo approach JAP (2007): Predict stellar density as proportional to collapse fraction in peak efficiency haloes ~ 50% of all stars we will ever get are now in place

46 What if Λ had been larger? Asymptotic stellar density exponentially suppressed

47 Semianthropic galaxy formation Ingredients: DM halo merging Cooling of gas Stars from cold gas Central black holes Feedback from SNe and BH to heat or remove gas Can match inefficiency of star formation (only 4% of baryons in stars) Observer weighting is fraction of baryons in stars but what about in the very long term?

48 Eternity is very long especially towards the end

49 Semianthropic galaxy formation Fraction of baryons in stars M. Koprowski: run Galform into future. No clear asymptote of stellar baryon fraction possible that all baryons cool given time: would remove observer bias on Λ 1 / time

50 Compare the Anthropic Principle Carter, Barrow & Tipler 1980s terminology: Weak anthropic principle Our location in time and space is biased according to where/when life forms more easily Less controversial (but Carbon??) Strong anthropic principle Cosmology/physics *must* be such as to allow life to develop Rightly disliked: sounds like religion But guaranteed in a sufficiently large/diverse physical multiverse ( why something rather than nothing problem)

51 The big question: what varies? Natural to extend Weinberg s ensemble: Other cosmological parameters For more complex inflation models, could vary horizon-scale amplitude, tilt, curvature All of physics String theory, or any theory with multiple moduli fields, can vary all dimensionless ratios: fine structure, proton/electron mass ratio Without a unique model, can still construct and test speculative ensembles Measure problem

52 Empirical hints on variation Neutrino masses Large-scale damping forbids galaxies (Tegmark et al. 2003) Fine-structure etc. from spectroscopy No evolution: d ln α / d ln a <~ 10-6 Carbon-12 resonance (Hoyle) Marginal existence of nuclei Higgs vacuum metastability

53 Marginal existence of nuclei : u & d quarks close to point where BBN could not build nuclei (unstable n, D)

54 Higgs metastability : quantum corrections can change effective Higgs potential so that normal vacuum is not ground state

55 Status of the anthropic multiverse Many un-natural aspects of cosmology & physics something rather than nothing needs more than Bayes Weinberg s explanation for Λ questionable But must contain part of truth; and no alternative exists Other ensembles remain to be explored Λ might vary in a manner coupled with other parameters that could affect observers (baryon density, fluctuation amplitude) But then not so easy to get priors without a detailed physical theory Controversy will remain unless we can probe physics of variable Λ and other parameters directly

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