CAN COSMOLOGICAL DATA CONTAIN SIGNATURES OF

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1 CAN COSMOLOGICAL DATA CONTAIN SIGNATURES OF QUANTUM GRAVITY/STRING THEORY? Koenraad Schalm with Brian Greene, Gary Shiu, Jan Pieter van der Schaar ISCAP, Columbia University & University of Amsterdam hep-th/ hep-th/ hep-th/ astro-ph/

2 Cosmological Data: linear matter power spectrum 2

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4 Ly-α Linear matter power spectrum (source: Easther, Kinney, Peiris) 4

5 Primordial power spectrum Linear Matter Power spectrum Temperature fluctuations in the CMB Large Scale Structure INPUT: Primordial Power Spectrum δρ ρ = kn n = 0: SCALE INVARIANCE Avoid δρ ρ 1: [Harrison, Zeldovich] n > 1: problematic at high k range (BH formation) n < 1: problematic at low k range (homogeneity; data) NOTE: Early times Large Scales Late times Small Scales (Counterintuitive to effective field theory expectations) 5

6 Primordial Power Spectrum: Quantum Origins SBB Cosmology: δρ ρ = kn INITIAL CONDITION Explanation: quantum gravity Horizon Problem Inflationary Cosmology: δρ ρ = kn Spontaneous pair creation from vacuum Cures SBB problems within GR! BIG SUCCESS (COBE, WMAP,... ) Can Cosmological Data contain signatures of Quantum Gravity? 6

7 Primordial Power Spectrum: Quantum Origins SBB Cosmology: δρ ρ = kn INITIAL CONDITION Explanation: quantum gravity Horizon Problem Inflationary Cosmology: δρ ρ = kn Spontaneous pair creation from vacuum Cures SBB problems within GR! BIG SUCCESS (COBE, WMAP,... ) Can Cosmological Data contain signatures of Quantum Gravity? BAD NEWS 7

8 Inflationary Cosmology Avoid δρ ρ > 1: Slow Roll Inflation ɛ = η = V 2 V V V < 1 < 1 Problems: Slow roll Very fine tuned action What/where is the inflaton? Massive redshifts (Transplanckian problem vs. Horizon problem) a(t end ) a(t init ) e [Brandenberger,...] QFT in cosmological spacetimes Spontaneous pair creation from the vacuum cosmological vacuum ambiguity/initial state problem OPPORTUNITIES TO DETECT QUANTUM GRAVITY REMAIN 8

9 Cosmic Variance 9

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11 Expected errors in the C l spectrum for the WMAP (light blue) and Planck (dark blue) satellites. (source: W. Hu) Cosmic Variance: Intrinsic Statistics Limited Error of order

12 Effective Actions and Cosmology GR is an effective field theory for p k a(t) M Effects of high energy physics encoded in irrelevant, higher derivative operators. Leading term: S irr.op. = 1 M 2 [D µ D ν φd µ D ν φ +...] [Kaloper, Kleban, Lawrence, Shenker;... ] Leading effect of order k 2 a 2 M H2 2 M %. (standard vacuum) UNOBSERVABLE Phenomenological models/toy studies Cut-off p(t) = M means an earliest time (different for each k) - Demand that at smallest scale ( t earliest k ) recover flat space (Minkowski vacuum) COSMOLOGICAL VACUUM AMBIGUITY NEW effects: Expansion in H 1014 = 1% M 1016 [Easther, Greene, Kinney, Shiu; Danielsson; Kempf, Niemeyer;... ] 12

13 The Cosmological Vacuum Ambiguity Can cosmological data contain signatures of new physics? Dominant effect H M arises from COSMOLOGICAL VACUUM AMBIGUITY E global ; E vac = E min? Are non-standard vacua consistent? PROBLEM: Non-standard vacua in cosmology are difficult to square with decoupling. - tend to be non-local with scale H (specific examples) - Backreaction diverges. EXPLICIT EXAMPLES: vac T µν vac T Mink,bare µν - suggest they are consistent [Vilenkin Ford, Burgess, Cline, Holman; Kaloper, Kaplinghat,... ] [KKLS; Banks; Larsen- Einhorn; Brandenberger, EGKS,... ] 13

14 Deciphering Initial State Physics Primordial Power Spectrum D µ D µ Φ ± (t, k) = 0 φ b (t, k) = Φ + (t, k) + b(k)φ (t, k) (b.c./vacuum choice) P (k) = k3 2π lim t φ b(t, k) 2 (Choose basis where b(k) = 0 standard Bunch-Davies vacuum) Characteristic signature initial state effects Mode mixing φ(k) = Φ + (k) + b(k)φ (k) results in oscillations δp = P BD (b(k) + b (k)) = 2P BD b(k) cos α(k) b = b e iα 14

15 Phenomenological NPH Approach Shortest length b.c. (New Physics Hypersurface) Boundary conditions imposed at p(t) = k/ah = M Symmetries: homogeneity, isotropy and scale invariance b(k) = M 2iM e 2i H(k)(1 ɛ) β H(k) [Danielson; Brandenberger; Easther, Greene, Kinney, Shiu; Kempf, Niemayer;... Slow roll H = k ɛ Power Spectrum P (k) = P BD (k) 1 + β H(k) M sin M H(k) 15

16 Boundary Effective Field Theory Boundary conditions can be encoded in a boundary action S = (Dφ) 2 + κφ 2 D 2 φ = 0 n φ = κφ Connection with Hamiltonian approach b(k) = κφ +(t 0 ) + n Φ + (t 0 ) κφ (t 0 ) + n Φ (t 0 ) New physics corrections to the initial state encoded in irrelevant boundary operators S irr bnd = β M ( φ) 2 [Symanzik;... Schalm,Shiu, vd- Schaar; Porrati] Boundary EFT parametrizes cosmological vacuum ambiguity Symmetries: homogeneity and isotropy b(k) = [ ia 3 0Φ 2 +,0 ] βk 2 a 2 0M Power Spectrum P (k) = P BD (k) 1 + β k a 0 M sin 2k a 0 H Can be shown to be consistent initial conditions Backreaction is under control: new boundary couplings absorb T Cosmo T Mink divergences 16

17 Deciphering New Physics Power Spectrum BEFT ( ( )) δp = P BD Ak sin 2πk C Amplitude A = β a 0 M SL-NPH δp = P BD (A sin A = β H M ( )) 2π C ln k k piv Period k = C = πa 0 H ln k k piv = C = πh Mɛ H # of Osc. N M πh N ɛ H M πh ln k max k min Ratio of scales A k = β H M A = β H M, ɛ H C π = H M BEFT bound k max < a 0 M k max < πmc/h Qualitative difference Symmetries Linear BEF T vs. Log SL NP H periodicity Preliminary studies (SL-NPH) Observable if βh M 1%. [Bergstrom, Danielsson; Elgaroy, Hannestad; Okamoto, Lim; Martin, Ringeval; Sriramkumar Padmanabda Easther, Kinney, Peiris] 17

18 Signature of SL-NPH corrections 18

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21 A. The modified perturbation spectrum P ( k) (for a power-law inflationary model) as a function of the momentum for a nearly scale invariant change in the initial conditions compared to Bunch- Davies. B. The percentage change in the observed spherical harmonic coefficients C l, P ( k, θ, φ) = l,m C l ( k )Y l m(θ, φ) for a canonical cosmological constant cold dark matter model. hep-th/ ) (Source Easther et.al. 21

22 Signature of BEFT corrections

23 A. Generic change in the power spectrum from initial state effects as deduced with boundary EFT. B. A refined estimate of the sensitivity of the CMB to new physics. 23

24 Linear matter power spectrum II 24

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26 Ly-α BEFT corrections to linear matter power spectrum (source: Easther, Kinney, Peiris) Growth of BEFT corrections with k suggests LSS- Ly α searches Absence suggests irrelevance of BEFT to observed cosmology. NOTE: Early times Large Scales Late times Small Scales (Counterintuitive to effective field theory expectations) BEFT CONUNDRUM 26

27 Conclusion and outlook Initial states in Effective Field Theory Phenomenological SL-NPH approach - Intuitively sensible; lacks interpretation/consistency - Indicates moderately large H/M corrections Theoretically controlled boundary action formalism - Manifest scaling behaviour: boundary RG-flow - dressing of initial state; - preferred b.c. are RG-fixed points. - growth with k LSS data suggests irrelevant Best of Both Universes approach? - Cosmological Effective Field theory (in progress) Application to Cosmology Parametrize the cosmological vacuum ambiguity - Preference? Bunch-Davies, transparent, adiabatic, thermal, etc. - Generically receive H/M corrections! Parameters encoding initial data are phenomenologically constrained. Connections with holography? Earliest time in cosmology guarantee irrelevant boundary corrections. Are quantum gravity contributions decipherable in cosmological data? 27

28 CMB Density fluctuations Measured (indirectly) Spatial curvature fluctuations P R = P M 2 p ɛ BD H2 M 2 p ɛ COBE WMAP Primordial Gravitational Waves P T = P M 2 p BD H2 M 2 p measures H M p directly! [not yet observed]. If H/M 1% primordial gravity waves observed, then initial state effects in the CMB due to UV physics are (potentially) observable 28

29 New CMB physics and String Theory If observed, what can we learn about quantum gravity/string theory? Observe effect of leading irrelevant operator in LEEA Can deduce scale M of new physics. -String theory? -Intermediate new scale physics (GUT)? To distinguish various models, need more information. GATHER ONE PIECE AT A TIME 29