Cosmological Collider Physics

Transcription

1 Cosmological Collider Physics GaryFest Santa Barbara 2016 Juan Maldacena IAS Based on: N. Arkani- Hamed and JM, arxiv:

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3 Strings on plane waves

4 Y 2 1 Y Y Y 2 d = R 2 SO(2,d)

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6 Now the talk

7 According to inflaronary theory cosmological perturbarons have a quantum mechanical origin. They were created during inflaron H, 3M 2 plh 2 = V Relevant modes have energies of order H. Hubble scale could be as high as Gev.

8 Collisions à interacrons during inflaron à leave a small imprint on the perturbarons. We need to do the ``collider physics, i.e. go from the signatures to the basic interacrons. How do we recognize new parrcles, measure their masses and spins?

9 In flat space

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11 In Cosmology

12 Study non- gaussianires in the cosmological correlators. InteresRng for the phenomenology of inflaron InteresRng conceptually, to understand how we reconstruct the past. Fossils à dinosaurs. What is the structure of the wavefuncron, or probability distriburon produced by inflaron?

13 Analogy QCD Hadrons = galaxies Cosmology HadronizaRon Energy correlators = Structure formaron = correlators of primordial density fluctuarons. Weak coupling at = weak coupling during inflaron high energies Approximate scale invariance = approximate scale invariance of wavefuncron = approximate de- Si_er invariance. OPE of energy correlators Time à scale = squeezed limits of primordial correlators. = Rme à scale

14 Both are controlled by (slightly broken) conformal symmetry

15 Basic Observable

16 Primordial Curvature PerturbaRons (x) x h (x 1 ) (x n )i

17 KinemaRcs (x 1 ) (x 2 ) (x n ) (k 1 ) (k n ) Fourier transform à set of momenta StaRsRcal homogeneity of the universe à Momentum conservaron This is similar to amplitudes. But no ``energy conservaron. k 1 k 2 k 4 k 3

18 Leading effect k 1 k 2 Two point funcron h k1 k2 i = H2 k ( k 1 + k 2 ) (0) (x) H 2 log x +

19 Suppose that a massive parrcle existed during inflaron, m of order H. k 1 k 2 k 3 k 4 Density fluctuaronsà Inflaton ~ massless scalar field in de- Si_er. Massive parrcle k I = k 1 + k 2 Another field, Beyond the inflaton

20 InteresRng limit k I = k I k i = k i, i =1, 2, 3, 4 h4pti h2pti 3 e µ " k 2 I k 1 k iµ # e i + c.c. µ = p m 2 /H 2 9/4 k 1 k 2 k 3 k 4 ~ ki Chen, Wang, (quasi single field) Noumi, Yamaguchi, Yokoyama, Assassi, Baumann, Green, Senatore, Silverstein, Zaldarriaga, Suyama, Yamaguchi,

21 h4pti h2pti 3 e µ " k 2 I k 1 k iµ # e i + c.c. µ = p m 2 /H 2 9/4 k 1 k 2 k 3 k 4 We see clear oscillarons a funcron of the log of the raro of scales Boltzman suppression Interference effect: nopair + e µ pair Phase is a funcron of the mass. InteresRng test of the quantum nature of fluctuarons.

22 Spin h4pti F (,, 0 ) k 1 k 2 k 3 k 4 k 3 k4 k 1 k 2 Further evidence of quantum mechanics! à View it as a measurement of the correlated spins of pair of produced parrcles. There is a constraint on their masses.

23 Spin h s 1.O s 2.Oi [ ( 1.ˆx)( 2.ˆx)] s x 2 hj z (0)j z (z)i 1 z 2

24 h4pti h2pti 3 H2 M 2 pl e µ " k 2 I k 1 k iµ # e i + c.c. Overall size is small. One factor of H/M from each interacron. Can we find a bigger effect?

25 Three point funcrons Consider instead the inflaronary background. Now, we have a Rme dependent background (t)

26 k 1 k 2 k 3 k 3 k 1 k 2 k 3 Only one very small coupling H/M pl (t) k 4 =0 h3pti Usual k 3 1 k3 3 e µ " k3 k 1 DiluRon 3 # 2 +iµ e i + c.c. P s (cos )

27 k 1 k 2 k 3 k 3 (t) Loops à give rise to a faster decay k3 k 1 3+2iµ

28 k 1 k 2 k 3 k 3 (t) Story: ParRcle is created by long wave mode k 3. It then decays. We see interference between decay products and the original unperturbed state. A striking evidence of quantum mechanics. Phase of oscillaron is calculable!. Cosmological double slit experiment

29 Finding massive parrcles Collider à peaks in the invariant mass distriburon. Cosmology à peaks in the Fourier transform of the cosmological correlator as a funcron of = log(k short /k long ) Spin à angular dependence.

30 How difficult is it to detect? Compare it with standard three point funcron. The standard 3 point funcron can be viewed as exchanging a graviton. Planck: f experimental NL. 5, f standard This one has extra factors of 3/2+iµ µ k3 e k 1 NL (n s 1) k 1 k 2 k 3 Both suppress the signal. So the number of modes has to grow like the square of the above factor. The interacrons could be larger than gravitaronal! k 3 (t) k Kundu, Shukla, Trivedi

31 Bounds on masses of spinning m 2 H 2 s(s 1) parrcles Comes from the fact that in de- Si_er we have a null state when the inequality is saturated. Follows simply from representaron theory. SaturaRon = ``parrally massless field. No AdS analog. Higuchi, WavefuncRonal of the universe becomes unbounded for the longitudinal mode when the inequality is violated. Deser Waldron

32 m 2 H 2 s(s 1) For spin =1 à no bound For spin = 2 à there is a non- trivial bound. There cannot be any parrcles with masses between the graviton and this bound!. Kaluza Klein theory à Size of internal dimension should be smaller than the size of de- Si_er. Spin > 2 : Vasiliev theory is not smoothly connected to an ordinary Einstein theory. Not allowed m=0 gauge fields m bound mass

33 De Si_er isometries and conformal symmetry ds 2 = d 2 + dx 2 2 ( 1, x 1 ) ( n, x n ) Invariant under de- Si_er isometries. At late Rmes, de- Si_er isometries act on x as conformal symmetries. At late Rmes we can oten expand X i i O i ( x) Strominger, Wi_en 3d operator of conformal dimension Δ i

34 k 1 k 2 k 3 k 3 Decompose in terms of X i O i ( x) (t) i X k3 i c i Leads to i k 1

35 X k3 i c i i k 1 Powers that appear: Dimensions of 3d Operators à energies of quasinormal modes in the de- Si_er starc patch. Can be complex! SensiRve to the spectrum of masses in the theory. The OPE region of the correlator, k 3 << k 1, k 2 is not where the largest Non- gaussian signal lies. But it is the region containing direct informaron about the spectrum of the theory.

36 AnalyRc structure of correlator SingulariRes: Small momentum, or small intermediate momentum à essenrally OPE. No ``colinear singularires when: k 3 k 1 Related to the absence of parrcles in the iniral adiabarc vacuum state. There can be such singularires when we conrnue k i k i k 2

37 Signature of local interacrons Signature of local interacrons are in singularires when: C(k i ) A k p t + k t = Gives the high energy limit of the bulk amplitudes. Note that we need to conrnue Conformal invariance of C à lorentz invariance of A nx i=1 k i 0 Like delta funcron of energy conservaron k i k i

38 Why? C Z d (Propagators) Z d p 1 e i k t A A k p t k 1 k 2 k 3 k 4

39 String inflaron? Usual picture: Strings à 10d à KK theory à inflaron. Another possibility: l s. 1/H = R = Hubble radius ObservaRons: higher spin massive parrcles! New structures in graviton three point funcrons. I do not know of a concrete stringy model

40 Graviton 3pt funcron k 3 k 1 k 2 hhhhi hhhi H FE (shape) + 3/2 M 4H 2 4 F 2 (shape) + o( ) pl JM, Pimentel Overall small coupling This is allowed by the approximate scale and conformal invariance of inflaron

41 k 3 k 1 k 2 hhhhi hhhi H FE (shape) + 3/2 M 4H 2 4 F 2 (shape) + o( ) pl JM, Pimentel S = 1 G N Z R + 2 4R 3 + If this is observed + causality of the de- Si_er theory à massive higher spin states This is only power suppressed in l s H. Camanho, Edelstein, J.M., Zhiboedov Long string crearon à suppressed exponenrally as e 2 (lsh) 2

42 Conclusions Non gaussianires in cosmological correlators have very interesrng informaron. Very interesrng evidence of the quantum nature of the perturbarons. It is useful to think about the conformal symmetry (or late Rme implicarons of de- Si_er isometries). Could be observable with futurisrc experiments (e.g. 21 cm tomography). Ater seeing other non- gaussian signals.

43 Happy Birthday Gary! Thank you!!