SEARCHING FOR OSCILLATIONS IN THE PRIMORDIAL POWER SPECTRUM
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1 SEARCHING FOR OSCILLATIONS IN THE PRIMORDIAL POWER SPECTRUM Daan Meerburg, David Spergel and Ben Wandelt based on and , PRD M. Benetti (13). Ade et al (13), R. Easther and R. Flauger (13)
2 MOTIVATION e.g. J. Martin and C. Ringeval, (4), C. Dvorkin and W. Hu, (11)., J. Hamann, L. Covi, A. Melchiorri, and A. Slosar (7). C. Pahud, M. Kamionkowski, and A. R. Liddle, (9), P. D. Meerburg, R. A. M. J. Wijers, and J. P. van der Schaar (1), H. Peiris, R. Easther, and R. Flauger (13) M. Aich, D. K. Hazra, L. Sriramkumar, and T. Souradeep (13)
3 MOTIVATION Motivations: e.g. J. Martin and C. Ringeval, (4), C. Dvorkin and W. Hu, (11)., J. Hamann, L. Covi, A. Melchiorri, and A. Slosar (7). C. Pahud, M. Kamionkowski, and A. R. Liddle, (9), P. D. Meerburg, R. A. M. J. Wijers, and J. P. van der Schaar (1), H. Peiris, R. Easther, and R. Flauger (13) M. Aich, D. K. Hazra, L. Sriramkumar, and T. Souradeep (13)
4 MOTIVATION Motivations: Phenomenological/Observational e.g. J. Martin and C. Ringeval, (4), C. Dvorkin and W. Hu, (11)., J. Hamann, L. Covi, A. Melchiorri, and A. Slosar (7). C. Pahud, M. Kamionkowski, and A. R. Liddle, (9), P. D. Meerburg, R. A. M. J. Wijers, and J. P. van der Schaar (1), H. Peiris, R. Easther, and R. Flauger (13) M. Aich, D. K. Hazra, L. Sriramkumar, and T. Souradeep (13)
5 MOTIVATION Motivations: Phenomenological/Observational e.g. J. Martin and C. Ringeval, (4), C. Dvorkin and W. Hu, (11)., J. Hamann, L. Covi, A. Melchiorri, and A. Slosar (7). C. Pahud, M. Kamionkowski, and A. R. Liddle, (9), P. D. Meerburg, R. A. M. J. Wijers, and J. P. van der Schaar (1), H. Peiris, R. Easther, and R. Flauger (13) M. Aich, D. K. Hazra, L. Sriramkumar, and T. Souradeep (13) Theoretical
6 MOTIVATION Motivations: Phenomenological/Observational e.g. J. Martin and C. Ringeval, (4), C. Dvorkin and W. Hu, (11)., J. Hamann, L. Covi, A. Melchiorri, and A. Slosar (7). C. Pahud, M. Kamionkowski, and A. R. Liddle, (9), P. D. Meerburg, R. A. M. J. Wijers, and J. P. van der Schaar (1), H. Peiris, R. Easther, and R. Flauger (13) M. Aich, D. K. Hazra, L. Sriramkumar, and T. Souradeep (13) Theoretical Do we learn something more? Observation--->Theory
7 MOTIVATION Motivations: Phenomenological/Observational e.g. J. Martin and C. Ringeval, (4), C. Dvorkin and W. Hu, (11)., J. Hamann, L. Covi, A. Melchiorri, and A. Slosar (7). C. Pahud, M. Kamionkowski, and A. R. Liddle, (9), P. D. Meerburg, R. A. M. J. Wijers, and J. P. van der Schaar (1), H. Peiris, R. Easther, and R. Flauger (13) M. Aich, D. K. Hazra, L. Sriramkumar, and T. Souradeep (13) Theoretical Do we learn something more? Observation--->Theory What do we predict? Theory ---> Observation
8 MOTIVATION Motivations: Phenomenological/Observational e.g. J. Martin and C. Ringeval, (4), C. Dvorkin and W. Hu, (11)., J. Hamann, L. Covi, A. Melchiorri, and A. Slosar (7). C. Pahud, M. Kamionkowski, and A. R. Liddle, (9), P. D. Meerburg, R. A. M. J. Wijers, and J. P. van der Schaar (1), H. Peiris, R. Easther, and R. Flauger (13) M. Aich, D. K. Hazra, L. Sriramkumar, and T. Souradeep (13) Theoretical Do we learn something more? Observation--->Theory What do we predict? Theory ---> Observation Generally: Future of early Universe cosmology is constraining correlated variables, i.e. Theory ----> {A,B,C,...} observables
9 MODELS Theoretical templates C l = Z 1 dk k R(k)( T l (k)) 1 R(k) =A 1 k k m (1 + A cos[! 1 log k/k + 1 ]) m n k k k R(k) =B 1 1+B cos[! k + ] k
10 MODELS Theoretical templates C l = Z 1 dk k R(k)( T l (k)) 1 R(k) =A 1 k k m (1 + A cos[! 1 log k/k + 1 ]) m n k k k R(k) =B 1 1+B cos[! k + ] k 1) e.g. Axion Monodromy, Natural inflation (similar), non-bd (NPH), unwinding inflation (Silverstein, Flauger, D Amico,Greene,Chen, Agullo, Parker, Shandera et al.)
11 MODELS Theoretical templates C l = Z 1 dk k R(k)( T l (k)) 1 R(k) =A 1 k k m (1 + A cos[! 1 log k/k + 1 ]) m n k k k R(k) =B 1 1+B cos[! k + ] k 1) e.g. Axion Monodromy, Natural inflation (similar), non-bd (NPH), unwinding inflation (Silverstein, Flauger, D Amico,Greene,Chen, Agullo, Parker, Shandera et al.) ) e.g. multifield (features), non-bd (BEFT) (Chen et al, Greene et al, Easther)
12 OSCILLATIONS issues Likelihood is very irregular (slow convergence) Oscillations at high frequency require high resolution (k and l) MCMC (MH) generally becomes impractical (MULTINEST) Recomputing all transfer functions is time consuming
13 PERTURBATIVE EXPANSION C l = Z 1 dk k R(k)( T l (k)) Corrections are small Perturbative expansion in oscillatory part C` = C ù + C p`
14 PERTURBATIVE EXPANSION Expand Transfer function in oscillatory part ( T l (k)) = ( T l ) + T l X ( i ) T l, i + O( i ) We then have for the perturbed part: C p` = C p( ) ` + C p( ) ` + X ( i i )( C p( ) `, i + C p( ) `, i )+O(( + ) i ) Power spectra and derivatives can be precomputed: C p` C p`, i Cp `, i j
15 PLANCK BEST FIT -5 c w 1 A =.35 1 =.15! 1 = 8.8 log L =
16 PLANCK BEST FIT -5 c w 1 Done by Planck team A =.35 1 =.15! 1 = 8.8 log L =
17 Consistency check: PLANCK COLLABORATION 13
18 Consistency check: PLANCK COLLABORATION 13
19 PLANCK BEST FIT. -Higher resolution - -Varied lensing amplitude -DLog@LD Mild Correlation between lensing amplitude and w 1! 1 = 13. oscillations. Slightly improves A. fit A lens
20 VS WMAP 9 PLANCK 1
21 VS DLog@LD DLog@LD w 1 w 1
22 SIMULATIONS MCMC (planck noise, 1 random seed) with mock data, with signal ÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏ Ï ÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏ ÏÏÏ ÏÏÏ ÏÏÏÏÏÏÏÏÏ Ï ÏÏÏÏ Ï ÏÏÏÏÏÏ Ï w 1 A =.1 A =.5 Ï A =.1 -DLog@LD -DLog@LD Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï w 1 A =.1 A =.5 Ï A =.1 Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï A =.1 A =.5 Ï A = Ï w 1
23 SIMULATIONS MCMC (planck noise, 1 random seed) with mock data, with signal -DLog@LD DLog@LD ÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏ Ï ÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏÏ ÏÏÏ ÏÏÏ ÏÏÏÏÏÏÏÏÏ Ï ÏÏÏÏ Ï ÏÏÏÏÏÏ Ï A =.1 A =.5 Ï A = w w 1 -DLog@LD w 1
24 SIMULATIONS Full MCMC (planck noise) with mock data, no signal Lin Log See also J. Hamann, A. Shafieloo, and T. Souradeep (1, R. Easther and R. Flauger (13)
25 SIMULATIONS Full MCMC (planck noise) with mock data, no signal Lin 6 5 Log 4 N N DLog@LD DLog@LD 5 Universes; WMAP 9 noise and cosmic variance, no signal Linear Log See also J. Hamann, A. Shafieloo, and T. Souradeep (1, R. Easther and R. Flauger (13)
26 SIMULATIONS 5 Universes; Real Planck noise and cosmic variance, no signal See also J. Hamann, A. Shafieloo, and T. Souradeep (1, R. Easther and R. Flauger (13)
27 SIMULATIONS 5 Universes; Real Planck noise and cosmic variance, no signal 4 Counts 3 1 Improvement as a function of maximum multipole: A.1 Lin Log See also J. Hamann, A. Shafieloo, and T. Souradeep (1, R. Easther and R. Flauger (13)
28 NEW Implement code into multinest. (will make code available soon) Marginalized likelihood computed in less than 16 hours, on 1 core node. Varying all cosmological parameters; can improve fit by going go higher order in the expansion Something else; have tried to fit a very long wavelength oscillation to Planck + BICEP, to relieve tension with data and deal with trans Planckian displacement (e.g. axion monodromy).
29 Multinest preliminary results: -5 c w 1
30 Multinest preliminary results: c w 1
31 Multinest Marginalized prob Planck P/Pmax !
32 Multinest Marginalized prob Planck.8 P/Pmax.6.4 P/Pmax ! !
33 PLANCK + BICEP.4.3 Planck+HST+BAO+Lensing+BICEP+n r +OSCILLATIONS r.5..1 Axion-monodromy prediction: R(k) = R(k ) k k ns dn s /d ln k (1 + n s cos[ k/f]) Flauger et al (9), Lewis
34 PLANCK + BICEP.4.3 Planck+HST+BAO+Lensing+BICEP+n r +OSCILLATIONS r.5..1 Axion-monodromy prediction: R(k) = R(k ) k k ns dn s /d ln k (1 + n s cos[ k/f]) k ' log(k/k )/ (k ) 11M p Flauger et al (9), Lewis
35 PLANCK + BICEP.4.3 Planck+HST+BAO+Lensing+BICEP+n r +OSCILLATIONS r.5..1 Axion-monodromy prediction: R(k) = R(k ) k k ns dn s /d ln k (1 + n s cos[ k/f]) k ' log(k/k )/ (k ) 11M p Best-fit Planck + Bicep! ' 1! f O(1)M p Planck+Bicep +Planck ! Flauger et al (9), Lewis
36 PLANCK + BICEP.4.3 Planck+HST+BAO+Lensing+BICEP+n r +OSCILLATIONS r.5..1 Axion-monodromy prediction: R(k) = R(k ) k k ns dn s /d ln k (1 + n s cos[ k/f]) k ' log(k/k )/ (k ) 11M p Best-fit Planck + Bicep! ' 1! f O(1)M p Planck+Bicep +Planck ! This also leads to large tilt, in tension with SPT/ACT Flauger et al (9), Lewis
37 CONCLUSIONS Perturbative approach; fast and accurate, now + multinest Constraints so far: Log spaced oscillations: WMAP 9 signature has mostly disappeared. New low freq. signatures. Mild correlation with lensing amplitude. Linear spaced oscillations. WMAP 9 and Planck are consistent Are these real? Most likely not (at 95% C.L.) Bicep results do not significantly favor running/long wavelength oscillation
38 IMPROVEMENT Log N 15 N DLog@LD -DLog@LD w=1-13 w=13-5 w=1-13 w=13-99 Notice the difference between high freq and low freq
39 IMPROVEMENT Lin N N DLog@LD -DLog@LD w=-46 w=46-9 w=-389 w=39-76 Notice the difference between high freq and low freq
40 LINEAR SPACE R(k) =B 1 k k m (1 + B k n cos[! k + ]) Linear spaced oscillations WMAP 9/PLANCK : apple! apple 9 88 steps Best-fit Planck:! = 734 =.45 B =.1785
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