1. Juan Carlos Bueno Sánchez Universidad del Valle (Santiago de Cali), Universidad Antonio Nariño (Bogotá), Universidad Industrial de Santander (Bucaramanga) CMB anisotropy constraint Liberating vector fields from their Based on: JCBS, Phys. Lett. B 739 (2014) 269-278 JCBS, arxiv 1509.XXXX (On a local approach to CMB anomalies) Warsaw, 9 Sept. 15

2. How much you need to twist the inflationary paradigm to obtain CMB anomalies? (i.e. breaking homogeneity & isotropy of the CMB) The question Apart from the inflaton, other scalar field(s) contributes to the perturbation spectrum imprinted on the CMB The ingredient (Isocurvature perturbation) A framework to understand CMB anomalies

3. Inhomogeneous distribution of the iso-field at the end of inflation Breaking of statistical homogeneity of the CMB The outcome Avenue towards CMB anomalies A framework to understand CMB anomalies How much you need to twist the inflationary paradigm to obtain CMB anomalies? (i.e. breaking homogeneity & isotropy of the CMB) The question Apart from the inflaton, other scalar field(s) contributes to the perturbation spectrum imprinted on the CMB The ingredient (Isocurvature perturbation) An initially excited isocurvature field does not fully decay due The set-up Inflaton responsible for most of the CMB perturbations (homogeneous & isotropic) to its interactions during inflation

4. Fluctuations + dynamics

8. Light fields can be caught ‘’in the middle’’ by the end of inflation

9. Snapshot at the end of inflation The link to CMB anomalies Field interactions become important before the end of inflation Field decay Field oblivious to interactions Slow-roll phase LSS

10. Interacting spectator  during inflation The setting Initial condition  retains a large EV where it is oblivious of interactions if interactions become important at x if  evoles as a free field Emergence of a patchy structure (JCBS ’14) Dynamical regimes (JCBS & Enqvist ’13) c integrated out s as a free field (slow-roll phase) c production (Kofman et al. ‘04) Trapping mechanism for s (decay phase) Cold Spot accounted for through localized inhomogeneous reheating (Separation between the slow-roll and decay phases is too crude)

11. A necessary (more) realistic probability density N  = O(10) N  = O(10 2 ) Free field dynamics: Interacting field dynamics: Numerical solution for the interacting dynamics

12. N end = 45 Free field dynamics: Interacting field dynamics: Numerical solution for the interacting dynamics A necessary (more) realistic probability density

13. N end = 50 Free field dynamics: Interacting field dynamics: Numerical solution for the interacting dynamics A necessary (more) realistic probability density

14. N end = 51 Free field dynamics: Interacting field dynamics: Numerical solution for the interacting dynamics A necessary (more) realistic probability density

15. N end = 52 Free field dynamics: Interacting field dynamics: Numerical solution for the interacting dynamics A necessary (more) realistic probability density

16. N end = 53 Free field dynamics: Interacting field dynamics: Numerical solution for the interacting dynamics A necessary (more) realistic probability density

17. N end = 54 Free field dynamics: Interacting field dynamics: Numerical solution for the interacting dynamics A necessary (more) realistic probability density

18. N end = 55 Free field dynamics: Interacting field dynamics: Numerical solution for the interacting dynamics A necessary (more) realistic probability density

19. N end = 56 Free field dynamics: Interacting field dynamics: Numerical solution for the interacting dynamics A necessary (more) realistic probability density

20. Can a Local direction-dependent contribution to the CMB be generated? Vector fields strongly constrained in the CMB g *  0.02 Kim & Komatsu, 2013 Local breaking of statistical isotropy LSS Planck, 2015

21. Local breaking of statistical isotropy Slow-roll phase Scale invariance for  = -4 Decay phase End of scaling A simple example: vector curvaton with varying kinetic function Dimopoulos et al. ‘10 A motivated choice:

22. Evolution of the vector field Energy density Modulated kinetic function Local breaking of statistical isotropy Center of the  distribution Left end of  distribution Right end of  distribution Dimopoulos et al. ’09, ‘10 Vector curvaton contribution to the CMB

23. Probability density for the curvature perturbation Probability density for  A,end Probability density for  or  x  sr  Interacting dynamics of  Kinetic function f(  ) Initial Probability density for  (Gaussian, fixed by fluctuations) Local breaking of statistical isotropy

24. Probability density for the curvature perturbation Probability density for  A,end Probability density for  or  x  sr  Interacting dynamics of  Kinetic function f(  ) Initial Probability density for  (Gaussian, fixed by fluctuations)

25. Local breaking of statistical isotropy Probability density for the curvature perturbation Probability density for  A,end Probability density for  or  x  sr  Interacting dynamics of  Kinetic function f(  ) Initial Probability density for  (Gaussian, fixed by fluctuations)

26. Local breaking of statistical isotropy Probability density for the curvature perturbation Probability density for  A,end Probability density for  or  x  sr  Interacting dynamics of  Kinetic function f(  ) Initial Probability density for  (Gaussian, fixed by fluctuations)

27. Local breaking of statistical isotropy Probability density for the curvature perturbation Probability density for  A,end Probability density for  or  x  sr  Interacting dynamics of  Kinetic function f(  ) Initial Probability density for  (Gaussian, fixed by fluctuations)

28. Local breaking of statistical isotropy Probability density for the curvature perturbation Probability density for  A,end Probability density for  or  x  sr  Interacting dynamics of  Kinetic function f(  ) Initial Probability density for  (Gaussian, fixed by fluctuations)

29. A cartoon Correlated spatial variation of r Full sky maps required with enough sensitivity (CORE,CMB-Pol,LiteBIRD) Correlated parity violating signal Non-vanishing EB correlations Local breaking of statistical isotropy

30. The contribution of these fields to the curvature perturbation (given the appropriate tuning) provides a mechanism to break statistical homogeneity and isotropy of the CMB (Local versions of inhomogeneous reheating, vector curvaton, …) Wishful thinking: The production of localized perturbations may provide a framework to understand some of the CMB anomalies (if they turn out to exist) Conclusions Vector fields source GW: Looking for correlated spatial variations of r might reveal the presence of a vector field hidden in the CMB Vector fields might be allowed to contribute substantially to  as long as they do it in a relatively small patch of the CMB The CMB Vector Spot