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
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
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
Fluctuations + dynamics
Fluctuations + dynamics
Fluctuations + dynamics
Fluctuations + dynamics
Fluctuations + dynamics
Light fields can be caught ‘’in the middle’’ by the end of inflation
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
Interacting spectator s during inflation
The setting
Initial condition
s retains a large EV where it is oblivious of interactions
if interactions become important at x
if s 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)
A necessary (more) realistic probability density
Nc = O(10)
Nc = O(102)
Free field dynamics: Interacting field dynamics:
Numerical solution for the interacting dynamics
Nend = 45
Free field dynamics: Interacting field dynamics:
Numerical solution for the interacting dynamics
A necessary (more) realistic probability density
Nend = 50
Free field dynamics: Interacting field dynamics:
Numerical solution for the interacting dynamics
A necessary (more) realistic probability density
Nend = 51
Free field dynamics: Interacting field dynamics:
Numerical solution for the interacting dynamics
A necessary (more) realistic probability density
Nend = 52
Free field dynamics: Interacting field dynamics:
Numerical solution for the interacting dynamics
A necessary (more) realistic probability density
Nend = 53
Free field dynamics: Interacting field dynamics:
Numerical solution for the interacting dynamics
A necessary (more) realistic probability density
Nend = 54
Free field dynamics: Interacting field dynamics:
Numerical solution for the interacting dynamics
A necessary (more) realistic probability density
Nend = 55
Free field dynamics: Interacting field dynamics:
Numerical solution for the interacting dynamics
A necessary (more) realistic probability density
Nend = 56
Free field dynamics: Interacting field dynamics:
Numerical solution for the interacting dynamics
A necessary (more) realistic probability density
Can a Local direction-dependent contribution to the CMB be generated?
Vector fields strongly constrained in the CMB
g* 0.02Kim & Komatsu, 2013
Local breaking of statistical isotropy
LSS
Planck, 2015
Local breaking of statistical isotropy
Slow-roll phase
Slow-roll phase
Slow-roll phase
Scale invariance for a = -4
Decay phase
Decay phase
Decay phase
End of scaling
A simple example: vector curvaton with varying kinetic functionDimopoulos et al. ‘10
A motivated choice:
Evolution of the vector field
Energy densityModulated kinetic function
Local breaking of statistical isotropy
Center of the s distribution
Left end of s distribution
Right end of s distribution
Dimopoulos et al. ’09, ‘10Vector curvaton contribution to the CMB
Probability density for the curvature perturbation
Probability density for rA,end
Probability density for (z or (z x)/ zsr)
Interacting dynamics of s
Kinetic function f(s)
Initial Probability density for s(Gaussian, fixed by fluctuations)
Local breaking of statistical isotropy
Local breaking of statistical isotropy
Probability density for the curvature perturbation
Probability density for rA,end
Probability density for (z or (z x)/ zsr)
Interacting dynamics of s
Kinetic function f(s)
Initial Probability density for s(Gaussian, fixed by fluctuations)
Local breaking of statistical isotropy
Probability density for the curvature perturbation
Probability density for rA,end
Probability density for (z or (z x)/ zsr)
Interacting dynamics of s
Kinetic function f(s)
Initial Probability density for s(Gaussian, fixed by fluctuations)
Local breaking of statistical isotropy
Probability density for the curvature perturbation
Probability density for rA,end
Probability density for (z or (z x)/ zsr)
Interacting dynamics of s
Kinetic function f(s)
Initial Probability density for s(Gaussian, fixed by fluctuations)
Local breaking of statistical isotropy
Probability density for the curvature perturbation
Probability density for rA,end
Probability density for (z or (z x)/ zsr)
Interacting dynamics of s
Kinetic function f(s)
Initial Probability density for s(Gaussian, fixed by fluctuations)
Local breaking of statistical isotropy
Probability density for the curvature perturbation
Probability density for rA,end
Probability density for (z or (z x)/ zsr)
Interacting dynamics of s
Kinetic function f(s)
Initial Probability density for s(Gaussian, fixed by fluctuations)
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
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 z as long as
they do it in a relatively small patch of the CMB
The CMB Vector Spot
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