Liberating vector fields from their
CMB anisotropy constraint
Juan Carlos Bueno Sánchez
Universidad del Valle (Santiago de Cali), Universidad Antonio Nariño (Bogotá),
Universidad Industrial de Santander (Bucaramanga)
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
A framework to understand CMB anomalies
The question
How much you need to twist the inflationary paradigm to obtain CMB anomalies?
(i.e. breaking homogeneity & isotropy of the CMB)
The ingredient
Apart from the inflaton, other scalar field(s) contributes to
the perturbation spectrum imprinted on the CMB
(Isocurvature perturbation)
A framework to understand CMB anomalies
The question
How much you need to twist the inflationary paradigm to obtain CMB anomalies?
(i.e. breaking homogeneity & isotropy of the CMB)
The ingredient
Apart from the inflaton, other scalar field(s) contributes to
the perturbation spectrum imprinted on the CMB
(Isocurvature perturbation)
The set-up
Inflaton responsible for most of the CMB perturbations (homogeneous & isotropic)
An initially excited isocurvature field does not fully decay due
to its interactions during inflation
The outcome
Inhomogeneous distribution of the iso-field at the end of inflation
Breaking of statistical homogeneity of the CMB
Avenue towards CMB anomalies
Fluctuations + dynamics
Fluctuations + dynamics
Fluctuations + dynamics
Fluctuations + dynamics
Fluctuations + dynamics
Light fields can be caught ‘’in the middle’’ by the end of inflation
The link to CMB anomalies
Snapshot at the end of inflation
LSS
Field interactions become important
before the end of inflation
Field decay
Field oblivious to interactions
Slow-roll phase
The setting
Interacting spectator s during inflation
Initial condition
Dynamical regimes
(JCBS & Enqvist ’13)
c integrated out
c production
Emergence of a patchy structure
s as a free field
(slow-roll phase)
Trapping mechanism for s
(Kofman et al. ‘04)
(decay phase)
(JCBS ’14)
s retains a large EV where it is oblivious of interactions
if interactions become important at x
if s evoles as a free field
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
Free field dynamics:
Interacting field dynamics:
Numerical solution for the interacting dynamics
Nc = O(10)
Nc = O(102)
A necessary (more) realistic probability density
Free field dynamics:
Interacting field dynamics:
Numerical solution for the interacting dynamics
Nend = 45
A necessary (more) realistic probability density
Free field dynamics:
Interacting field dynamics:
Numerical solution for the interacting dynamics
Nend = 50
A necessary (more) realistic probability density
Free field dynamics:
Interacting field dynamics:
Numerical solution for the interacting dynamics
Nend = 51
A necessary (more) realistic probability density
Free field dynamics:
Interacting field dynamics:
Numerical solution for the interacting dynamics
Nend = 52
A necessary (more) realistic probability density
Free field dynamics:
Interacting field dynamics:
Numerical solution for the interacting dynamics
Nend = 53
A necessary (more) realistic probability density
Free field dynamics:
Interacting field dynamics:
Numerical solution for the interacting dynamics
Nend = 54
A necessary (more) realistic probability density
Free field dynamics:
Interacting field dynamics:
Numerical solution for the interacting dynamics
Nend = 55
A necessary (more) realistic probability density
Free field dynamics:
Interacting field dynamics:
Numerical solution for the interacting dynamics
Nend = 56
Local breaking of statistical isotropy
Vector fields strongly constrained in the CMB
g*
Kim & Komatsu, 2013
0.02 Planck, 2015
LSS
Can a Local direction-dependent contribution to the CMB be generated?
Local breaking of statistical isotropy
A simple example: vector curvaton with varying kinetic function Dimopoulos et al. ‘10
Slow-roll phase
Scale invariance for a = -4
Decay phase
End of scaling
Slow-roll phase
Decay phase
Slow-roll phase
A motivated choice:
Decay phase
Local breaking of statistical isotropy
Evolution of the vector field
Modulated kinetic function
Energy density
Right end of
s distribution
Center of the
s distribution
Left end of
s distribution
Vector curvaton contribution to the CMB Dimopoulos et al. ’09, ‘10
Local breaking of statistical isotropy
Probability density for the curvature perturbation
Initial Probability density for s
(Gaussian, fixed by fluctuations)
Probability density for rA,end
Interacting dynamics of s
Kinetic function f(s)
Probability density for z (or z(x)/ zsr)
Local breaking of statistical isotropy
Probability density for the curvature perturbation
Initial Probability density for s
(Gaussian, fixed by fluctuations)
Probability density for rA,end
Interacting dynamics of s
Kinetic function f(s)
Probability density for z (or z(x)/ zsr)
Local breaking of statistical isotropy
Probability density for the curvature perturbation
Initial Probability density for s
(Gaussian, fixed by fluctuations)
Probability density for rA,end
Interacting dynamics of s
Kinetic function f(s)
Probability density for z (or z(x)/ zsr)
Local breaking of statistical isotropy
Probability density for the curvature perturbation
Initial Probability density for s
(Gaussian, fixed by fluctuations)
Probability density for rA,end
Interacting dynamics of s
Kinetic function f(s)
Probability density for z (or z(x)/ zsr)
Local breaking of statistical isotropy
Probability density for the curvature perturbation
Initial Probability density for s
(Gaussian, fixed by fluctuations)
Probability density for rA,end
Interacting dynamics of s
Kinetic function f(s)
Probability density for z (or z(x)/ zsr)
Local breaking of statistical isotropy
Probability density for the curvature perturbation
Initial Probability density for s
(Gaussian, fixed by fluctuations)
Probability density for rA,end
Interacting dynamics of s
Kinetic function f(s)
Probability density for z (or z(x)/ zsr)
Local breaking of statistical isotropy
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
Conclusions
Wishful thinking: The production of localized perturbations may provide a
framework to understand some of the CMB anomalies (if they turn out to exist)
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 , …)
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
Vector fields source GW: Looking for correlated spatial variations of r might
reveal the presence of a vector field hidden in the CMB