The role of gauge fields
in inflation
Ricardo Zambujal Ferreira
ICC, U. Barcelona
In collaboration with:
J. Ganc, R. Jain, J. Noreña, A. Notari, M. Sloth
[arXiv: 1305.7151, 1403.5516, 1409.5799, 1411.5362,
1512.06116, 17XX.S00N]
Outline
• Inflation
• What is it?
• Generic properties
• Gauge fields in inflation
• Motivation
• Inflationary magnetogenesis & the axial
coupling
• Conclusions
Distance > speed of light x age of the
Universe
T=2.7 K
T=2.7 K
Θ>1°
Distance > speed of light x age of the
Universe
T=2.7 K
How do they know
they should have the
same properties?
Θ>1°
??
T=2.7 K
Inflation
• Inflation provides a common origin for our observable universe
• Space-time itself expanded exponentially and “faster than light"
Inflation: how does it work?
Inflaton
exponential expansion
Quantum world
Fluctuations (scalar ζ, vector
v and tensor h) in the spacetime
After inflation
Anisotropies in matter and
radiation
Observables
• What do we observe:
– 2-point function of adiabatic scalar modes:
amplitude and spectral dependence
– In all other observables we only have
constraints:
• 3,4-point function (non-Gaussianities)
• Tensor 2-point function
• Isocurvature modes
[Planck 15’]
Gauge fields in inflation
Motivation
• Indirect observation of large
scale magnetic fields on very
large scales
B > 10
16
G ( > M pc)
• Generation of seeds for the
intragalactic magnetic fields
• On generic grounds gauge
fields are expected to
couple to the inflaton
Neronov and Vovk ‘10
Gauge fields in inflation
– Free gauge fields are conformally coupled ➔ diluted
with the universe expansion ➔ no signatures
1
µ⌫
Fµ⌫ F
4
• Gauge fields interact. Conformality can be (strongly) broken:
int
Lgauge fields
= f ( )Fµ⌫ F
µ⌫
+
f
Fµ⌫ F̃
µ⌫
f ( )Fµ⌫ F
✓
A00k + k 2
⇠
⌘2
◆
µ⌫
Ak = 0
• Large magnetic fields but:
– Strong coupling regimes, back
reaction and non-gaussianity
constraints
[Turner, Widrow ’88; Ratra ’92; Demozzi et al. 09’;
Martin et al. 07’; Bartolo et al. 12’]
– Some new ideas: Stiff reheating, low-scale
inflation, kinetic mixing f
Fµ⌫ F̃ µ⌫
[Ferreira, Jain, Sloth 13’, 14’; Ferreira & Ganc 14’]
• Strong particle production at
the Hubble horizon [Anber and Sorbo 06’]
• Gauge fields can (inverse)
decay into scalars and gravitons:
• Large loop corrections, NonGaussianities, Tensor modes;
[Barnaby and Peloso 11’; Barnaby et al. 12', Shiraishi et
al. 13', Cook , Sorbo 13', Mukohyama et al. 14]
• Coupling to gravity is universal:
=> strong observational (and
perturbative) constraints
[Ferreira, Sloth 14’; Ferreira, Ganc, Noreña, Sloth 14’]
Conclusions
• Inflation is the ultimate lab and the largest energy scale we
can probably have access to;
• We still don’t know much about inflation apart from being
driven by a scalar field.
• Identifying new fossils and/or observables (magnetic fields,
spectral distortions) would tell us more about the early
universe and high energy physics.
• Gauge fields can play an interesting role and leave some
observable signatures from their couplings with scalar fields.