DARK ENERGY AND NEUTRINOS

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DARK ENERGY AND NEUTRINOS
STEEN HANNESTAD UNIVERSITY OF AARHUS MPI, 8
AUGUST 2007
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THIS IS REALLY TWO SEPARATE TALKS IN ONE
NEUTRINO DARK ENERGY REVISITING THE STABILITY
ISSUE Ole Eggers Bjælde, Anthony Brookfield,
Carsten van de Bruck, STH, David F. Mota, Lily
Schrempp, Domenico Tocchini-Valentini,
arXiv0705.2018
THE MATRIX RELOADED DARK ENERGY AND THE SEESAW
MECHANISM Kari Enqvist, STH, Martin S. Sloth,
hep-ph/0702236 (PRL)
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NEUTRINO DARK ENERGY REVISITING THE STABILITY
ISSUE
Dark energy is associated with a very low
energy scale
Such a low energy scale is extremely hard to
realise in realistic particle physics models of
dark energy
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Possible solutions are
Modified gravity DGP, f(R), etc.
A slowly rolling scalar field - Quintessence
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Problems in quintessence
Why a new scalar field with characteristic energy
scale 10-3 eV?
In order to have w -1 the scalar field mass
must be extremely small (i.e. the potential is
extremely flat)
How can such a small mass be radiatively stable?
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Coupling neutrinos to dark energy
The neutrino mass scale is suspiciously close to
the required quintessence energy scale
There are models on the market in which
neutrino masses are generated by the interaction
with a new scalar field (Majoron type
models) Normally the neutrino mass comes from
the breaking of a U(1) symmetry at some high
energy scale However, what if the breaking scale
is put by hand to be very low?
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We assume the existence of a new scalar field
interacting with neutrinos The scalar field is
not at its global minimum, but rolling in a
potential In this case the neutrino mass becomes
a dynamical quantity, calculable from the VEV of
the scalar field -gt Mass varying neutrinos
(Fardon, Nelson, Weiner 2003)
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The Lagrangian of the combined system is then
given by
where the neutrino mass is now given from the
scalar field VEV
Why is this good? The effective scalar field
potential now has a contribution from the
neutrino energy density
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If chosen properly the additional neutrino
contribution can provide a minimum of the
effective scalar field potential This in turn
means that it is possible to have
while still maintaining the slow-roll condition
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Only the non-relativistic regime is important for
understanding the scenario We will assume that
the field evolves adiabatically so that at any
given point
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Introduction

• Quintessence
• Requires an extremely small scalar mass
• Technically unnatural unless protected by some
  symmetry
• Requires a new light scale ?0.001eV ltlt 1TeV where
• the symmetry is broken

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• Loop corrections will in general give large
  contributions
• to scalar masses ? ?2
• Symmetry needed!
• SUSY protects scalar masses, but is broken at a
  TeV
• SUSY masses naturally of order TeV
• Shift symmetry f -gt f const. forbids a mass
  term for f
• A symmetry breaking term ?4f(f/M) introduces a
  technically
• natural small mass
• Successful quintessence requires a new light
• mass scale ? 0.001eV of explicit sym.
  breaking

Example pNBG quintessence Frieman et al. 95
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• Example Neutrino mass seesaw
• The neutrino mass matrix
• Has a small neutrino mass eigenvalue

Different approach Seesaw
Is it possible to get a small quintessence mass
from a scalar mass seesaw?
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• Problems with a scalar mass seesaw
• The neutrino seesaw mass m2/M is never small
  enough if
• m gt TeV !
• No chiral symmetries to protect zeros in
  diagonal
• However - for 8x8 matrices we do have matrices
  with
• Mass eigenvalues m5/M4
• Only Ms in the diagonal
• Consider a potential of the type
• where mij is 0, m or M

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A CONCRETE EXAMPLE
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• The Matrix can be diagonalized, yielding
• where the ais are all of order one.
• Negative eigenvalues ? tachyonic instabilities
• (for Fermions these can be cured by chiral
  rotation)
• Adding Yukawas in tachyonic directions will in
  general also lift
• the mass of the light direction
• we need to be more careful!

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• The light mass eigenstate ?8 can be written in
  terms of the
• original interaction eigenstates
• It turns out that
• The light direction ?8 has a very suppressed
  contribution of
• ?2
• We can lift the tachyonic directions by adding
  Yukawas
• in the ?2 direction - without harming our
  light mass eigenstate

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• Since the m s break all discrete symmetries, we
  may worry if we can
• protect the zeros in the matrix from obtaining
  values of order m
• Brane configuration
• Suppose each of the scalar fields are
  quasi-localized on each their brane
• with wave functions in the extra dimensions
  proportional to
• If the branes are on top of each other, one has
  bilinear
• mixing terms of the type
• However, if the branes are geographically
  separated in the extra dimensions,
• the overlap of the wavefunctions are
  exponentially suppressed

The Origin of the Matrix
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• Now, assume that all the elements (m2)ij are
  given by M2,
• The suppression of the bilinear interaction
  terms is given
• by M2exp(-Mr) with M ? MGUT
• The branes can be taken to lie on top of each
  other in the
• directions where bilinear elements in the mass
  matrix of
• scale M are induced
• While the branes are separated by r ? 60/M in
  the directions
• where bilinear elements at the soft scale m ? v
  are induced.
• In the directions where there are zeros in the
  off-diagonal, the
• branes are separated by a distance r gtgt 262/M.

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• Assume that there are three brane fixed points,
  A, B and C,
• in each dimension
• A and B are separated from each other by r ?
  60/M
• C separated from A and B at a distance r gtgt
  262/M,
• This leads to the following brane configuration
  for eight branes
• in six extra dimensions