Inflation and the origin of Dark Energy
Principal Investigator: V. Mukhanov (LMU Munich)
The origin of Dark Energy and Dark Matter
might be related to the problem of initial conditions in the very early
universe. According to inflationary model the universe must be eternal and
it has a complicated structure on very large scales. In the eternal
self-reproducing universe constants of
Nature can be variables related to some slowly varying
fields. In this case they take different values within different spatial
regions. As a result cosmological constant and/or some scalar condensate
could survive after inflation and serve as Dark Energy component. Another
scalar field can play the role of Dark Matter.
The first purpose of the project is to understand how could inflation
naturally lead to the observable matter composition of the universe. One of
the basic problems here to be resolved is the determination of measure of
initial conditions in eternal universe with variable
constants of Nature which could lead to a particular
matter content within an observable patch of the universe. This problem is
closely related to the gauge-invariant description of the
eternal self-reproducing universe. After such a measure is found we will
need to investigate the preheating and reheating in the context of the
eternal universe and determine the typical amount of the produced Dark
Energy and Dark Matter after inflation. In particular, it is interesting to
study the models where a second scalar field (curvaton) can play an essential
role for the structure formation. The main aim of the project is to resolve
the cosmic coincidence problem and thus to understand why Dark Energy must
dominate today. Besides of that we have to explain why Dark Matter
constitutes a substantial fraction of the total energy density of the present
The second purpose of the project is to understand how standard robust predictions of simple inflation could
be changed if the anisotropy of the expansion can play a significant role during earlier and later time
universe acceleration. Such anisotropy can arise, for example in vector inflation. A second task is to
find out what kind of possible non-Gaussianities can be generated, in particular in curvaton models.
Finally we would like to investigate among others those models of inflation based on particle physics
beyond the Standard Model where large anisotropies and non-Gaussianities can arise, including axion
and DBI inflation in string theory.
A. Anisotropic inflation and Dark Energy
To describe the early time (inflation) or late time (Dark Energy) acceleration one often employs
the use of scalar fields, which were never seen in the high energy experiments. Golovnev, Mukhanov
and Vanchurin proposed a new class models of inflation where the quasi de Sitter expansion is driven
by vector fields . Approximate isotropy of the expansion can be achieved by a triad of mutually
orthogonal vector fields or by a large number of randomly oriented fields. The well-known problem
of slow-roll was resolved by non-minimal coupling of the vector fields to gravity.
From the point of view of the background evolution, the proposed model is very similar to the
standard scalar field models (inflation or quintessence). However, in contrast to the scalar fields, the
expansion with vector fields must not be isotropic, which could lead to very distinct observational
predictions. In fact, the current observational bounds on isotropy of inflation or Dark Energy are very weak and one can easily allow ≃ 10% of global anisotropy. For example, the vector fields driving
quasi de Sitter expansion with ≃ 100 randomly oriented vector fields can give rise to anisotropy of
the order of 1/
N ≃ 10%.
A somewhat closer look at the proposed scenarios had shown that some large fields models are
unstable due to tachyonic instabilities of gravitational waves , nevertheless the evolution at small
values of the fields is generically stable to tensor perturbations of the metric. The investigation of
the behaviour of scalar perturbations in the vector inflation models was started in .
The Dark Energy can also be due to the vector fields. This opens an interesting possibility to
have anisotropic Dark Energy at present. Such anisotropic Dark Energy has distinctive observational
predictions which can be tested in the future supernova and cosmic microwave background fluctuations
B. Measure of eternal inflation
The existing measure prescriptions differ in their methods of introducing the cutoff and can be
grouped into two classes. One class of measures completely ignores the growth of the volume and
counts only the volume visible to a single randomly chosen world line. Measures of this class are called
the worldline-based measures, in distinction from the class of volume-based measures that attempt
to sample the entire volume in the inflationary spacetime. The different methods of regularising
the infinite volume of an eternally inflating universe often give different results. In the absence of a
mathematically unique cutoff on an infinite set of observers, one evaluates the competing prescriptions
on their own merits. A measure prescription is discarded if it gives pathological results that are clearly
in conflict with observation.
One of the most promising volume-based measure was recently developed for the string theory
motivated landscape models of eternal inflation. The basic idea of the stationary measure is to extract
a gauge dependent factor for the overall probability distribution by adjusting the “clocks” for different
vacua. Vanchurin and collaborators (Linde and Winitzki) showed that the stationary measure leads
to simple and gauge-invariant results  and suffers neither from the “Boltzmann brain” problem nor
from the “youngness” paradox that makes some other measures predict a high CMB temperature
at present. A satisfactory performance of the stationary measure in predicting the results of local
experiments, such as proton decay, was also demonstrated.
In another project Vanchurin had studied the worldline-based class of measures, which generically
depend on the initial conditions . He constructed a fine-grained classification of the worldline-based
measure proposals and showed that all of the measures suffer from the problem of choosing the right
ensemble, which is directly related to the decision problems with imperfect recall in probability theory.
C. Cosmic strings
To study the statistical properties and dynamics of cosmic strings Vanchurin developed an exact
cosmic strings network simulation. He showed that the small perturbations obey a scaling law described
by universal power spectrum . After a long transient regime, characterised by production of tiny
loops at the scale of the initial conditions the true scaling regime takes over. In this final regime the
characteristic length of loops scales linearly with time - in sharp contrast to earlier simulations which
found very small loops at the scales of the gravitational backreaction. The new scenario with large
loops has very important cosmological implications. In particular, the nucleosynthesis bound becomes
Gμ < 10−7 , much tighter than before.
To better understand the production of the loops of various sizes directly from infinite strings,
Vanchurin developed a probabilistic analytical model , which allows one to estimate the spectrum
of loops at arbitrary scale. For an exponential form of the spectrum of wiggles, there are two different
scales corresponding to large (one order below horizon) and small (few orders below horizon) loops.
The small loops are produced by large bursts of similar loops moving with very high velocities in the
same direction and the large loops usually consist of few kinks and few cusps per oscillation cycle.
References in the project
 Alexey Golovnev, Vitaly Vanchurin, “Cosmological perturbations from vector inflation,”
 Andrei Linde, Vitaly Vanchurin, Sergei Winitzki, “Stationary Measure in the Multiverse,” JCAP
 Alexey Golovnev, Viatcheslav Mukhanov, Vitaly Vanchurin, “Vector Inflation,” JCAP
 Alexey Golovnev, Viatcheslav Mukhanov, Vitaly Vanchurin, “Gravitational waves in vector inflation,” JCAP 0811:018,2008.
 Vitaly Vanchurin, “Cosmic string loops: Large and small, but not tiny,”
 Vitaly Vanchurin, “Numerical search for fundamental theory,” Phys.Rev.D77:043503,2008.
 Vitaly Vanchurin, “Geodesic measures of the landscape,” Phys.Rev.D75:023524,2007.
 Ken Olum, Vitaly Vanchurin, “Cosmic string loops in the expanding Universe,”
 Jin Kang, Vitaly Vanchurin, Sergei Winitzki, “Attractor scenarios and superluminal signals in
k-essence cosmology,” Phys.Rev.D76:083511,2007.
Role within the Transregional Collaborative Research Centre
The theoretical aspects of this project link closely to A1, A3, A6, B3, B10, B11, B14, C4, C6.