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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 universe.

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.

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 [3]. 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 [4], 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 [1].

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 measurements.

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 [2] 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 [7]. 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.

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 [8]. 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 [5], 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.

[1] Alexey Golovnev, Vitaly Vanchurin, “Cosmological perturbations from vector inflation,” Phys.Rev.D79:103524,2009.

[2] Andrei Linde, Vitaly Vanchurin, Sergei Winitzki, “Stationary Measure in the Multiverse,” JCAP 0901:031,2009.

[3] Alexey Golovnev, Viatcheslav Mukhanov, Vitaly Vanchurin, “Vector Inflation,” JCAP 0806:009,2008.

[4] Alexey Golovnev, Viatcheslav Mukhanov, Vitaly Vanchurin, “Gravitational waves in vector inflation,” JCAP 0811:018,2008.

[5] Vitaly Vanchurin, “Cosmic string loops: Large and small, but not tiny,” Phys.Rev.D77:063532,2008.

[6] Vitaly Vanchurin, “Numerical search for fundamental theory,” Phys.Rev.D77:043503,2008.

[7] Vitaly Vanchurin, “Geodesic measures of the landscape,” Phys.Rev.D75:023524,2007.

[8] Ken Olum, Vitaly Vanchurin, “Cosmic string loops in the expanding Universe,” Phys.Rev.D75:063521,2007.

[9] Jin Kang, Vitaly Vanchurin, Sergei Winitzki, “Attractor scenarios and superluminal signals in k-essence cosmology,” Phys.Rev.D76:083511,2007.

The theoretical aspects of this project link closely to A1, A3, A6, B3, B10, B11, B14, C4, C6.

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