[en] In the recent years the quantization methods of Loop Quantum Gravity have been successfully applied to the homogeneous and isotropic Friedmann-Robertson-Walker space-times. The resulting theory, called Loop Quantum Cosmology (LQC), resolves the Big Bang singularity by replacing it with the Big Bounce. We argue that the LQC holonomy corrections generate also certain corrections to field theoretical inflationary scenarios. These corrections imply that in the LQC the effective sonic horizon becomes infinite at some point after the bounce and that the scale of the inflationary potential implied by the COBE normalisation increases. The evolution of scalar fields immediately after the Bounce becomes modified in an interesting way. We point out that one can use COBE normalisation to establish an upper bound on the quantum of length of LQG. LQC corrections other than the holonomy one are assumed to be subdominant

[en] In the context of the Loop Quantum Cosmology we have analysed the holonomy correction to the classical evolution of the simplified Bianchi I model in the presence of vector fields. For the Universe dominated by a massive vector field or by a combination of a scalar field and a vector field a smooth transition between Kasner-like and Kasner-unlike solutions for a Bianchi I model has been demonstrated. In this case a lack of initial curvature singularity and a finite maximal energy density appear already at the level of General Relativity, which simulates a classical Big Bounce

[en] We introduce a set of generic conditions for the slow contracting Universe and for a narrowed-down category of models called fast-roll models. We present general conditions for superhorizon freeze-out of scalar and tensor perturbations and show that any fast-roll model satisfies them, as in the case of inflation. We are interested in the “Sourced Bounce” scenario, where perturbations are sourced by a U(1) gauge field coupled to a bouncer scalar field. The requirement of a slightly red tilted scalar spectrum greatly restricts the allowed couplings between the scalar and the gauge field. We show that a viable slightly red scalar spectrum is achievable. However, within the fast-roll approximation the tensor-to-scalar ratio is in general r ≃ 1/9, inconsistent with current observations. We demonstrate the general result with an explicit example we dub "Intermediate contraction". We prove that small modifications in fast-roll that do not alter the Green's functions, do not result in r < 0.06 consistent with the data for more than an e-fold. Hence, a successful “Sourced Bounce” requires a different source or a significant deviation from fast-roll. (paper)

[en] We consider the Brans-Dicke theory motivated by the f(R)=R+αR"n−βR"2"−"n model to obtain a stable minimum of the Einstein frame scalar potential of the Brans-Dicke field. As a result we have obtained an inflationary scalar potential with non-zero value of residual vacuum energy, which may be a source of dark energy. In addition we discuss the probability of quantum tunnelling from the minimum of the potential. Our results can be easily consistent with PLANCK or BICEP2 data for appropriate choices of the value of n and ω

[en] We investigate two approaches to non-minimally coupled gravity theories which present linear inflation as attractor solution: a) the scalar-tensor theory approach, where we look for a scalar-tensor theory that would restore results of linear inflation in the strong coupling limit for a non-minimal coupling to gravity of the form of f (φ) R /2; b) the particle physics approach, where we motivate the form of the Jordan frame potential by loop corrections to the inflaton field. In both cases the Jordan frame potentials are modifications of the induced gravity inflationary scenario, but instead of the Starobinsky attractor they lead to linear inflation in the strong coupling limit.

[en] Reheating after inflation can proceed even if the inflaton couples to Standard Model (SM) particles only gravitationally. However, particle production during the transition between de-Sitter expansion and a decelerating Universe is rather inefficient and the necessity to recover the visible Universe leads to a non-standard cosmological evolution initially dominated by remnants of the inflaton field. We remain agnostic to the specific dynamics of the inflaton field and discuss a generic scenario in which its remnants behave as a perfect fluid with a general barotropic parameter w. Using CMB and BBN constraints we derive the allowed range of inflationary scales. We also show that this scenario results in a characteristic primordial Gravitational Wave (GW) spectrum which gives hope for observation in upcoming runs of LIGO as well as in other planned experiments.

[en] We consider the Starobinsky inflation with a set of higher order corrections parametrised by two real coefficients λ_1 , λ_2. In the Einstein frame we have found a potential with the Starobinsky plateau, steep slope and possibly with an additional minimum, local maximum or a saddle point. We have identified three types of inflationary behaviour that may be generated in this model: i) inflation on the plateau, ii) at the local maximum (topological inflation), iii) at the saddle point. We have found limits on parameters λ_i and initial conditions at the Planck scale which enable successful inflation and disable eternal inflation at the plateau. We have checked that the local minimum away from the GR vacuum is stable and that the field cannot leave it neither via quantum tunnelling nor via thermal corrections

[en] In this paper we investigate the induced inflation with two flat regions: one Starobinsky-like plateau in strong coupling regime and one shorter plateau around the saddle point of the Einstein frame potential. This multi-phase inflationary scenario can be used to solve problems of classical cosmology as well as the problem of initial conditions for inflation. The inflation at the saddle-point plateau is consistent with the data and can have arbitrarily low scale. The results can be useful in the context of the Higgs-Axion relaxation and in a certain limit they are equivalent to the α-attractors.

[en] The article addresses the possibility of obtaining cosmologically relevant effects from the quantum nature of the Hubble horizon. Following the observation made by Bianchi and Rovelli (Phys Rev D 84:027502, 2011) we explore the relationship between the Planck scale discreteness of the Hubble horizon and deformations of the symmetry of rotations. We show that the so-called q-deformations in a natural way lead to a mechanism of condensation in the very early Universe. We argue that this provides a possible resolution of the problem of the initial homogeneity at the onset of inflation. Furthermore, we perform an analysis in terms of entropy of the quantum Hubble horizon and show that the ΛCDM model may arise from a linearly corrected Bekenstein–Hawking entropy (that is, linearly in area of the horizon). Based on this, we show that the current accelerating expansion can be associated with the entropy decrease in the Hubble volume. The results presented open new ways to explore the relation between the Planck scale effects and observationally relevant features of our Universe.

[en] For the anisotropic Universe filled with massless vector field in the General Relativity frame we obtain bouncing solution for one of scale factors. We obtain the Universe with finite maximal energy density, finite value of R,R^μνR_μν,R^μναβR_μναβ and non-zero value of a scale factor for directions transverse to a vector field. Such a bounce can be also obtained for a massive vector field with kinetic initial conditions, which gives isotropic low energy limit. We discuss the existence of a bounce for a massless vector field with additional matter fields, such as cosmological constant or dust. We also discuss bouncing solution for massless vector field domination in n+2-dimensional space-time.