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...ll parameters in the regime µ � m Pl. 3.5. Hybrid inflation Let us now turn to hybrid inflation. This case is slightly different since hybrid inflation is in fact a two-field model with the potential =-=[75, 76, 16]-=- V (φ, ψ) = 1 2 m2φ 2 + λ′ ( 2 2 ψ − ∆ 4 ) 2 λ + 2 φ2ψ 2 , (108) where φ is the inflaton, ψ the waterfall field and λ ′ and λ are two coupling constants. Inflation proceeds along the valley given by ψ...

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... ≪ 1, (1) where V ′ and V ′′ are the first and second derivatives of V with respect to the inflaton, and Mpl is the Planck scale ≃ 2.4× 1018 GeV. Suppose that there is vacuum energy v40, and then one can see that even gravitational corrections to the potential V (σ) = v40 ( 1 + c ( σ Mpl ) + c′ ( σ Mpl )2 + · · · ) (2) are not allowed by the slow-roll conditions if the coefficients c, c′ are of the order of unity. Thus, the slow-roll inflation is sensitive even to the physics at the Planck scale, and can be a good probe in uncovering the fundamental laws of physics. The hybrid inflation model [2] is realized by quite simple models of D = 4 N = 1 supergravity (SUGRA) [3, 4, 5, 6]. Thus, the inflaton potential is protected from radiative corrections. However, D = 4 N = 1 SUGRA is not enough in controlling the gravitational corrections. In SUGRA as an effective-field-theory approach, no assumption except symmetries is imposed on ultraviolet physics. Then, higher order terms are expected to be in Kahler potential with O(1) coefficients: K = X†X + k (X†X)2 M2pl + · · · , (3) where X is a chiral multiplet containing the inflaton σ. The second term contributes to the slow-roll parameter η, ...

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... a review about gauged supergravity theories of various dimensions that have been studied extensively since then, see [4]. 3 For a general review and further references on inflationary cosmology, see =-=[5]-=-. 4 V ′ ≡ ∂V/∂φ 2Figure 1: Examples of de Sitter extrema in supergravity theories: (a) Stable minima with a flat direction. The potential belongs to the 4D, N = 2 supergravity coupled to 3 vector mul...

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...en, even in simple potentials with fairly well-understood physics they admit exceptions that allow steady-state eternal inflation. What if we allow more general physics? As noted above (and see e.g., =-=[89]-=-) even if most past-directed geodesics meet singularities, that may still square perfectly with past-eternal inflation, since most geodesics in future-eternal inflation do not keep inflating indefinit...

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...onary trajectories fall from a ridge in field space. Such a process is a crucial element of the hybrid inflationary scenario, introduced by Linde, in which inflation ends through a sudden instability =-=[1, 2, 3]-=-. Quantum fluctuations lead to slight differences in field values at the top of the ridge, causing different regions of the universe to follow one of a narrow bundle of trajectories. Trajectories near...

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...e of gauge symmetries may be related to isometries of extra space1 [8–10]. (Maximally) symmetric metrics of extra space as a starting point are among the most popular in the literature, see e.g. [9,11,12]. This assumption makes it possible to obtain clear and valuable results. In particular, specific symmetries of extra space manifest as gauge symmetries of effective low-energy physics. At the same time we must take into account the quantum origin of space itself due to fluctuations in the space-time foam. There is no reason to assume that the geometry or/and topology of extra space is simple [13, 14]. Moreover it seems obvious that a measure M of all symmetrical spaces equals zero so that the probability of their nucleation P = 0. Hence some period of extra space symmetrization has to exist [8, 15–18]. ∗kirillov-aa@yandex.ru †korotkevich aa@mail.ru ‡sergeirubin@list.ru 1Hereinafter we consider compact extra spaces 1 In the present paper we investigate the entropic mechanism of space symmetrization after its nucleation. It is shown that the stabilization of the extra space and its symmetrization are proceeding simultaneously. This process is accompanied by a decrease in entropy for the ext...

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...m, isotropy, flatness and dimensionality of the present Universe, ... Much work has been done in order to solve these problems, in particular in the framework of inflationary models (see e.g. [1] and =-=[2]-=- and the references therein), but these models have in general to be fine tuned in order to give expected results. Some years ago appeared string cosmology [3]. We do not consider here string theory a...

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...g after intermediate-scale inflation In many models of inflation the energy scale of inflation is set by the intermediate scale ρ 1/4 inf = Minf ≃ 10 10 GeV [39]. Such models include hybrid inflation =-=[40, 41, 42]-=- in which case the inflaton mass and Hubble-scale at the end of inflation is of order TeV. Tachyonic instability leads to the end of inflation when the inflaton reaches a critical value and the vacuum...