Friedmann–Robertson–Walker universes with a presently large fraction of the energy density stored in an X-component with wX<-1/3, are considered. We find all the critical points of the system for constant equations of state in that range. We consider further several background quantities that can distinguish the models with different wXvalues. Using a simple toy model with a varying equation of state, we show that even a large variation of wXat small redshifts is very difficult to observe with dL(z) measurements up to z~1. Therefore, it will require accurate measurements in the range 1<z<2 and independent accurate knowledge of Ωm,0(and/or ΩX,0) in order to resolve a variable wXfrom a constant wX.

We derive the conditions under which dark energy models whose Lagrangian densities f are written in terms of the Ricci scalar R are cosmologically viable. We show that the cosmological behavior of f (R) models can be understood by a geometrical approach consisting in studying the m(r) curve on the (r, m) plane, where m ≡ Rf,RR/f,R and r ≡ −Rf,R/f with f,R ≡ df /dR. This allows us to classify the f (R) models into four general classes, depending on the existence of a standard matter epoch and on the final accelerated stage. The existence of a viable matter dominated epoch prior to a late-time acceleration requires that the variable m satisfies the conditions m(r) ≈ +0 and dm/dr > −1 at r ≈ −1. For the existence of a viable late-time acceleration we require instead either (i) m = −r − 1 , ( √ 3 − 1)/2 < m ≤ 1 and dm/dr < −1 or (ii) 0 ≤ m ≤ 1 at r = −2. These conditions identify two regions in the (r, m) space, one for the matter era and the other for the acceleration. Only models with a m(r) curve that connects these regions and satisfy the requirements above lead to an acceptable cosmology. The models of the type f (R) = αR −n and f = R + αR −n do not satisfy these conditions for any n > 0 and n < −1 and are thus cosmologically unacceptable. Similar conclusions can be reached for many other examples discussed in the text. In most cases the standard matter era is replaced by a cosmic expansion with scale factor a ∝ t 1/2 . We also find that f (R) models can have a strongly phantom attractor but in this case there is no acceptable matter era.

The present acceleration of the Universe strongly indicated by recent observational data can be modeled in the scope of a scalar-tensor theory of gravity. We show that it is possible to determine the structure of this theory (the scalar field potential and the functional form of the scalar-gravity coupling) along with the present density of dustlike matter from the following two observable cosmological functions: the luminosity distance and the linear density perturbation in the dustlike matter component as functions of redshift. Explicit results are presented in the first order in the small inverse Brans-Dicke parameter ω −1 .PACS numbers: 98.80. Cq, 04.50.+h Recent observational data on type Ia supernovae explosions at high redshifts z ≡ a(t0) a(t) −1 ∼ 1 obtained independently by two groups [1,2], as well as numerous previous arguments (see the recent reviews [3,4]), strongly support the existence of a new kind of matter in the Universe whose energy density not only is positive but also dominates the energy densities of all previously known forms of matter [here a(t) is the scale factor of the FriedmannRobertson-Walker (FRW) isotropic cosmological model, and t 0 is the present time]. This form of matter has a strongly negative pressure and remains unclustered at all scales where gravitational clustering of baryons and (nonbaryonic) cold dark matter (CDM) is seen. Its gravity results in the present acceleration of the expansion of the Universe:ä(t 0 ) > 0. In a first approximation, this kind of matter may be described by a constant Λ-term in the gravity equations as first introduced by Einstein. However, a Λ-term could also be slowly varying with time. If so, this will be soon determined from observational data. In particular, if we use the simplest model of a variable Λ-term (also called quintessence in [5]) borrowed from the inflationary scenario of the early Universe, namely an effective scalar field Φ with some self-interaction potential U (Φ) minimally coupled to gravity, then the functional form of U (Φ) can be determined from observational cosmological functions: either from the luminosity distance D L (z) [6,7], or from the linear density perturbation in the dustlike component of matter in the Universe δ m (z) for a fixed comoving smoothing radius [6]. However, this model cannot account for any future observational data, in particular, for any functional form of D L (z). This happens because a variable Λ-term in this model should satisfy the weak-energy condition ε Λ +p Λ ≥ 0. In terms of the observable quantity H(z) ≡ȧ(t)/a(t) describing the evolution of the expanding Universe at recent epochs, the following inequality should be satisfied [4]Here, H 0 = H(z = 0) is the Hubble constant, Ω m,0 is the present energy density of the dustlike (CDM+baryons) matter component in terms of the critical density ε crit = 3H 2 0 /8πG (c =h = 1, and an index 0 stands for the present value of the corresponding quantity). Note that the inequality (1) saturates when the Λ-term is exactly constant. It is not clear fr...

Transition to the semiclassical behaviour and the decoherence process for inhomogeneous perturbations generated from the vacuum state during an inflationary stage in the early Universe are considered both in the Heisenberg and the Schrödinger representations to show explicitly that both approaches lead to the same prediction: the equivalence of these quantum perturbations to classical perturbations having stochastic Gaussian amplitudes and belonging to the quasi-isotropic mode. This equivalence and the decoherence are achieved once the exponentially small (in terms of the squeezing parameter r k ) decaying mode is neglected. In the quasi-classical limit |r k | → ∞, the perturbation mode functions can be made real by a time-independent phase rotation, this is shown to be equivalent to a fixed relation between squeezing angle and phase for all modes in the squeezed-state formalism. Though the present state of the gravitational wave background is not a squeezed quantum state in the rigid sense and the squeezing parameters loose their direct meaning due to interaction with the environment and other processes, the standard predictions for the rms values of the perturbations generated during inflation are not affected by these mechanisms (at least, for scales of interest in cosmological applications). This stochastic background still occupies a small part of phase space.

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We consider scalar-tensor theories of gravity in an accelerating universe. The equations for the background evolution and the perturbations are given in full generality for any parametrization of the Lagrangian, and we stress that apparent singularities are sometimes artifacts of a pathological choice of variables. Adopting a phenomenological viewpoint, i.e., from the observations back to the theory, we show that the knowledge of the luminosity distance as a function of redshift up to z ∼ (1 − 2), which is expected in the near future, severely constrains the viable subclasses of scalar-tensor theories. This is due to the requirement of positive energy for both the graviton and the scalar partner. Assuming a particular form for the Hubble diagram, consistent with present experimental data, we reconstruct the microscopic Lagrangian for various scalar-tensor models, and find that the most natural ones are obtained if the universe is (marginally) closed.

According to the inflationary scenario for the very early Universe, all inhomogeneities in the Universe are of genuine quantum origin. On the other hand, looking at these inhomogeneities and measuring them, clearly no specific quantum mechanical properties are observed. We show how the transition from their inherent quantum gravitational nature to classical behavior comes about -a transition whereby none of the successful quantitative predictions of the inflationary scenario for the present-day universe is changed. This is made possible by two properties. First, the quantum state for the spacetime metric perturbations produced by quantum gravitational effects in the early Universe becomes very special (highly squeezed) as a result of the expansion of the Universe (as long as the wavelength of the perturbations exceeds the Hubble radius). Second, decoherence through the environment distinguishes the field amplitude basis as being the pointer basis. This renders the perturbations presently indistinguishable from stochastic classical inhomogeneities. 455 Int. J. Mod. Phys. D 1998.07:455-462. Downloaded from www.worldscientific.com by NANYANG TECHNOLOGICAL UNIVERSITY on 08/21/15. For personal use only.

Dynamics of long-wave isocurvature perturbations during an inationary stage in multiple (multi-component) inationary models is calculated analytically for the case where scalar elds producing this stage interact between themselves through gravity only. This enables to determine correct amplitudes of such perturbations produced by vacuum quantum uctuations of the scalar elds during the multiple inationary stage. Exact matching to a post-inationary evolution that gives the amplitude of isocurvature perturbations in the cold dark matter model with radiation is performed in the case where a massive inaton eld remains uncoupled from usual matter up to the present time. For this model, isocurvature perturbations are smaller than adiabatic ones in the region of the break in the perturbation spectrum which arises due to a transition between the two phases of ination, but they may b e m uch bigger and have a maximum at much shorter scales. The case of an inaton with a quartic coupling which remains uncoupled after ination is considered, too. 0