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...

We consider the possibility to produce a bouncing universe in the framework of scalar-tensor gravity models in which the scalar field potential may be negative, and even unbounded from below. We find a set of viable solutions with nonzero measure in the space of initial conditions passing a bounce, even in the presence of a radiation component, and approaching a constant gravitational coupling afterwards. Hence we have a model with a minimal modification of gravity in order to produce a bounce in the early universe with gravity tending dynamically to general relativity (GR) after the bounce.

Final version to appear in Nucl. Phys. B. Some references added correctlyInternational audienceThe relation between the Wilson-Polchinski and the Litim optimized ERGEs in the local potential approximation is studied with high accuracy using two different analytical approaches based on a field expansion: a recently proposed genuine analytical approximation scheme to two-point boundary value problems of ordinary differential equations, and a new one based on approximating the solution by generalized hypergeometric functions. A comparison with the numerical results obtained with the shooting method is made. A similar accuracy is reached in each case. Both two methods appear to be more efficient than the usual field expansions frequently used in the current studies of ERGEs (in particular for the Wilson-Polchinski case in the study of which they fail)

We present a new efficient analytical approximation scheme to two-point boundary value problems of ordinary differential equations (ODEs) adapted to the study of the derivative expansion of the exact renormalization group equations. It is based on a compactification of the complex plane of the independent variable using a mapping of an angular sector onto a unit disc. We explicitly treat, for the scalar field, the local potential approximations of the Wegner-Houghton equation in the dimension d = 3 and of the Wilson-Polchinski equation for some values of d ∈ ]2, 3]. We then consider, for d = 3, the coupled ODEs obtained by Morris at the second order of the derivative expansion. In both cases the fixed points and the eigenvalues attached to them are estimated. Comparisons of the results obtained are made with the shooting method and with the other analytical methods available. The best accuracy is reached with our new method which presents also the advantage of being very fast. Thus, it is well adapted to the study of more complicated systems of equations.Key words: Exact renormalisation group, Derivative expansion, Critical exponents, Two-point boundary value problem PACS: 02.30. Hq, 02.30.Mv, 02.60.Lj, 05.10.Cc, 11.10.Gh, 64.60.Fr In a previous article [1] we presented two analytical approaches for studying the derivative expansion of the exact renormalization group equation (ERGE,

A new (algebraic) approximation scheme to find global solutions of two point boundary value problems of ordinary differential equations (ODE's) is presented. The method is applicable for both linear and nonlinear (coupled) ODE's whose solutions are analytic near one of the boundary points. It is based on replacing the original ODE's by a sequence of auxiliary first order polynomial ODE's with constant coefficients. The coefficients in the auxiliary ODE's are uniquely determined from the local behaviour of the solution in the neighbourhood of one of the boundary points. To obtain the parameters of the global (connecting) solutions analytic at one of the boundary points, reduces to find the appropriate zeros of algebraic equations. The power of the method is illustrated by computing the approximate values of the "connecting parameters" for a number of nonlinear ODE's arising in various problems in field theory. We treat in particular the static and rotationally symmetric global vortex, the skyrmion, the Nielsen-Olesen vortex, as well as the 't Hooft-Polyakov magnetic monopole. The total energy of the skyrmion and of the monopole is also computed by the new method. We also consider some ODE's coming from the exact renormalization group. The ground state energy level of the anharmonic oscillator is also computed for arbitrary coupling strengths with good precision.

We assume that a self-gravitating thin string can be locally described by what we shall call a smoothed cone. If we impose a specific constraint on the model of the string, then its central line obeys the Nambu-Goto equations. If no constraint is added, then the worldsheet of the central line is a totally geodesic surface.Comment: 20 pages, latex, 1 figure, final versio

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We derive the effective action for a domain wall with small thickness in curved spacetime and show that, apart from the Nambu term, it includes a contribution proportional to the induced curvature. We then use this action to study the dynamics of a spherical thick bubble of false vacuum (de Sitter) surrounded by an infinite region of true vacuum (Schwarzschild).