Showing papers on "Friedmann–Lemaître–Robertson–Walker metric published in 2004"

Cosmology in Scalar-Tensor Gravity

Abstract: 1. Scalar-Tensor Gravity.- 1 Introduction.- 2 Brans-Dicke theory.- 3 Brans-Dicke cosmology in the Jordan frame.- 4 The limit to general relativity.- 5 Relation to Kaluza-Klein theory.- 6 Brans-Dicke theory from Lyra's geometry.- 7 Scalar-tensor theories.- 7.1 Effective Lagrangians and Hamiltonians.- 8 Motivations for scalar-tensor theories.- 9 Induced gravity.- 10 Generalized scalar-tensor theories.- 11 Conformal transformation techniques.- 11.1 Conformal transformations.- 11.2 Brans-Dicke theory.- 11.3 Kaluza-Klein cosmology.- 11.4 Scalar-tensor theories.- 11.5 Generalized scalar-tensor theories.- 12 Singularities of the gravitational coupling.- 2. Effective Energy-Momentum Tensors and Conformal Frames.- 1 The issue of the conformal frame.- 1.1 The first viewpoint.- 1.2 The second viewpoint.- 1.3 The third viewpoint.- 1.4 Other viewpoints.- 1.5 Einstein frame or Jordan frame?.- 1.6 Energy conditions in relativistic theories.- 1.7 Singularity theorems and energy conditions.- 2 Effective energy-momentum tensors.- 2.1 Time-dependence of the gravitational coupling.- 2.2 Conservation equations for the various Tab(J) [oo].- 3. Gravitational Waves.- 1 Introduction.- 2 Einstein frame scalar-tensor waves.- 2.1 Gravitational waves in the Einstein frame.- 2.2 Corrections to the geodesic deviation equation.- 3 Gravitational lensing by scalar-tensor gravitational waves.- 3.1 Jordan frame analysis.- 3.2 Einstein frame analysis.- 3.3 Propagation of light through a gravitational wave background.- 4. Exact Solutions of Scalar-Tensor Cosmology.- 1 Introduction.- 2 Exact solutions of Brans-Dicke cosmology.- 2.1 K = 0 FLRW solutions.- 2.1.1 The O'Hanlon and Tupper solution.- 2.1.2 The Brans-Dicke dust solution.- 2.1.3 The Nariai solution.- 2.1.4 Other solutions with cosmological constant.- 2.1.5 Generalizing Nariai's solution.- 2.1.6 Phase space analysis for K = 0 and V(o) = 0.- 2.1.7 Phase plane analysis for K = 0 and V(o) = Ao.- 2.2 K = +-1 solutions and phase space for V = 0.- 2.3 Phase space for any K and V = m2o2/2.- 2.3.1 The Dehnen-Obregon solution.- 2.4 Bianchi models.- 2.4.1 Bianchi V universes.- 3 Exact solutions of scalar-tensor theories.- 5. The Early Universe.- 1 Introduction.- 2 Extended inflation.- 2.1 The original extended inflationary scenario.- 2.2 Alternatives.- 3 Hyperextended inflation.- 4 Real inflation?.- 5 Constraints from primordial nucleosynthesis.- 6. Perturbations.- 1 Introduction.- 2 Scalar perturbations.- 3 Tensor perturbations.- 7. Nonminimal Coupling.- 1 Introduction.- 1.1 Generalized inflation.- 1.2 Motivations for nonminimal coupling.- 1.3 Which value of.- 2 Effective energy-momentum tensors.- 2.1 Approach a la Callan-Coleman-Jackiw.- 2.2 Effective coupling.- 2.3 A mixed approach.- 2.4 Discussion.- 2.5 Energy conditions in FLRW cosmology.- 2.6 Nonminimal coupling and gravitational waves.- 3 Conformal transformations.- 4 Inflation and ? 0: the unperturbed universe.- 4.1 Necessary conditions for generalized inflation.- 4.1.1 Specific potentials.- 4.2 The effective equation of state with nonminimal coupling.- 4.3 Critical values of the scalar field.- 5 The slow-roll regime of generalized inflation.- 5.1 Derivation of the stability conditions.- 5.2 Slow-roll parameters.- 6 Inflation and ? 0: perturbations.- 6.1 Density perturbations.- 6.2 Tensor perturbations.- 7 Conclusion.- 8. The Present Universe.- 1 Present acceleration of the universe and quintessence.- 1.1 Coupled quintessence.- 1.2 Multiple field quintessence.- 1.3 Falsifying quintessence models.- 2 Quintessence with nonminimal coupling.- 2.1 Models using the Ratra-Peebles potential.- 2.2 Necessary conditions for accelerated expansion.- 2.3 Doppler peaks with nonminimal coupling.- 3 Superquintessence.- 3.1 An exact superaccelerating solution.- 3.2 Big Smash singularities.- 4 Quintessence in scalar-tensor gravity.- 5 Conclusion.- References.

Jerk, snap, and the cosmological equation of state

Abstract: Taylor expanding the cosmological equation of state around the current epoch is the simplest model one can consider that does not make any a priori restrictions on the nature of the cosmological fluid. Most popular cosmological models attempt to be 'predictive', in the sense that once some a priori equation of state is chosen the Friedmann equations are used to determine the evolution of the FRW scale factor a(t). In contrast, a 'retrodictive' approach might usefully take observational data concerning the scale factor, and use the Friedmann equations to infer an observed cosmological equation of state. In particular, the value and derivatives of the scale factor determined at the current epoch place constraints on the value and derivatives of the cosmological equation of state at the current epoch. Determining the first three Taylor coefficients of the equation of state at the current epoch requires a measurement of the deceleration, jerk and snap—the second, third and fourth derivatives of the scale factor with respect to time. Higher-order Taylor coefficients in the equation of state are related to higher-order time derivatives of the scale factor. Since the jerk and snap are rather difficult to measure, being related to the third and fourth terms in the Taylor series expansion of the Hubble law, it becomes clear why direct observational constraints on the cosmological equation of state are so relatively weak, and are likely to remain weak for the foreseeable future.

Evolution of second-order cosmological perturbations.

Abstract: We present a method for constructing gauge-invariant cosmological perturbations which are gauge-invariant up to second order. As an example, we give the gauge-invariant definition of the second-order curvature perturbation on uniform density hypersurfaces. Using only the energy conservation equation, we show that this curvature perturbation is conserved at second order on large scales for adiabatic perturbations.

Tracking solutions in tachyon cosmology

Abstract: We perform a thorough phase-plane analysis of the flow defined by the equations of motion of a FRW Universe filled with a tachyonic fluid plus a barotropic one. The tachyon potential is assumed to be of inverse square form, thus allowing for a two-dimensional autonomous system of equations. The Friedmann constraint, combined with a convenient choice of coordinates, renders the physical state compact. We find the fixed-point solutions, and discuss whether or not they represent attractors. The way the two fluids contribute at late times to the fractional energy density depends on how fast the barotropic fluid redshifts. If it does it fast enough, the tachyonic fluid takes over at late times, but if the opposite happens, the situation will not be completely dominated by the barotropic fluid; instead there will be a residual non-negligible contribution from the tachyon subject to restrictions coming from nucleosynthesis.

Can codimension-two branes solve the cosmological constant problem?

Abstract: It has been suggested that codimension-two braneworlds might naturally explain the vanishing of the 4D effective cosmological constant, due to the automatic relation between the deficit angle and the brane tension. To investigate whether this cancellation happens dynamically, and within the context of a realistic cosmology, we study a codimension-two braneworld with spherical extra dimensions compactified by magnetic flux. Assuming Einstein gravity, we show that when the brane contains matter with an arbitrary equation of state, the 4D metric components are not regular at the brane, unless the brane has nonzero thickness. We construct explicit 6D solutions with thick branes, treating the brane matter as a perturbation, and find that the universe expands consistently with standard Friedmann-Robertson-Walker (FRW) cosmology. The relation between the brane tension and the bulk deficit angle becomes $\ensuremath{\Delta}=2\ensuremath{\pi}{G}_{6}(\ensuremath{\rho}\ensuremath{-}3p)$ for a general equation of state. However, this relation does not imply a self-tuning of the effective 4D cosmological constant to zero; perturbations of the brane tension in a static solution lead to deSitter or anti-deSitter braneworlds. Our results thus confirm other recent work showing that codimension-two braneworlds in nonsupersymmetric Einstein gravity do not lead to a dynamical relaxation of the cosmological constant, but they leave open the possibility that supersymmetric versions can be compatible with self-tuning.

Nonsingular FRW cosmology and nonlinear electrodynamics

Abstract: The possibility to avoid the cosmic initial singularity as a consequence of nonlinear effects on the Maxwell eletromagnetic theory is discussed. For a flat Friedmann-Robertson-Walker (FRW) geometry we derive the general nonsingular solution supported by a magnetic field plus a cosmic fluid and a nonvanishing vacuum energy density. The nonsingular behavior of solutions with a time-dependent $\ensuremath{\Lambda}(t)$ term are also examined. As a general result, it is found that the functional dependence of $\ensuremath{\Lambda}(t)$ can uniquely be determined only if the magnetic field remains constant. All these models are examples of bouncing universes which may exhibit an inflationary dynamics driven by the nonlinear corrections of the magnetic field.

Inhomogeneous Gravity

Abstract: We study the inhomogeneous cosmological evolution of the Newtonian gravitational 'constant' G in the framework of scalar-tensor theories. We investigate the differences that arise between the evolution of G in the background universes and in local inhomogeneities that have separated out from the global expansion. Exact inhomogeneous solutions are found which describe the effects of masses embedded in an expanding FRW Brans-Dicke universe. These are used to discuss possible spatial variations of G in different regions. We develop the technique of matching different scalar-tensor cosmologies of different spatial curvature at a boundary. This provides a model for the linear and non-linear evolution of spherical overdensities and inhomogeneities in G. This allows us to compare the evolution of G and \dot{G} that occurs inside a collapsing overdense cluster with that in the background universe. We develop a simple virialisation criterion and apply the method to a realistic lambda-CDM cosmology containing spherical overdensities. Typically, far slower evolution of \dot{G} will be found in the bound virialised cluster than in the cosmological background. We consider the behaviour that occurs in Brans-Dicke theory and in some other representative scalar-tensor theories.

Accelerating cosmologies from exponential potentials

Abstract: An exponential potential of the form V ~ exp(−2c/Mp) arising from the hyperbolic or flux compactification of higher-dimensional theories is of interest for getting short periods of accelerated cosmological expansions. Using a similar potential but derived for the combined case of hyperbolic–flux compactification, we study the four-dimensional flat (and open) FLRW cosmologies and give analytic (and numerical) solutions with exponential behaviour of scale factors. We show that, for the M-theory motivated potentials, the cosmic acceleration of the universe can be eternal if the spatial curvature of the 4d spacetime is negative, while the acceleration is only transient for a spatially flat universe. We also briefly comment on the size of the internal space and its associated geometric bounds on massive Kaluza–Klein excitations.

Decoupling in an expanding universe: boundary RG-flow affects initial conditions for inflation

Abstract: We study decoupling in FRW spacetimes, emphasizing a Lagrangian descrip- tion throughout. To account for the vacuum choice ambiguity in cosmological settings, we introduce an arbitrary boundary action representing the initial conditions. RG flow in these spacetimes naturally affects the boundary interactions. As a consequence the boundary conditions are sensitive to high-energy physics through irrelevant terms in the boundary action. Using scalar field theory as an example, we derive the leading dimension four irrelevant boundary operators. We discuss how the known vacuum choices, e.g. the Bunch-Davies vacuum, appear in the Lagrangian description and square with decoupling. For all choices of boundary conditions encoded by relevant boundary operators, of which the known ones are a subset, backreaction is under control. All, moreover, will generically feel the influence of high-energy physics through irrelevant (dimension four) boundary correc- tions. Having established a coherent effective field theory framework including the vacuum choice ambiguity, we derive an explicit expression for the power spectrum of inflationary density perturbations including the leading high energy corrections. In accordance with the dimensionality of the leading irrelevant operators, the effect of high energy physics is linearly proportional to the Hubble radius H and the scale of new physics l = 1/M.

The Einstein static universe with torsion and the sign problem of the cosmological constant

Abstract: In the field equations of Einstein?Cartan theory with cosmological constant a static spherically symmetric perfect fluid with spin density satisfying the Weyssenhoff restriction is considered. This serves as a rough model of space filled with (fermionic) dark matter. From this the Einstein static universe with constant torsion is constructed, generalizing the Einstein cosmos to Einstein?Cartan theory. The interplay between torsion and the cosmological constant is discussed. A possible way out of the cosmological constant's sign problem is suggested.

Cosmological Scaling Solutions of Multiple Tachyon Fields with Inverse Square Potentials

Abstract: We investigate the cosmological dynamics of multiple tachyon fields with inverse square potentials. A phase-space analysis of the spatially flat FRW models shows that there exist power-law cosmological scaling solutions. We study the stability of the solutions only for the case of two tachyon fields and find that the potential - kinetic- scaling solution is a global attractor. However, in the presence of a barotropic fluid the solution is an attractor only in one region of the parameter space, and the tracking solution is an attractor in the other region. We briefly discuss the physical consequences of these results.

Arnowitt–Deser–Misner gravity with variable G and Λ and fixed-point cosmologies from the renormalization group

Abstract: Models of gravity with variable G and Λ have acquired greater relevance after the recent evidence in favour of the Einstein theory being non-perturbatively renormalizable in the Weinberg sense The present paper applies the Arnowitt–Deser–Misner (ADM) formalism to such a class of gravitational models A modified action functional is then built which reduces to the Einstein–Hilbert action when G is constant, and leads to a power-law growth of the scale factor for pure gravity and for a massless 4 theory in a universe with Robertson–Walker symmetry, in agreement with the recently developed fixed-point cosmology Interestingly, the renormalization-group flow at the fixed point is found to be compatible with a Lagrangian description of the running quantities G and Λ

Cosmological Solution from D-brane motion in NS5-Branes background

Abstract: We study dynamics of a D3-brane propagating in the vicinity of k coincident NS5 branes. We show that when $g_s$ is small, there exists a regime in which dynamics of the D-brane is governed by Dirac-Born-Infeld action while higher order derivative in the expansion can not be neglected. This leads to a restriction on how fast scalar field may roll. We analyze the motion of a rolling scalar field in this regime, and extend the analysis to cosmological systems obtained by coupling this type of field theory to four dimensinal gravity. It also leads to some FRW cosmologies, some of which are related to those obtained with tachyon matter.

Can the Stephani model be an alternative to FRW accelerating models

Abstract: A class of Stephani cosmological models as a prototype of a non-homogeneous universe is considered. The non-homogeneity can lead to accelerated evolution, which is now observed from the SNe Ia data. Three samples of type Ia supernovae obtained by Perlmutter et al, Tonry et al and Knop et al are taken into account. Different statistical methods (best fits as well as maximum likelihood method) to obtain estimation for the model parameters are used. The Stephani model is considered as an alternative to the ΛCDM model in the explanation of the present acceleration of the universe. The model explains the acceleration of the universe at the same level of accuracy as the ΛCDM model (χ2 statistics are comparable). From the best fit analysis it follows that the Stephani model is characterized by a higher value of density parameter Ωm0 than the ΛCDM model. It is also shown that the model is consistent with the location of CMB peaks.

Inflationary Cosmologies from Compactification

Abstract: We consider the compactification of $(d+n)$-dimensional pure gravity and of superstring or M-theory on an n-dimensional internal space to a d-dimensional Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) cosmology, with a spatial curvature $k=0,\ifmmode\pm\else\textpm\fi{}1,$ in the Einstein conformal frame. The internal space is taken to be a product of Einstein spaces, each of which is allowed to have arbitrary curvature and a time-dependent volume. By investigating the effective d-dimensional scalar potential, which is a sum of exponentials, it is shown that such compactifications, in the $k=0,+1$ cases, do not lead to large amounts of accelerating expansion of the scale factor of the resulting FLRW universe, and, in particular, do not lead to inflation. The case $k=\ensuremath{-}1$ admits solutions with eternal accelerating expansion for which the acceleration, however, tends to zero at late times.

Cosmology of intersecting brane-world models in Gauss–Bonnet gravity

Abstract: We study the cosmological properties of a codimension two brane world that sits at the intersection between two four-branes, in the framework of six-dimensional Einstein–Gauss–Bonnet gravity. Due to contributions of the Gauss–Bonnet terms, the junction conditions require the presence of localized energy density on the codimension two defect. The induced metric on this surface assumes a FRW form, with a scale factor associated with the position of the brane in the background; we can embed in the codimension two defect the preferred form of energy density. We present the cosmological evolution equations for the three-brane, showing that, for the case of pure AdS6 backgrounds, they acquire the same form as the ones for the Randall–Sundrum II model. When the background is different from pure AdS6, the cosmological behaviour is potentially modified in respect to the typical one of codimension one brane worlds. We discuss, in a particular model embedded in an AdS6 black hole, the conditions one should satisfy in order to obtain standard cosmology at late epochs.

Arbitrary-dimensional Schwarzschild-FRW black holes

Abstract: The metric of an arbitrary-dimensional Schwarzschild black hole in the background of a Friedmann–Robertson–Walker universe is presented in the cosmic coordinates system. In particular, the arbitrary-dimensional Schwarzschild–de Sitter metric is rewritten in the Schwarzschild coordinates system, based on which the even more generalized higher dimensional Schwarzschild–de Sitter metric with other extra dimensions is found. The generalized solution shows that the cosmological constant may root in the extra dimensions of space.

Viscous Fluid Cosmological Models in LRS Bianchi Type V Universe with Varying Λ

Abstract: Some LRS Bianchi type V viscous-fluid cosmological models are investigated, in which the coefficient of shear viscosity is considered as proportional to the scale of expansion in the model. This leads toA=Bn, whereA andB are metric potentials,n being a constant. The coefficient of bulk viscosity is also assumed to be a power function of mass density. The cosmological constant is found to be a decreasing function of time, which is supported by results from recent type Ia supernovae observations. Some physical aspects of the models are also discussed.

Generation of Bianchi type V cosmological models with varying $\Lambda$-term

Abstract: Bianchi type V perfect fluid cosmological models are investigated with cosmological term $\Lambda$ varying with time. Using a generation technique (Camci {\it et al.}, 2001), it is shown that the Einstein's field equations are solvable for any arbitrary cosmic scale function. Solutions for particular forms of cosmic scale functions are also obtained. The cosmological constant is found to be decreasing function of time, which is supported by results from recent type Ia supernovae observations. Some physical aspects of the models are also discussed.

Cosmology with exponential potentials

Abstract: We examine in the context of general relativity the dynamics of a spatially flat Robertson?Walker universe filled with a classical minimally coupled scalar field of exponential potential V() ~ exp(??) plus pressureless baryonic matter. This system is reduced to a first-order ordinary differential equation for ?(w) or q(w), providing direct evidence on the acceleration/deceleration properties of the system. As a consequence, for positive potentials, passage into acceleration not at late times is generically a feature of the system for any value of ?, even when the late-times attractors are decelerating. Furthermore, the structure formation bound, together with the constraints ?m0 ? 0.25 ? 0.3, ?1 ? w0 ? ?0.6, provides, independently of initial conditions and other parameters, the necessary condition , while the less conservative constraint ?1 ? w ? ?0.93 gives . Special solutions are found to possess intervals of acceleration. For the almost cosmological constant case w ? ?1, the general relation ?(w) is obtained. The generic (nonlinearized) late-times solution of the system in the plane (w, ?) or (w, q) is also derived.

Cosmology of intersecting brane world models in Gauss-Bonnet gravity

Abstract: We study the cosmological properties of a codimension two brane world that sits at the intersection between two four branes, in the framework of six dimensional Einstein-Gauss-Bonnet gravity. Due to contributions of the Gauss-Bonnet terms, the junction conditions require the presence of localized energy density on the codimension two defect. The induced metric on this surface assumes a FRW form, with a scale factor associated to the position of the brane in the background; we can embed on the codimension two defect the preferred form of energy density. We present the cosmological evolution equations for the three brane, showing that, for the case of pure AdS$_6$ backgrounds, they acquire the same form of the ones for the Randall-Sundrum II model. When the background is different from pure AdS$_6$, the cosmological behavior is potentially modified in respect to the typical one of codimension one brane worlds. We discuss, in a particular model embedded in an AdS$_6$ black hole, the conditions one should satisfy in order to obtain standard cosmology at late epochs.

Cosmological string models from milne spaces and sl(2, ℤ) orbifold

Abstract: The (n + 1)-dimensional Milne universe with extra free directions is used to construct simple FRW cosmological string models in four dimensions, describing expansion in the presence of matter with p= κρ, κ = (4 - n)/3n. We then consider the n = 2 case and make SL(2, ℤ) orbifold identifications. The model is surprisingly related to the null orbifold with an extra reflection generator. The study of the string spectrum involves the theory of harmonic functions in the fundamental domain of SL(2, ℤ). In particular, from this theory one can deduce a bound for the energy gap and the fact that there are an infinite number of excitations with a finite degeneracy. We discuss the structure of wave functions and give examples of physical winding states becoming light near the singularity.

Correspondence between n- and m-dimensional inflationary cosmologies

Abstract: It is shown that, from any n-dimensional Friedmann-Robertson-Walker (FRW) cosmology determined for a single scalar field minimally coupled to gravity, one can construct its m-dimensional counterpart, under the assumption of a common time coordinate and a structurally invariant scale factor for both spacetimes, by means of a simple algebraic correspondence relating gravitational constants and scalar field structural functions. If the considered cosmologies are supplemented with a perfect fluid, fitting a wide class of state equations of the form $p+\ensuremath{\rho}=\ensuremath{\gamma}f(\ensuremath{\rho}),$ then any n-dimensional FRW cosmology, coupled to a perfect fluid and a scalar field, possesses an m-dimensional counterpart, and vice versa. In particular, these assertions hold for single scalar field inflation models. A theorem on this respect is demonstrated. Various families of solutions are explicitly given and exhibit their correspondence with 3+1 cosmological spacetimes.

Cosmological Models with Variable G and Λ

Abstract: Einstein's equations with variable gravitational and cosmological constants are considered in the presence of a perfect fluid for the anizotropic Bianchi I universe in a way which conserving the energy-momentum tensor. Two solutions are found, one of which the cosmological term varies inversely with power law of time. The other of which cosmological term is constant.

Fundamental aspects of the expansion of the universe and cosmic horizons

Abstract: We use standard general relativity to clarify common misconceptions about fundamental aspects of the expansion of the Universe. In the context of the new standard ΛCDM cosmology we resolve conflicts in the literature regarding cosmic horizons and the Hubble sphere (distance at which recession velocity = c) and we link these concepts to observational tests. We derive the dynamics of a non-comoving galaxy and generalize previous analyses to arbitrary FRW universes. We also derive the counter-intuitive result that objects at constant proper distance have a non-zero redshift. Receding galaxies can be blueshifted and approaching galaxies can be redshifted, even in an empty universe for which one might expect special relativity to apply. Using the empty universe model we demonstrate the relationship between special relativity and Friedmann-Robertson-Walker cosmology. We test the generalized second law of thermodynamics (GSL) and its extension to incorporate cosmological event horizons. In spite of the fact that cosmological horizons do not generally have well-defined thermal properties, we find that the GSL is satisfied for a wide range of models. We explore in particular the relative entropic ‘worth’ of black hole versus cosmological horizon area. An intriguing set of models show an apparent entropy decrease but we anticipate this apparent violation of the GSL will disappear when solutions are available for black holes embedded in arbitrary backgrounds. Recent evidence suggests a slow increase in the fine structure constant α = e/hc over cosmological time scales. This raises the question of which fundamental quantities are truly constant and which might vary. We show that black hole thermodynamics may provide a means to discriminate between alternative theories invoking varying constants, because some variations in the fundamental ‘constants’ could lead to a violation of the generalized second law of thermodynamics.

Brane-world evolution with brane-bulk energy exchange

Abstract: A rich variety of brane cosmologies is obtained once one allows for energy exchange between the brane and the bulk, depending on the precise form of energy transfer, on the equation of state of matter on the brane and on the spatial topology. This is demonstrated in the context of a non-factorizable background geometry with zero effective cosmological constant on the brane. An accelerating era is generically a feature of these solutions. In the case of low-density flat universe more dark matter than in the conventional FRW picture is predicted, while spatially compact solutions are found to delay their re-collapse. In addition to the above, which the interested reader will find in greater detail in [1], a first attempt towards a complete description of the full dynamics of both the bulk and the brane is reported.