Back-reaction equations for isotropic cosmologies when nonconformal particles are created

A model proposed some years ago by Hartle to study the back reaction in a cosmological model due to the creation of massless non-conformally coupled particles is reexamined. The model consists of a spatially flat FRW spacetime with a classical source made of two perfect fluids one a radiative fluid and the other a baryonic fluid with the equation of state of dust, and it is assumed that the ratio of baryons to photons is small. The back-reaction equations for the cosmological scale factor are derived using a CTP (closed time path) effective action method. Making use of the connection, in the semiclassical context, between the CTP effective action and the influence functional in quantum statistical mechanics, improved back-reaction equations are derived which take into account the fluctuations of the stress-energy tensor of the quantum field. These new dynamical equations are real and causal and predict stochastic fluctuations for the cosmological scale factor.     

On the thermodynamic and quantum fluctuations of the cosmological constant

We discuss, from a condensed-matter point of view, the recent idea that the Poisson fluctuations of the cosmological constant about zero could be a source of the observed dark energy [1, 2]. We argue that the thermodynamic fluctuations of Λ are much bigger. Since the amplitude of the fluctuations is ∝ V^?1/2, where V is the volume of the universe, the present constraint on the cosmological constant provides a lower limit for V that is much larger than the volume within the cosmological horizon.     

What initial perturbations may be generated in inflationary cosmological models

Isothermal (isoinflaton) perturbations generated in cosmological models at the inflationary stage are discussed. The spectrum of such perturbations has been calculated for the example of a cosmological model with axion-type matter. The possibility of the cut-off of the spectrum at long wavelengths has been shown. This leads to the suppression of large-scale fluctuations of the temperature of the background radiation.     

Quantum fluctuations near the classical space-time singularity

The method of path integration is used to study the effects of quantum fluctuations in the space-time geometry near the classical singularity of general relativity. It is shown that in certain special cases explicit Feynman propagators can be constructed which enable us to evaluate these fluctuationsquantitatively. The cases discussed are (i) the gravitational collapse of a uniform dust ball, (ii) the Friedmann cosmologies, (iii) the axisymmetric Bianchi type I cosmological model, and (iv) the general anisotropic Bianchi type I cosmological model. In all cases discussed here the quantum uncertainty grows to infinity as the classical space-time singularity is approached. In this wider regime of quantum gravitation nonsingular solutions can occur with finite probabilities.     

Producing a scale-invariant spectrum of perturbations in a Hagedorn phase of string cosmology

We study the generation of cosmological perturbations during the Hagedorn phase of string gas cosmology. Using tools of string thermodynamics we provide indications that it may be possible to obtain a nearly scale-invariant spectrum of cosmological fluctuations on scales which are of cosmological interest today. In our cosmological scenario, the early Hagedorn phase of string gas cosmology goes over smoothly into the radiation-dominated phase of standard cosmology, without having a period of cosmological inflation.     

Surface tension and the cosmological constant

One of the few predictions from quantum gravity models is Sorkin's observation that the cosmological constant has quantum fluctuations originating in the fundamental discreteness of spacetime at the Planck scale. Here we present a compelling analogy between the cosmological constant of the Universe and the surface tension of fluid membranes. The discreteness of spacetime on the Planck scale translates into the discrete molecular structure of a fluid membrane. We propose an analog quantum gravity experiment which realizes Sorkin's idea in the laboratory. We also notice that the analogy sheds light on the cosmological constant problem, suggesting a mechanism for dynamically generating a vanishingly small cosmological constant. We emphasize the generality of Sorkin's idea and suggest that similar effects occur generically in quantum gravity models.     

A confirmation of agreement of different approaches for?scalar?gauge-invariant metric perturbations during inflation

We revisit an extension of the well-known formalism for gauge-invariant scalar metric fluctuations to study the spectra for both the inflaton and gauge-invariant (scalar) metric fluctuations in the framework of a single-field inflationary model, in which the quasi-exponential expansion is driven by an inflaton which is minimally coupled to gravity. The proposal here examined is valid also for fluctuations with large amplitudes, but for cosmological scales, where vector and tensor perturbations can be neglected and the fluid is irrotacional.     

“CMB-Slow” or How to Determine Cosmological Parameters by Hand?

I derive analytically the spectrum of the CMB fluctuations. The final result for C _l is presented in terms of elementary functions with an explicit dependence on the basic cosmological parameters. This result is in a rather good agreement with CMBFAST for a wide range of parameters around concordance model. This allows us to understand the physical reasons for dependence of the particular features of the CMB spectrum on the basic cosmological parameters and to estimate the possible accuracy of their determination. I also analyze the degeneracy of the spectrum with respect to certain combinations of the cosmological parameters.     

Vacuum fluctuations of the supersymmetric field in curved background

We study a supersymmetric model in curved background spacetime. We calculate the effective action and the vacuum expectation value of the energy momentum tensor using a covariant regularization procedure. A soft supersymmetry breaking induces a nonzero contribution to the vacuum energy density and pressure. Assuming the presence of a cosmic fluid in addition to the vacuum fluctuations of the supersymmetric field an effective equation of state is derived in a self-consistent approach at one loop order. The net effect of the vacuum fluctuations of the supersymmetric fields in the leading adiabatic order is a renormalization of the Newton and cosmological constants.     

The cosmological constant is probably zero

It is suggested that the apparent cosmological constant is not necessarily zero but that zero is by far the most probable value. One requires some mechanism like a three-index antisymmetric tensor field or topological fluctuations of the metric which can give rise to an effective cosmological constant of arbitrary magnitude. The action of solutions of the euclidean field equations is most negative, and the probability is therefore highest, when this effective cosmological constant is very small.     

Signature of local motion in the microwave sky

For observers moving with respect to the cosmic rest frame, the microwave background temperature fluctuations will no longer be statistically isotropic. Aside from the familiar temperature dipole, an observer's velocity will also induce changes in the temperature angular correlation function and create nonzero off-diagonal correlations between multipole moments. We show that both of these effects should be detectable in future full-sky maps from the Planck satellite, and can constrain modifications of the standard cosmological model proposed to explain anomalous current observations.     

Exact Solution in Chaotic Inflation Model with Potential Minima

Taking the cosmological expansion rate directly as a function of field φ, H=H(φ), we present a new exact solution to Einstein's equations that describe the evolution of cosmological chaotic inflation model. The inflation is driven by the evolution of scalar field with inflation potential V(φ)=(λ/8)(φ²-υ²)². The spectral indices of the scalar density n_s and gravitational wave fluctuations n_g are computed. The value of n_s lies well inside the limits set by the cosmic background explorer satellite.     

Consequences of a Cosmological Phase Transition at the TeV Scale

A finite vacuum energy density implies the existence of a UV scale for gravitational modes. This gives a phenomenological scale to the dynamical equations governing the cosmological expansion that must satisfy constraints consistent with quantum measurability and spatial flatness. Examination of these constraints for the observed dark energy density establishes a time interval from the transition to the present, suggesting major modifications from the thermal equations of state far from Planck density scales. The assumption that a phase transition initiates the radiation dominated epoch is shown under several scenarios to be able to produce fluctuations to the CMB of the order observed. Quantum measurability constraints (eg. uncertainly relations) define cosmological scales bounded by luminal expansion rates. It is shown that the dark energy can consistently be interpreted as being due to the vacuum energy of collective gravitational modes which manifest as the zero-point motions of coherent Planck scale mass units prior to the UV scale onset of gravitational quantum de-coherence for the cosmology. A cosmological model with multiple scales, one of which replaces an apparent cosmological “constant”, is shown to reproduce standard cosmology during intermediate times, while making the exploration of the early and late time cosmology more accessible. Talk presented at the 2006 biennial conference of the International Association for Relativistic Dynamics, June 12–14, University of Connecticut (Storrs).     

Isotropic Space with Discrete Gravitational-Field Sources. On the Theory of a Nonhomogeneous Isotropic Universe

Existing cosmological theories are based on Einstein's law of gravitation (7). In this equation the average is taken only in the right-hand side by a substitution of the energy momentum tensor corresponding to uniform and continuous distribution of matter. In this paper a new cosmological equation (48), which is more correct from the physical and mathematical point of view, is obtained by space-time averaging of all the terms of Eq. (7) and taking into account the fluctuations of the gravitational field due to nonuniformities in the distribution of matter. An estimate of these fluctuations within the framework of Newton's approximation leads to the cosmological equations (51), (52) and (53) for flat space and positive and negative curvature. The solutions of these equations, in distinction from all the variants of Friedman's theory, do not have a singular point for some initial moment of time with an infinitely large density of matter. However, this result follows when the relations obtained are extrapolated beyond the range of their applicability, and therefore final conclusions can be made on the basis of the solutions of the new cosmological equations (48) when we go beyond the Newtonian approximation.     

The imprint of inflation on the cosmic microwave background

The cosmic microwave background is the most precise and the most simple cosmological dataset. This makes it our most prominent window to the physics of the very early Universe. In this article I give an introduction to the physics of the cosmic microwave background and show in some detail how primordial fluctuations from inflation are imprinted in the temperature anisotropy and polarisation spectrum of the CMB. I discuss the main signatures that are suggesting an inflationary phase for the generation of initial fluctuations.     

Models of the universe

In this paper a theory of models of the universe is proposed. We refer to such models ascosmological models, where a cosmological model is defined as an Einstein-inextendible Einstein spacetime. A cosmological model isabsolute if it is a Lorentz-inextendible Einstein spacetime,predictive if it is globally hyperbolic, andnon-predictive if it is nonglobally-hyperbolic. We discuss several features of these models in the study of cosmology. As an example, any compact Einstein spacetime is always a non-predictive absolute cosmological model, whereas a noncompact complete Einstein spacetime is an absolute cosmological model which may be either predictive or non-predictive. We discuss the important role played by maximal Einstein spacetimes. In particular, we examine the possible proper Lorentz-extensions of such spacetimes, and show that a spatially compact maximal Einstein spacetime is exclusively either a predictive cosmological model or a proper sub-spacetime of a non-predictive cosmological model. Provided that the Strong Cosmic Censorship conjecture is true, a generic spatially compact maximal Einstein spacetime must be a predictive cosmological model. It isconjectured that the Strong Cosmic Censorship conjecture isnot true, and converting a vice to a virtue it is argued that the failure of the Strong Cosmic Censorship conjecture would point to what may be general relativity's greatest prediction of all, namely,that general relativity predicts that general relativity cannot predict the entire history of the universe.     

Cosmological Constant and Stability of the Cosmological Models

The importance of cosmological constant for the cosmological models is given. The variations of the cosmological model for parameters λ and k were discussed respectively. Near λ = 0, the cosmological model is unstable with the change of λ, and near λ = β = 0, the cosmological model is unstable with the change of k. So when we consider the stable cosmological model, we must consider the nonzero cosmological constant.     

Generating the curvature perturbation at the end of inflation in string theory

In brane inflationary scenarios, the cosmological perturbations are supposed to originate from the vacuum fluctuations of the inflaton field corresponding to the position of the brane. We show that a significant, and possibly dominant, contribution to the curvature perturbation is generated at the end of inflation through the vacuum fluctuations of fields, other than the inflaton, which are light during the inflationary trajectory and become heavy at the brane-antibrane annihilation. These fields appear generically in string compactifications where the background geometry has exact or approximate isometries and parametrize the internal angular directions of the brane.     

On the cosmological constant problem and brane-world geometry

The cosmological constant problem is examined within the context of the covariant brane-world gravity, based on Nash’s embedding theorem for Riemannian geometries. We show that the vacuum structure of the brane-world is more complex than General Relativity’s because it involves extrinsic elements, in specific, the extrinsic curvature. In other words, the shape (or local curvature) of an object becomes a relative concept, instead of the “absolute shape” of General Relativity. We point out that the immediate consequence is that the cosmological constant and the energy density of the vacuum quantum fluctuations have different physical meanings: while the vacuum energy density remains confined to the four-dimensional brane-world, the cosmological constant is a property of the bulk’s gravitational field that leads to the conclusion that these quantities cannot be compared, as it is usually done in General Relativity. Instead, the vacuum energy density contributes to the extrinsic curvature, which in turn generates Nash’s perturbation of the gravitational field. On the other hand, the cosmological constant problem ceases to be in the brane-world geometry, reappearing only in the limit where the extrinsic curvature vanishes.