Quantum Cosmology for the General Bianchi Type II, VI(Class A) and VII(Class A) vacuum geometries

The canonical quantization of the most general minisuperspace actions --i.e. with all six scale factor as well as the lapse function and the shift vector present-- describing the vacuum type II, VI and VII geometries, is considered. The reduction to the corresponding physical degrees of freedom is achieved through the usage of the linear constraints as well as the quantum version of the entire set of classical integrals of motion.Comment: 23 pages, LaTeX2e, No figure

A note on wavemap-tensor cosmologies

We examine theories of gravity which include finitely many coupled scalar fields with arbitrary couplings to the curvature (wavemaps). We show that the most general scalar-tensor $\sigma$-model action is conformally equivalent to general relativity with a minimally coupled wavemap with a particular target metric. Inflation on the source manifold is then shown to occur in a novel way due to the combined effect of arbitrary curvature couplings and wavemap self-interactions. A new interpretation of the conformal equivalence theorem proved for such `wavemap-tensor' theories through brane-bulk dynamics is also discussed.Comment: 8 pages, LaTeX, to appear in the Proceedings of the 2nd Hellenic Cosmology Workshop, National Observatory of Athens, April 21-22, 2001, (Kluwer 2001

Maximum tension: With and without a cosmological constant

We discuss various examples and ramifications of the conjecture that there exists a maximum force (or tension) in general relativistic systems. We contrast this situation with that in Newtonian gravity, where no maximum force exists, and relate it to the existence of natural units defined by constants of Nature and the fact that the Planck units of force and power do not depend on Planck's constant. We discuss how these results change in higher dimensions where the Planck units of force are no longer non-quantum. We discuss the changes that might occur to the conjecture if a positive cosmological constant exists and derive a maximum force bound using the Kottler-Schwarzschildde Sitter black hole

Further Exact Cosmological Solutions to Higher-Order Gravity Theories

15 pages and 2 figures15 pages and 2 figures15 pages and 2 figuresWe investigate the effect of deviations from general relativity on approach to the initial singularity by finding exact cosmological solutions to a wide class of fourth-order gravity theories. We present new anisotropic vacuum solutions of modified Kasner type and demonstrate the extent to which they are valid in the presence of non-comoving perfect-fluid matter fields. The infinite series of Mixmaster oscillations seen in general relativity will not occur in these solutions, except in unphysical cases

Observational constraints on new exact inflationary scalar-field solutions

An algorithm is used to generate new solutions of the scalar-field equations in homogeneous and isotropic universes. Solutions can be found for pure scalar fields with various potentials in the absence and presence of spatial curvature and other perfect fluids. A series of generalizations of the Chaplygin gas and bulk viscous cosmological solutions for inflationary universes are found. Furthermore other closed-form solutions which provide inflationary universes are presented. We also show how the Hubble slow-roll parameters can be calculated using the solution algorithm and we compare these inflationary solutions with the observational data provided by the Planck 2015 collaboration in order to constrain and rule out some of these models.J.D.B. acknowledges support from the STFC. A.P. acknowledges financial support of FONDECYT Grant No. 3160121

Redshifting of cosmological black bodies in Bekenstein-Sandvik-Barrow-Magueijo varying-alpha theories

We analyse the behaviour of black-body radiation in theories of electromagnetism which allow the electron charge and the fine structure constant to vary in space and time. We show that such theories can be expressed as relativistic generalizations of a conventional dielectric. By making the appropriate definition of the vector potential and associated gauge transformations, we can identify the equivalent of the electric and displacement fields, E and D, as well as the magnetic B and H fields. We study the impact of such dielectrics on the propagation of light in the so-called “BSBM” theory. We examine the form of simple cosmological solutions and conclude that no changes are created to the standard cosmological evolution of the temperature and energy-density of black-body radiation. Nonetheless the matter evolution changes and the behaviour of the entropy per baryon is modified, and the ratios of different dark matter components may be changed too.We acknowledge STFC for consolidated grant support.This is the accepted manuscript. The final version is available from APS at http://journals.aps.org/prd/abstract/10.1103/PhysRevD.90.12350

Singular inflation

We prove that a homogeneous and isotropic universe containing a scalar field with a power-law potential, V(ϕ)=Aϕ^n, with 00 always develops a finite-time singularity at which the Hubble rate and its first derivative are finite, but its second derivative diverges. These are the first examples of cosmological models with realistic matter sources that possess weak singularities of “sudden” type. We also show that a large class of models with even weaker singularities exists for noninteger n>1. More precisely, if k<n<k+1 where k is a positive integer then the first divergence of the Hubble rate occurs with its (k+2)th derivative. At early times these models behave like standard large-field inflation models but they encounter a singular end state when inflation ends. We term this singular inflation.A.A.H.G. and J.D.B. are supported by the STFC.This is the author accepted manuscript. The final version is available from APS via http://dx.doi.org/10.1103/PhysRevD.91.08351

Cosmological models in energy-momentum-squared gravity

We study the cosmological effects of adding terms of higher-order in the usual energy-momentum tensor to the matter lagrangian of general relativity. This is in contrast to most studies of higher-order gravity which focus on generalising the Einstein-Hilbert curvature contribution to the lagrangian. The resulting cosmological theories give rise to field equations of similar form to several particular theories with different fundamental bases, including bulk viscous cosmology, loop quantum gravity, K-essence, and brane-world cosmologies. We find a range of exact solutions for isotropic universes, discuss their behaviours with reference to the early and late-time evolution, accelerated expansion, and the occurrence or avoidance of singularities. We briefly discuss extensions to anisotropic cosmologies and delineate the situations where the higher-order matter terms will dominate over anisotropies on approach to cosmological singularities

New singularities in unexpected places

Spacetime singularities have been discovered which are physically much weaker than those predicted by the classical singularity theorems. Geodesics evolve through them and they only display infinities in the derivatives of their curvature invariants. So far, these singularities have appeared to require rather exotic and unphysical matter for their occurrence. Here, we show that a large class of singularities of this form can be found in a simple Friedmann cosmology containing only a scalar-field with a power-law self-interaction potential. Their existence challenges several preconceived ideas about the nature of spacetime singularities and has an impact upon the end of inflation in the early universe. This is the author accepted manuscript. The final version is available from World Scientific via http://dx.doi.org/10.1142/S021827181544012

Hyperbolic inflation in the light of Planck 2015 data

Rubano and Barrow have discussed the emergence of a dark energy, with late-time cosmic acceleration arising from a self-interacting homogeneous scalar field with a potential of hyperbolic power type. Here, we study the evolution of this scalar field potential back in the inflationary era. Using the hyperbolic power potential in the framework of inflation, we find that the main slow-roll parameters, like the scalar spectral index, the running of the spectral index and the tensor-to-scalar fluctuation ratio can be computed analytically. Finally, in order to test the viability of this hyperbolic scalar field model at the early stages of the Universe, we compare the predictions of that model against the latest observational data, namely Planck 2015.S. B. acknowledges support by the Research Center for Astronomy of the Academy of Athens in the context of the program “Tracing the Cosmic Acceleration.” J. D. B. acknowledges STFC support.This is the author accepted manuscript. The final version is available from APS via http://dx.doi.org/10.1103/PhysRevD.91.10351