A New Solution of The Cosmological Constant Problems

We extend the usual gravitational action principle by promoting the bare cosmological constant (CC) from a parameter to a field which can take many possible values. Variation leads to a new integral constraint equation which determines the classical value of the effective CC that dominates the wave function of the universe. In a realistic cosmological model, the expected value of the effective CC, is calculated from measurable quantities to be O(t_U), as observed, where t_U is the present age of the universe in Planck units,. Any application of our model produces a falsifiable prediction for $\Lambda$ in terms of other measurable quantities. This leads to a specific falsifiable prediction for the observed spatial curvature parameter of Omega_k0=-0.0055. Our testable proposal requires no fine tunings or extra dark-energy fields but does suggest a new view of time and cosmological evolution.Comment: 5 pages; v3: version accepted by Phys. Rev. Let

The Local Effects of Cosmological Variations in Physical 'Constants' and Scalar Fields I. Spherically Symmetric Spacetimes

We apply the method of matched asymptotic expansions to analyse whether cosmological variations in physical `constants' and scalar fields are detectable, locally, on the surface of local gravitationally bound systems such as planets and stars, or inside virialised systems like galaxies and clusters. We assume spherical symmetry and derive a sufficient condition for the local time variation of the scalar fields that drive varying constants to track the cosmological one. We calculate a number of specific examples in detail by matching the Schwarzschild spacetime to spherically symmetric inhomogeneous Tolman-Bondi metrics in an intermediate region by rigorously construction matched asymptotic expansions on cosmological and local astronomical scales which overlap in an intermediate domain. We conclude that, independent of the details of the scalar-field theory describing the varying `constant', the condition for cosmological variations to be measured locally is almost always satisfied in physically realistic situations. The proof of this statement provides a rigorous justification for using terrestrial experiments and solar system observations to constrain or detect any cosmological time variations in the traditional `constants' of Nature.Comment: 30 pages, 3 figures; corrected typo

Some Late-time Asymptotics of General Scalar-Tensor Cosmologies

We study the asymptotic behaviour of isotropic and homogeneous universes in general scalar-tensor gravity theories containing a p=-rho vacuum fluid stress and other sub-dominant matter stresses. It is shown that in order for there to be approach to a de Sitter spacetime at large 4-volumes the coupling function, omega(phi), which defines the scalar-tensor theory, must diverge faster than |phi_infty-phi|^(-1+epsilon) for all epsilon>0 as phi rightarrow phi_infty 0 for large values of the time. Thus, for a given theory, specified by omega(phi), there must exist some phi_infty in (0,infty) such that omega -> infty and omega' / omega^(2+epsilon) -> 0 as phi -> 0 phi_infty in order for cosmological solutions of the theory to approach de Sitter expansion at late times. We also classify the possible asymptotic time variations of the gravitation `constant' G(t) at late times in scalar-tensor theories. We show that (unlike in general relativity) the problem of a profusion of ``Boltzmann brains'' at late cosmological times can be avoided in scalar-tensor theories, including Brans-Dicke theory, in which phi -> infty and omega ~ o(\phi^(1/2)) at asymptotically late times.Comment: 14 page

Observable Effects of Scalar Fields and Varying Constants

We show by using the method of matched asymptotic expansions that a sufficient condition can be derived which determines when a local experiment will detect the cosmological variation of a scalar field which is driving the spacetime variation of a supposed constant of Nature. We extend our earlier analyses of this problem by including the possibility that the local region is undergoing collapse inside a virialised structure, like a galaxy or galaxy cluster. We show by direct calculation that the sufficient condition is met to high precision in our own local region and we can therefore legitimately use local observations to place constraints upon the variation of "constants" of Nature on cosmological scales.Comment: Invited Festscrift Articl

Evolution of the fine-structure constant in the non-linear regime

We study the evolution of the fine-structure constant, $\alpha$, induced by non-linear density perturbations in the context of the simplest class of quintessence models with a non-minimal coupling to the electromagnetic field, in which the two available free functions (potential and gauge kinetic function) are Taylor-expanded up to linear order. We show that the results obtained using the spherical infall model for an infinite wavelength inhomogeneity are inconsistent with the results of a local linearized gravity study and we argue in favour of the second approach. We also discuss recent claims that the value of $\alpha$ inside virialised regions could be significantly different from the background one on the basis of these findings.Comment: 5 pages, 3 figure

Varying Alpha: New Constraints from Seasonal Variations

We analyse the constraints obtained from new atomic clock data on the possible time variation of the fine structure `constant' and the electron-proton mass ratio and show how they are strengthened when the seasonal variation of Sun's gravitational field at the Earth's surface is taken into account. We compare these bounds with those obtainable from tests of the Weak Equivalence Principle and high-redshift observations of quasar absorption spectra consistent with time variations in the fine structure constant.Comment: 4 pages, 1 figur