https://www.physics.rutgers.edu/grad/690/Padmanabhan-2003.pdf

Cosmological constant—the weight of the vacuum

Recent observations of Type 1a supernovae indicating an accelerating universe have once more drawn attention to the possible existence, at the present epoch, of a small positive Λ-term (cosmological constant). In this paper we review both observational and theoretical aspects of a small cosmological Λ-term. We discuss the current observational situation focusing on cosmological tests of Λ including the age of the universe, high redshift supernovae, gravitational lensing, galaxy clustering and the cosmic microwave background. We also review the theoretical debate surrounding Λ: the generation of Λ in models with spontaneous symmetry breaking and through quantum vacuum polarization effects — mechanisms which are known to give rise to a large value of Λ hence leading to the "cosmological constant problem." More recent attempts to generate a small cosmological constant at the present epoch using either field theoretic techniques, or by modelling a dynamical Λ-term by scalar fields are also extensively discussed. Anthropic arguments favouring a small Λ-term are briefly reviewed. A comprehensive bibliography of recent work on Λ is provided.

http://cds.cern.ch/record/385991/files/9904398.pdf

The Case for a Positive Cosmological Λ-Term

Exact interior and exterior solutions to Einstein's field equations are derived for vacuum strings. The exterior solution for a uniform density vacuum string corresponds to a conical space while the interior solution is that of a spherical cap. For Mu equals 0-1/4 the external metric is ds-squared = -dt-squared + dr-squared + (1-4 Mu)-squared r-squared dphi-squared + dz-squared, where Mu is the mass per unit length in the string in Planck masses per Planck length. A maximum mass per unit length for a string is 6.73 x 10 to the 27th g/cm. It is shown that strings cause temperature fluctuations in the cosmic microwave background and produce equal brightness double QSO images separated by up to several minutes of arc. Formulae for lensing probabilities, image splittings, and time delays are derived for strings in a realistic cosmological setting. String searches using ST, the VLA, and the COBE satellite are discussed.

Gravitational Lensing Effects of Vacuum Strings: Exact Solutions

A new method of variation of the gravitational Lagrangian is proposed. This method leads in a simple and straightforward way to the canonical description of the gravitational field dynamics in a finite volume V with boundary. No boundary terms are neglected or subtracted ad hoc. Two different forms of gravitational quasi-local energy are derived. Each of them is equal to the field Hamiltonian, corresponding to a specific way of controlling the field boundary data. They play the role of the “internal energy” and the “free energy” respectively. A relation with the boundary formula governing the thermodynamics of black holes is discussed.

A Simple Derivation of Canonical Structure and Quasi-local Hamiltonians in General Relativity

We study the magnitude-redshift relation for the type?Ia supernovae data and the angular size-redshift relation for the updated compact radio sources data (from Gurvits et?al) by considering four variable ?-models: ?~S-2, ?~H2, ?~? and ?~t-2. It is found that all the variable ?-models, as well as the constant ?-Friedmann model, fit the supernovae data equally well with ?2/dof?1 and require non-zero, positive values of ? and an accelerating expansion of the universe. The estimates of the density parameter for the variable ?-models are found to be higher than those for the constant ?-Friedmann model. From the compact radio sources data, it is found, by assuming the no-evolution hypothesis, that the Gurvits et al model (Friedmann model with ? = 0) is not the best-fitting model for the constant ? case. The best-fitting Friedmann model (with constant ?) is found to be a low-density, vacuum-dominated accelerating universe. The fits of this data set to the (variable, as well as, constant ?-) models are found to be very good with ?2/dof?0.5 and require non-zero, positive values of ? with either sign of the deceleration parameter. However, for realistic values of the matter density parameter, the only interesting solutions are (a) estimated from the supernovae data: the best-fitting solutions for the flat models (including the constant ? case); (b) estimated from the radio sources data: the global best-fitting solutions for the models ?~H2 and ?~?, the best-fitting solution for the flat model with ? = {}constant and the Gurvits et al model. It is noted that, as in the case of recent cosmic microwave background analyses, the data sets seem to favour a spherical universe (k>0).

http://repository.iucaa.in:8080/jspui/bitstream/11007/1322/1/062001.PDF

Consequences on variable Λ-models from distant type Ia supernovae and compact radio sources

We study flat and nonflat static models obeying the Brans-Dicke theory and RW metric, including the case which considers Bertolami's time-dependent cosmological term. We find several solutions where the density remains constant, while the gravitational constant varies with time.

Brans-Dicke static universes

More general solutions than those presented by Bertolami are deduced in the Brans-Dicke cosmology, endowed with a time-dependent cosmological term, for a Robertson-Walker metric and a perfect fluid obeying the perfect gas law of state.

Brans-Dicke models with time-dependent cosmological term

When Brans and Dicke published their alternative gravitational framework, they proved that it led to Machian solutions in the static case, and for a pressureless (dust) Euclidean universe We extend their demonstration to Euclidean and non-Euclidean models with non-null pressure, employing the perfect fluid model We findρ andp both ∝G

M. M. Som

Papers

Brans-Dicke static universes

Brans-Dicke models with time-dependent cosmological term

Whitrow-Randall's relation and Brans-Dicke cosmology

Inflationary phase in Brans-Dicke cosmology

The Schwarzschild interior metric: a new look