Modified Gravity and Cosmology

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

The Inflationary Universe

Progress of theoretical physics

Berman presented elsewhere a law of variation for Hubble's parameter that yields constant deceleration parameter models of the universe. By analyzing Einstein, Pryce-Hoyle and Brans-Dicke cosmologies, we derive here the necessary relations in each model, considering a perfect fluid.

Cosmological models with constant deceleration parameter

We consider the Einstein field equations with perfect fluid source and variable Λ andG for the Robertson-Walker metric. When conservation of energy momentum is postulated and the deceleration parameter is assumed constant, we find perfect gas equation of state models in the Euclidean and non-Euclidean cases. The resulting models offer an alternative to the inflationary scenario; they also explain the huge value of the cosmological term in the early universe.

Cosmological models with variable gravitational and cosmological “constants”

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

We derive a static model of the universe, where density and pressure are constant, but the gravitational “constant” and the cosmological term vary with time, by means of the Endo-Fukui modified Brans-Dicke theory

Marcelo Samuel Berman

Papers

Cosmological models with constant deceleration parameter

Cosmological models with variable gravitational and cosmological “constants”

Brans-Dicke static universes

Brans-Dicke models with time-dependent cosmological term

Static Universe in a Modified Brans-Dicke Cosmology