Adventures in Friedmann cosmology: A detailed expansion of the cosmological Friedmann equations

@article{Nemiroff2007AdventuresIF,
  title={Adventures in Friedmann cosmology: A detailed expansion of the cosmological Friedmann equations},
  author={Robert J. Nemiroff and Bijunath R. Patla},
  journal={American Journal of Physics},
  year={2007},
  volume={76},
  pages={265-276}
}
The general relativistic cosmological Friedmann equations, which describe how the scale factor of the universe evolves, are expanded explicitly to include energy forms not usually seen. The evolution of the universe as predicted by the Friedmann equations when dominated by a single, isotropic, stable, static, perfect-fluid energy form is discussed for different values of the gravitational pressure to density ratio w. These energy forms include phantom energy (w 1∕3). A brief history and… 

Tables from this paper

Qualitative study of perfect-fluid Friedmann-Lemaître-Robertson-Walker models with a cosmological constant

The evolution of spatially homogeneous and isotropic cosmological models containing a perfect fluid with equation of state p = wρ and a cosmological constant Λ is investigated for arbitrary

FIRST-ORDER QUANTUM-GRAVITATIONAL CORRECTION TO FRIEDMANNIAN COSMOLOGY FROM COVARIANT, HOLOMORPHIC SPINFOAM COSMOLOGY

The first-order loop quantum gravity correction of the simplest, classical general relativistic Friedmann Hamiltonian constraint, emerging from a holomorphic spinfoam cosmological model peaked on

Stability of Friedmann equation with respect to small changes in the density parameter

We show that the solution of the Friedmann equation for a universe with matter and cosmological constant is stable with respect to small changes in the density parameter Ω0. We find an expression for

First-order quantum-gravitational correction to Friedmannian cosmology from covariant, holomorphic spinfoam cosmology

The first-order loop quantum gravity correction of the simplest, classical general relativistic Friedmann Hamiltonian constraint, emerging from a holomorphic spinfoam cosmological model peaked on

Explicit integration of Friedmann's equation with nonlinear equations of state

In this paper we study the integrability of the Friedmann equations, when the equation of state for the perfect-fluid universe is nonlinear, in the light of the Chebyshev theorem. A series of

QUASI-PERIODIC SOLUTIONS OF EINSTEIN-FRIEDMAN EQUATIONS

A new quasi-periodic solutions of Einstein-Friedman equations are presented here. The equation for law of energy saving is proved to be transformed to the proper Abel ordinary differential equation.

QUASI-PERIODIC SOLUTIONS OF

A new quasi-periodic solutions of Einstein-Friedman equations are presented here. The equation for law of energy saving is proved to be transformed to the proper Abel ordinary differential equation.

Computing Accurate Age and Distance Factors in Cosmology

As the universe expands astronomical observables such as brightness and angular size on the sky change in ways that differ from our simple Cartesian expectation. We show how observed quantities

An exposition on Friedmann cosmology with negative energy densities

How would negative energy density affect a classic Friedmann cosmology? Although never measured and possibly unphysical, certain realizations of quantum field theories leaves the door open for such a

A Cyclic Cosmological Model Based on the f(ρ) Modified Theory of Gravity

We consider FLRW cosmological models for perfect fluid (with ρ as the energy density) in the frame work of the f(ρ) modified theory of gravity [V. N. Tunyak, Russ. Phys. J. 21, 1221 (1978); J. R.

References

SHOWING 1-10 OF 50 REFERENCES

An analysis of helium primordial nucleosynthesis with a variable cosmological coupling

The synthesis of helium in the early Universe depends on many input parameters, including the value of the gravitational coupling during the period when the nucleosynthesis takes place. We compute

Thermal relics: Do we know their abundances?

TLDR
Three nonstandard possibilities for the Universe at the time a species’ abundance froze in are considered: energy density dominated by shear, energy density dominance of the scalar field that sets the gravitational constant in a Brans-Dicke-Jordan cosmological model, and a component of the energy density at early times with a very stiff equation of state.

Branes on the horizon

Models with extra dimensions are often invoked to resolve cosmological problems. We investigate the possibility of apparent acausality as seen by a brane-based observer resulting from signal

Inflationary universe: A possible solution to the horizon and flatness problems

The standard model of hot big-bang cosmology requires initial conditions which are problematic in two ways: (1) The early universe is assumed to be highly homogeneous, in spite of the fact that

Cosmological consequences of a Chaplygin gas dark energy

A combination of recent observational results has given rise to what is currently known as the dark energy problem. Although several possible candidates have been extensively discussed in the

Formation of galaxies and large-scale structure with cold dark matter

The dark matter that appears to be gravitationally dominant on all scales larger than galactic cores may consist of axions, stable photinos, or other collisionless particles whose velocity dispersion

Integration of the Friedmann equation for universes of arbitrary complexity

An explicit and complete set of constants of the motion are constructed algorithmically for Friedmann-Lemaitre-Robertson-Walker (FLRW) models consisting of an arbitrary number of noninteracting

Turning around the sphaleron bound: Electroweak baryogenesis in an alternative post-inflationary cosmology

The usual sphaleron bound and the statement of the impossibility of baryon production at a second order phase transition or analytic cross-over are reformulated in the first part of the paper as