“…[1,40,41] for non-gravitational couplings and BBN). Among the constants which are effective during BBN, the gravitational constant plays a key role, and hence there have been many published studies of the effects of a varying G on the primordial abundance of the light elements [42,43,44,45,46,47,48,49,50,51]. However, since G is a dimensional constant, we calculate the abundance of helium synthesized during BBN in an explicit dimensionless way in this section, focusing on the dominant parts of the physics and neglecting some of the finer details.…”
Although it is well known that any consideration of the variations of
fundamental constants should be restricted to their dimensionless combinations,
the literature on variations of the gravitational constant $G$ is entirely
dimensionful. To illustrate applications of this to cosmology, we explicitly
give a dimensionless version of the parameters of the standard cosmological
model, and describe the physics of Big Bang Neucleosynthesis and recombination
in a dimensionless manner. The issue that appears to have been missed in many
studies is that in cosmology the strength of gravity is bound up in the
cosmological equations, and the epoch at which we live is a crucial part of the
model. We argue that it is useful to consider the hypothetical situation of
communicating with another civilization (with entirely different units),
comparing only dimensionless constants, in order to decide if we live in a
Universe governed by precisely the same physical laws. In this thought
experiment, we would also have to compare epochs, which can be defined by
giving the value of any {\it one} of the evolving cosmological parameters. By
setting things up carefully in this way one can avoid inconsistent results when
considering variable constants, caused by effectively fixing more than one
parameter today. We show examples of this effect by considering microwave
background anisotropies, being careful to maintain dimensionlessness
throughout. We present Fisher matrix calculations to estimate how well the fine
structure constants for electromagnetism and gravity can be determined with
future microwave background experiments. We highlight how one can be misled by
simply adding $G$ to the usual cosmological parameter set
“…[1,40,41] for non-gravitational couplings and BBN). Among the constants which are effective during BBN, the gravitational constant plays a key role, and hence there have been many published studies of the effects of a varying G on the primordial abundance of the light elements [42,43,44,45,46,47,48,49,50,51]. However, since G is a dimensional constant, we calculate the abundance of helium synthesized during BBN in an explicit dimensionless way in this section, focusing on the dominant parts of the physics and neglecting some of the finer details.…”
Although it is well known that any consideration of the variations of
fundamental constants should be restricted to their dimensionless combinations,
the literature on variations of the gravitational constant $G$ is entirely
dimensionful. To illustrate applications of this to cosmology, we explicitly
give a dimensionless version of the parameters of the standard cosmological
model, and describe the physics of Big Bang Neucleosynthesis and recombination
in a dimensionless manner. The issue that appears to have been missed in many
studies is that in cosmology the strength of gravity is bound up in the
cosmological equations, and the epoch at which we live is a crucial part of the
model. We argue that it is useful to consider the hypothetical situation of
communicating with another civilization (with entirely different units),
comparing only dimensionless constants, in order to decide if we live in a
Universe governed by precisely the same physical laws. In this thought
experiment, we would also have to compare epochs, which can be defined by
giving the value of any {\it one} of the evolving cosmological parameters. By
setting things up carefully in this way one can avoid inconsistent results when
considering variable constants, caused by effectively fixing more than one
parameter today. We show examples of this effect by considering microwave
background anisotropies, being careful to maintain dimensionlessness
throughout. We present Fisher matrix calculations to estimate how well the fine
structure constants for electromagnetism and gravity can be determined with
future microwave background experiments. We highlight how one can be misled by
simply adding $G$ to the usual cosmological parameter set
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 its gravitational pressure to density ratio w. These energy forms include phantom energy (w < −1), cosmological constant (w = −1), domain walls (w = −2/3), cosmic strings (w = −1/3), normal matter (w = 0), radiation and relativistic matter (w = 1/3), and a previously little-discussed form of energy called "ultralight" (w > 1/3). A brief history and possible futures of Friedmann universes dominated by a single energy form are discussed. * Electronic address: nemiroff@mtu.edu † Electronic address: brpatla@mtu.edu 1 John A. Peacock, Cosmological Physics (Cambridge University Press, Cambridge, 1999).
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