The Opposite of Dark
Energy: Limits on
Ultralight Energy in the
Early Universe
Robert J. Nemiroff
Michigan Technological University
Abstract
Might energy species "lighter" than radiation, with w > 1/3, exist? A
dimensional expansion of the cosmological Friedmann Equation of
energy has a clear place for them. Such energies would affect the
universe much differently than dark energies, and so are here
dubbed "ultralight." As the universe expands, ultralight dilutes even
faster than light. Ultralight is not considered a candidate to make a
significant contribution to the energy budget of the universe today,
although ultralight might have affected the universe in the distant
past. In particular, the w=2/3 ultralight energy specie appears to
have relatively mundane physical attributes. A discussion of
properties and falsifiable attributes of ultralight is given. Limits on
the possible cosmological density of ultralight in the early universe
are determined from existing microwave background and primordial
nucleosynthesis data.
What energy species are there?
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w<-1: Phantom Energy
w=-1: Cosmological Constant
w=-2/3: Domain Walls
w=-1/3: Cosmic Strings
w=0: Atoms, molecules, dark matter
w=1/3: Radiation, relativistic matter
w>1/3: Ultralight (this work)
A Brief History of the Universe in
Terms of Energy Species
First w=1/3 energy dominated.
Then w=-1 energy dominated.
Then w=1/3 energy dominated again.
Then w=0 energy dominated for a while.
Now w=-1 energy is beginning to
dominate again.
Classic Friedmann Equation
As printed in many textbooks
Expanded Friedmann Equation
Includes more fun energy species
Sound Speed of Ultralight
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Assume energy species are perfect fluids
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w=P/ρ
Sound speed: cs=w1/2
For ultralight with 1/3 < w < 1 then cs<1
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Not unphysical
Sound speed is not imaginary (not true for
dark energy)
Sound speed can be less than speed of light
(not true for phantom energy)
Ultralight is not a scalar field
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Evolving scalar fields can have any
effective w=P/ρ
(Possible) examples of scalar fields
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Field that caused inflation
Quintessence fields that create dark energy
Higgs fields that give matter mass
Ultralight is stable
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not a scalar field
w does not evolve
Ultralight is not significant today
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Ultralight is not today’s dark energy
Ultralight dilutes more quickly than any
other energy specie including radiation
Ultralight might have been important,
even dominant, in the early universe
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We might not know since it is effectively gone
now
Nucleosynthesis Limits on
w=2/3 Ultralight
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Radiation dominated nucleosynthesis:
a ~ t1/2
Ultralight dominated nucleosynthesis:
a ~ t2/5
Ultralight dominated nucleosynthesis lasts
too long! Therefore, universe not
dominated by w=2/3 ultralight at z~3E8.
Extrapolating: Ωultralight < 10-11 today