This looks at the energy of the universe not just in terms of mass and radiation, but particles at particular temperatures. The average energy per bit is estimated, to give a measure of increasing information energy which creates effects, equivalent in magnitude to dark energy.

The Number of particles in universe is constant but the universe is increasing in volume. As gravity clumps matter together, stars form creating hot spots which increase the average energy per particle overall.

As the universe expands the amount of information required to pinpoint a particle, the ‘bit space’ increases, so the total amount of information increases.

The reduction in information density caused by expansion is lessened, because the total information energy increases. This creates a negative-pressure state parameter, equivalent to dark energy, which increases the rate of expansion.

Number of bits in universe, N_u = 10^91 bits.

http://www.mdpi.com/1099-4300/10/3/150/pdf

Looks at the average temperature per bit as the universe expands.
i.e. its high in baryons in stars and less in baryons in expanding, cooling universe.

(but what about bits required to describe points in universe that are a vacuum)

“the information equation of state was negative and equal to the dark energy
value wDE ~ -1.0 during the rapid star formation period 10>z>0.8, or for over one half of cosmic time.
Any negative equation of state, and specifically the value wi ~ -1.0, implies that information energy
must make a contribution to dark energy. ”

“The universe information energy total is given by the product of total universe information content
with the average information bit energy.”

“concentrated on information associated with baryons, ignoring the information energy density contributions from other universe components such as dark matter or the cosmic microwave background, CMB. Other components may have similar information bit contents but their information energy densities will not be significant as characteristic temperatures are orders of magnitude below stellar temperatures.”

“In the above estimation of wi during stellar evolution we have ignored the loss of entropy, or
reduction of information, resulting from the reduction in the number of microstates assumed to take
place on star formation as initially highly disordered matter collapses to form the more ordered
structure of a star” - Not a prob. There is no loss of entropy here, with ‘clumping under gravity’, see Penrose.

See also: http://arxiv.org/pdf/astro-ph/0603084v4

“4
We can compare this to the
situation at decoupling approximated by a single content-temperature product of 100% matter at
3×103K. Since characteristic information energy is directly proportional to component temperature
this corresponds to an increase by a factor of 1.13×102 in total universe information energy since the
time of decoupling if the information bit content remained constant. An increase in total
information bits, or entropy, is also expected over this period from the change in distribution of
matter over time, from the second law of thermodynamics with the number of degrees of freedom
increasing as a3. Classically, total information bit content increases as log2 (a3), corresponding to a
factor of 30 since decoupling when the universe was a thousand times smaller.
Thus our first attempt at a more realistic model provides both an increasing component weighted
average energy per bit by a factor of 1.13×102 and an increasing bit number by a factor of at least 30
since decoupling. Both factors contribute to an increase in total information energy to provide an
information energy density that falls less steeply than a-3, and hence provide a significantly negative
wi.”

If I read this correctly, a position in space implies a bit, rather than merely a position which is occupied by a particle.

“[total] information energy that increases with time due to the increase in average
temperature caused by stellar formation. This increase is linear with temperature and therefore
much greater than the reduction of information bit content which varies only logarithmically with
the lost degrees of freedom on star formation…reduction in bits per
particle on star formation was typically ~ 35%”

The information content of the matter and radiation in the universe has been estimated at N ~ 10^90 bits registered in quantum fields. [Lloyd, S. Ultimate physical limits to computation, Nature, 406, 1047-1054, (2000)].
There are also possible gravitational quantum state degrees of freedom that could take the total towards the absolute maximum possible limit of 10^120 bits set by the surface area of the universe expressed in Planck units according to the Holographic principle”. [Bekenstein, J.D., Information in the Holographic Universe, Scientific American, 289, 58-65, (2003). ]

Deriving this classically:
Number of bits in universe (N_u):
10^88 particles in universe (10^79 nucleons)
Size of universe 10^26m
Size of nucleon 10^-15m
i.e. 10^41 nucleons in length = 2^136
each particles co-ordinate requires a 136 bit binary number.
Therefore to describe classically (i.e. 3 space and 3 momentum co-ordinates), each particle requires: 816 bits, giving 8 x 10^90
N_u = 10^91 bits.

Equating average mass energy with equivalent average radiation energy we can estimate the average temperature of the universe, the average energy density of the universe (ρ_tot = average mass density, radiation constant, α = 4σ/c, σ = Stefan-Boltzmann constant = (pi^2k^4)/(60hbar^3c^2)):

ρ_tot(c)^2= α T_u^4

T_u = [(ρ_tot(c)^2)/α]¼

energy per bit, e_u = kT_u = [15ρ_tot(hbar^3c^5)/π^2]¼

This equation is same as that representing the energy of a cosmological constant, calculated by Peebles as 3meV (much lower than particles), for kT_u, 3meV =35K

The 35K average temperature comprises:
2.7K background radiation, cold dark matter and 0.4% of mass energy equivalent or 1.7% of actual mass in stars at 2 x 10^7K.

omega (w) is the equation of state parameter, relating pressure to energy density w_m= 0 for matter, and w_r = +1/3 for electromagnetic radiation, dark energy, negative pressure with w_de in the range: -1.2< w_de <-0.8.

“causes the total information energy to increase over time and thus provide a negatively valued equation of state parameter” why?