One of the outstanding problems in cosmology is the problem of the arrow of
time for the Universe. . Because physical processes are time symmetric ,
the existence of an arrow of time requires a boundary condition of low
entropy , a state of high order at the beginning of the Universe. This has
often led to claims of fine tuning. In this post I will be arguing that claims
of fine tuning are erroneous and that there exist a natural mechanism to
explain the low entropy required at the beginning of the Universe. This was
first pointed out by DR Vic Stenger in several of his books but I will be
re stating this with a somewhat different Mathematical formalism.
.
In John Gribbin's " In Search of the Multiverse" he writes
" After all , from the perspective of Bubble Universe in the metaverse,
the Universe is a black hole, and its surface area is then the minimum
size corresponding to the amount of information it contains."
Gribbin uses this fact to argue that a Universe can't be simulated by
anything smaller than a Universe , since anything smaller would lack sufficient
information content. However, in this post I will use this assertion to
provide an explanation for the low entropy boundary condition of the Universe.
( or any Universe based on the theory of inflation.)
Of course , strictly speaking, the Universe is not a black hole. Its
horizon is observer dependent, it has neither a singularity or tidal force ,
which would be the case for any black hole. However, as will be made
obvious every given Hubble volume contains the maximum information possible (
Gribbin's claim)
To illustrate this we start with the FRW equation , the homogenous
solution of Einstein's General relativity equations.
H^2= 8*pi*G*rho/(3*c^2) - k*c^2/a^2
Where H is the Hubble parameter, rho is the energy density, a is the
scale factor and k is the curvature term
By inspection we can see that the first term saturates the entropy bound
and the addition of the second term violates Bekenstein's bound. Nonetheless
, given an inflating Universe we can see that the second term falls off to
zero very rapidly leaving us ;
S_H= pi*c^5/(hbar*G*H^2)
A Hubble volume where effectively k=0 , a flat Universe. This result
agrees with a paper by Susskind and Ficshler which demonstrates that closed
Universes violates the Bekenstein bound.
*******************************************
Holography and Cosmology
Authors: _W. Fischler_
(mip://042dd378/find/hep-th/1/au:+Fischler_W/0/1/0/all/0/1) , _L. Susskind_
(mip://042dd378/find/hep-th/1/au:+Susskind_L/0/1/0/all/0/1) Holography and Cosmology
Authors: _W. Fischler_
(mip://042dd378/find/hep-th/1/au:+Fischler_W/0/1/0/all/0/1) , _L. Susskind_
(mip://042dd378/find/hep-th/1/au:+Susskind_L/0/1/0/all/0/1)
(Submitted on 4 Jun 1998 (_v1_ (mip://042dd378/abs/hep-th/9806039v1) ),
last revised 11 Jun 1998 (this version, v2))
Abstract: A cosmological version of the holographic principle is proposed.
Various consequences are discussed including bounds on equation of state
and the requirement that the universe be infinite.
Interestingly the late Heinz Pagels and Atkatz were able to demonstrate
that only closed Universes can tunnel into existence. A Chilean physicist
Victor H Carenas has used this point to postulate that inflation is a process
that occurs to protect the entropy bound.
*********************************************
Inflation as a response to protect the Holographic Principle
Authors: _Victor H. Cardenas_
(mip://042dd378/find/gr-qc/1/au:+Cardenas_V/0/1/0/all/0/1)
(Submitted on 3 Aug 2009)
Abstract: A model where the inflationary phase emerges as a response to
protect the Fischler-Susskind holographic bound is described. A two fluid
model in a closed universe inflation picture is assumed, and a discussion on
conditions under which is possible to obtain an additional exponential
expansion phase as those currently observed is given.
We can from this equation that upon the exit of inflation ( dH/dt
<<<< 0) the entropy density falls off rapidly giving us our low entropy
boundary condition. This is completely natural explanation for the low entropy
boundary condition for our Universe.
In addition in a normally expanding Universe , even in a Universe
undergoing accelerated expansion as ours is, the ever decreasing Hubble parameter
continues to make more and more room for additional entropy. An expanding
Universe containing non vacuum energy never runs out of "room" for the
creation of more disorder. However, as the Universe empties of non vacuum mass
energy the Hubble parameter becomes constant, a pure De Sitter space has no
arrow of time.
An interesting consequence of all this is that the local creation of
disorder is correlated with the global entropy bound. This is a strangely non
local correlation, which is a characteristic of the Holographic principle ,
the principle that defines the entropy bound of any given volume of space.