Accelerating Expansion Without Dark Energy?

Nobel Prize for the discovery of something of which nothing is known

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Today the 2011 Nobel Prize in Physics is awarded to Saul Perlmutter, Brian P. Schmidt and Adam G. Riess

  • for the discovery of the accelerating expansion of the Universe through observations of distant supernovae.

To explain the observed acceleration a new mystical form of energy named dark energy has been postulated. It appears that the 2011 Nobel Prize is given for the discovery of something of which nothing is known, not even that it exists!

The Swedish State Television presents the event as a

  • celebration of something we do not know anything about,

where “we” apparently includes the awardees.

As skeptics let us ask if there is an explanation of the observed acceleration which is natural and does not require any new form of energy of which nothing is known? Let’s go:

The expansion of the Universe observed by Edwin Hubble is commonly connected to a mystical form of dark energy (and/or to a mystical cosmological_constant of relativity theory).It is natural to ask if Hubble’s observation can be explained by Newtonian mechanics without mysticism?

Hubble observed that far away galaxies appear to recede from the Earth with a velocity V proportional to distance D according to Hubble’s Law:

  • V = H \cdot D

where H is Hubble’s constant (about ~ 70 km/s per 1 Mpc ~ 3 million light-years).

Let us assume a Big Bang scenario with the Universe starting out at time T_0 = 0 in a hot dense uniform spherical initial state centered at the origin of a Euclidean coordinate system, and then expanding under a pressure gradient force increasing linearly with the distance to the origin. This could be the force from a (quadratic) pressure satisfying a Poisson equation with constant right hand side connecting to a heat source of constant intensity.

Allowing the Universe to expand from rest under this force for a certain length of time T_1 will bring it into a state with velocity V(r,T_1) increasing linearly with distance r to the origin, that is in accordance with a Hubble Law V(r,T_1) = H_1 r.

Assume now that after time T_1 the expansion force disappears, reflecting that the heat source is no longer active. The Universe will then expand with each galaxy having a constant radial velocity increasing linearly with the distance to the origin at any given time.

Assume now that the galaxies of the Universe visible at a time T > T_1 are observed by an observer at the origin measuring velocity through red-shift and distance by brightness.

Assuming first an infinite speed of light, the observer will thus record

  • D(r,T) = r + V(r,T_1) (T-T_1) V(r,T) = V(r,T_1) = H_1 r

for a galaxy at distance r at time T_1. Thus

  • V(r,T)/D(r,T) = H_1/(1 + H_1(T-T_1)) = H(T),

for a galaxy at distance r,which is again a Hubble Law (recorded at the specific time T), with a modified Hubble constant H(T).

In the case of a finite speed of light the time T has to adjusted to T -\frac{r}{c} with c the speed of light with a corresponding Hubble constant H(T-\frac{r}{c}).

Since H(T) increases with decreasing T, this gives the impression of a Hubble constant increasing with distance r as if the expansion of the Universe is accelerating.

We have thus derived a Hubble Law which is consistent with a Newtonian Big Bang scenario with an initial expansion phase from a uniform hot dense state with accelleration from a pressure force from a constant heat forcing, into a state with expansion velocity proportional to distance, which is then maintained under continued inertial expansion with constant velocity and heat forcing put to zero.

The Hubble constant in this simple model governed by inertial effect is increasing with increasing distance without any forcing, thus without any need to ad hoc introduce some new mysterious dark energy.

Notice that the fact that the observer can see only visible galaxies, makes it impossible to detect if the apparent increase of velocity with distance is the effect of (i) a constant contiunued accelleration or (ii) an accelleration during an initial expansion phase after which the expansion force is shut off.

A similar conclusion is obtained with the Newton law of many-minds relativity of the form

  • 1/(1+V) dV/dt = F,

which allows the initial expansion to be exponentially fast with (assuming F(r) = r) V(r,t) = exp(rt) being superlinear in r, which is compatible with observations of accellerating expansion.

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