Accelerating Expanding Universe: Reality or Illusion?

Hubble's Law collects observations of redshifts of the light from galaxies suggesting that the Universe is expanding away from the Earth at speeds proportional to the distance from the Earth. The Nobel Prize in Physics was awarded work showing larger expansion suggesting an Accelerating Universe with redshifts seemingly corresponding to superluminal speeds at the edge of the observable Universe. 

Speculations about an enormous amount of dark energy as driver of the acceleration expansion were made but, nothing is known about this type of energy supposed to make up 68% of the total energy of the Universe. 

Other speculations seek to solve the mystery generated by the observations of large redshifts by suggesting they are just illusions resulting from measurement techniques. Like the apparent decrease of size with view distance.

Let us make a connection to Many-Minds Relativity where velocities are computed from observed Doppler effects and includes a law of adding two velocities $v$ and $w$ from composite Doppler effects of the form 

• $v+w+vw$ 

as a variant of Einstein's velocity addition law of Special Relativity. Here $v+w+vw$ is the velocity perceived by an observer X moving with velocity $v$ with respect to another observer Y observing the velocity $w$. 

The computed velocity is seen to be larger than the standard $v+w$, and will increase with increasing number of composite Doppler shifts, which could be connected to increasing distance. In the limit that gives from a nominal real velocity $v$ a computed velocity $\exp(v)$ suggesting an expansion of the Universe which is exponentially increasing with distance. We understand that this is an illusion depending on the way we compute velocities from composite Doppler shifts.

So, we have two possibilities of explaining observations of an expanding Universe: 

1. dark matter
2. illusion. 

Which is more reasonable? To believe in 1. requires a massive addition to the total energy of the Universe, a big deal. To believe in 2.  requires simply some understanding of how velocities are computed from redshift observations, no big deal. Your choice.    

Hubble's Law and Exponential Expansion vs Many-Minds Relativity

The Hubble law

• $v=Hx$ 

with $x$ distance to a galaxy with velocity $v=\frac{dx}{dt}$ vs the Earth with $t$ time and $H$ Hubble's constant, is the most celebrated law of cosmology. Solving the equation $\frac{dx}{dt}=Hx$ with $x=1$ for $t=0$, we have

• $x(t)=\exp(Ht)$  and $v(t)=H\exp(Ht)$ for $t\gt 0$. 

The galaxy thus appears to be receding from the Earth with both distance and velocity increasing exponentially in time. The Universe thus appears to be expanding exponentially. What is driving such a violent expansion?

Newton's 2nd Law takes the following form in Many-Minds Relativity MMR:

• $\frac{dv}{dt} = (1+v)F$,

where again $v$ is velocity and $F$ force and mass is normalised. With $F$ a positive constant the solution with $v(0)=0$ for $t=0$ is given by 

•  $v(t)=\exp(Ft)-1$.

We thus see an exponentially increasing velocity from a constant force in MMR. We compare with the standard form of Newtons 2nd law $\frac{dv}{dt}=F$, which gives $v(t)=Ft$  with much slower  linear increase in time in the case of a constant force.

In MMR a constant expansion force thus appears to be compatible with observations of exponential expansion. In a Big Bang scenario it is thinkable that such a constant expansion force was active over an initial period of time resulting in observations of exponential expansion later.  

We thus find exponential expansion in both observations and MMR with constant expansion force. 

Is this a coincidence?

Of course, exponential expansion appears to require massive dark energy, but nobody knows anything about this new form of energy.

In MMR, the exponential expansion appears as an optical effect from using (composite) Doppler shifts to determine velocities, and so the exponential expansion could be more illusion than reality. If so, less dark energy would seem to be needed which could easy the task of finding an explanation of its apparent presence.   

Nobel Prize of Dark Energy

By a funny coincidence my previous post Hubble Law Without Dark Energy appears to have triggered the 2011 Nobel Prize in Physics for

• the discovery that the Universe is expanding at an ever-accelerating rate

with the following motivation:

• The discovery came as a complete surprise even to the Laureates themselves.
• If the expansion will continue to speed up the Universe will end in ice.
• The acceleration is thought to be driven by dark energy, but what that dark energy is remains an enigma - perhaps the greatest in physics today.
• What is known is that dark energy constitutes about three quarters of the Universe.
• Therefore the findings of the 2011 Nobel Laureates in Physics have helped to unveil a Universe that to a large extent is unknown to science.
• And everything is possible again.

But to introduce a completely new phenomenon of dark energy as explanation of the seemingly accelerating expansion of the Universe, does not seem to help understanding much, if understanding is what science is about.

In the previous post I reflected over a simple idea to explain the observations, based on expansion by inertia from an initial inflated state resulting from a Big Bang expansion driven by a pressure increasing with distance caused by a heat source creating a velocity also increasing with distance. Observations made today would then represent space-time cuts with again velocities increasing with distance. The velocity distribution would then be set by the pressure distribution in the Big Bang expansion determined by the specifics of the heat source, without any need to introduce new forces (beyond inertia) of unknown nature.

Note that the observations of more distant (dimmer) far away galaxies than expected behind the Nobel Prize, would correspond to a sublinear increase of velocity with distance at the start of the inertial expansion after Big Bang expansion, which would not as such appear to be surprising. The surprising observations may thus in fact not be so surprising, which is surprising.

Remember what Einstein adviced:

• Everything should be made as simple as possible, but not simpler.

Hubble Law Without Dark Energy

The expansion of the Universe observed by 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 x 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).

The conclusion is similar in the case of a finite speed of light causing a linear shift in time of observation depending on the distance to the origin.

We have thus derived a Hubble's 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 expansion with constant velocity and heat forcing put to zero.

The apparent increase of expansion velocity with distance is here not an effect of a permanent accelleration, but instead a reflection of the linearly increasing velocity of an initial expansion under linearly increasing pressure compatible with a constant heat source.

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.

In the case (ii) there is no need to introduce any dark energy to explain Hubble's Law and since (ii) is consistent with observation, by Ockham's razor, it seems to be preferable. We understand that (ii) is a universe with large scale structure governed by inertia and not gravitation, a universe described by Newton's 2nd law.

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 a velocity V(r,t) = exp(rt) which is superlinear in the distance r in accordance with observations of accelerating expansion.

Many-Minds Relativity: Hubble's Law

The American astronomer Edwin Hubble discovered in 1929 that far away galaxies seem to recede from the Earth with a velocity V approximately proportional to their distance D according to Hubble's Law:

• V = H x D ,

where H is the Hubble constant (about 70 km/s/Mpc with 1 Mpc about 3 million light-years). The velocity V is computed from observed redshift and the distance D is determined from observed luminosity. Galaxies with greatest observed distances (about 13-14 billion light-years) appear to recede with a velocity greater than the speed of light.

Hubble's law is a corner stone in the Big-Bang theory with the Universe being initiated in a very hot dense state and then expanding under high pressure.

Let us now see what many-minds relativity has to say about Hubble's law. We recall Newton's law in its many-minds relativity form:

• 1/(1+V) dV/dt = F ,

where V(t) is the velocity of a unit mass moving under the action of a force F and we assume the velocity of light is normalized to 1. We get if F is a (positive) constant, for t > 0:

• V(t) = exp(Ft) - 1
• D(t) = exp(Ft)/F - t

for the velocity V(t) and position D(t) of a galaxy starting from rest at t = 0. We see that for t >> 1

• V/D ~ F

which looks like Hubble's Law if F = H.

But how can we motivate that F = H? What is this mystical force F (directly connecting to equally mystical dark energy) causing the Universe to expand?

Note that with the usual Newton's Law dV/dt = F, we would get V/D = 1/t which does not conform with Hubble's Law. Neither does Einstein's relativistic form with 1/(1 + V) replaced by 1/ the square-root of 1 - V^2.