"The Alternate View" columns of John G. Cramer

Published in the May-June-2017 issue of

This column was written and submitted 11/10/2016 and is copyrighted ©2016 by John G. Cramer.

All rights reserved. No part may be reproduced in any form without

Modern cosmology is not without its problems. One such
problem is that the Hubble constant (symbol **H _{0}**) has a lower
value when extracted from cosmic microwave background data then when extracted
from the red-shift recession velocities of "standard candle" stars and
galaxies. Another problem is that the value of the cosmological constant (symbol
, as calculated from quantum field theory, has a ridiculously large value as
compared to the value extracted from cosmic microwave background data. Two
recent theoretical works suggest fixes for these problems by hypothesizing
"leaks" in our universe in which dark matter is decaying and energy is
disappearing. We will start with Hubble constant problem.

The Hubble constant **H _{0}** is named for
Edwin Hubble (1889-1953), the astronomer who first discovered that the universe
is expanding. It is the cosmological measure of how the recession velocity of
distant stars depends on their distance, which is the rate at which the universe
is expanding. It has been best determined from the detailed structure of the
cosmic microwave background radiation, as measured by the data from the European
Space Agency's 2013 Planck mission. It can also be determined from direct
observation of the red-shift rate of recession of "standard candle"
stars and galaxies. Curiously, these two ways of determining

In July 2016 a group of Russian astrophysicists led by I.
Takachev of the Russian Academy of Sciences has published a paper in ** Physical
Review D** suggesting that this difference in

This brings us to the cosmological constant. Theoretical physics has two
major unsolved issues that are of great importance: the problem of quantum
gravity and the problem of the cosmological constant . Quantum gravity is an
expected but not-yet-existing theory, a theory yet to be formulated, that would
include quantum mechanics and gravitation seamlessly within the same theoretical
framework. Over the past few decades there has been much theoretical effort
aimed at unifying the quantum and the gravitational domains, but there is not
much to show for all of this work. One monumental indication of the problems
with such unification is that quantum field theory, our standard model for
quantum processes at the highest energies, appears to overestimate the energy
content of the quantum vacuum, what we call the cosmological constant , by 120
orders of magnitude (i.e., by a factor of 10^{120}).

The cosmological constant is related to the fraction of dark energy present in the universe. Analysis of Planck data indicates that the dark-energy fraction of mass-energy in the universe is about 68.3%. Because the dark energy content of a given volume of space increases as that volume increases, dark energy creates a "negative pressure" that causes the expansion rate of the universe to increase. If the cosmological constant actually had the value calculated from quantum field theory, its huge gravitational effects would have prevented the formation of galaxies, stars and planets in the early universe, and we would not be here to worry about the issue. This is the problem, the problem of the cosmological constant.

One possible way of dealing with the dilemma of the cosmological constant is to use a variation of general relativity called "unimodular gravity". Unimodular gravity was first introduced by Albert Einstein in 1919, four years after he introduced general relativity, in an unsuccessful attempt to connect gravitation to elementary particles. Unimodular gravity has slightly different space symmetry properties from standard general relativity. Nevertheless, it would appear, in general, to make the same observational predictions. However, it has two important differences. First, unimodular gravity has the property that vacuum fluctuations of the energy-momentum tensor, of the type that lead to the absurdly huge quantum-field-theory estimate of the cosmological constant, do not couple to gravity. This absence of coupling separates the energy present in quantum vacuum fluctuations from dark energy and the cosmological constant.

Second, energy and momentum are not strictly conserved in the framework of unimodular gravity. There is a "slow leak" in energy that can arise, for example, from space-granularity at the Planck scale. It is as if some "friction" within the particle interactions in the early universe causes energy to slowly leak away.

In theoretical physics, failure to conserve energy is normally viewed as a "show-stopper", an unacceptable flaw in any given theory. However, three theorists, T. Josset and A. Perez of the University of Toulon in France and D. Sudarsky of the Universidad Nacional Autonoma in Mexico have posted a preprint in December 2016 in which they consider unimodular gravity's failure to conserve energy to be a useful asset. In their scenario, the cosmological constant is not related to the energy present in quantum vacuum fluctuations. Instead, it represents the quantity of energy that has disappeared due to energy non-conservation during the evolution of the universe. The energy that has leaked away since the Big Bang is reflected in the dark energy that we now observe to be accelerating the expansion of the universe.

They implement this idea by using several foundational models (some rather peculiar) and produce estimates of the cosmological constant that are consistent with Planck mission data. They also show that in the evolution of the universe, the cosmological constant fairly rapidly reaches an equilibrium value and holds thereafter as the universe expands, consistent with the expectation that the cosmological constant is fairly constant in value.

If one takes this approach seriously, the implications are that (a) we should be using unimodular gravity instead of standard general relativity to analyze gravitational phenomena like neutron stars, black-hole accretion discs, and gravitational waves, and (b) the early universe burned through 2/3 of its energy in its early evolution, leaving behind the "scar" of the dark energy we see today.

It is not clear whether either of these theoretical extrapolations will withstand the test of closer scrutiny. However, from the point of view of science fiction these new ideas may offer opportunities. If dark matter can decay, it can perhaps also be annihilated on demand as an energy source. It is also interesting that there may be circumstances in which both energy and momentum are not conserved and can be created or destroyed. One can imagine a space drive based on unimodular gravity, in which thrust for propulsion is achieved by creating new momentum. And if energy is not conserved and can disappear into dark energy, perhaps it can also be made to appear in situations where energy is needed or useful or destructive (i.e., a "unimodular bomb").

Whenever cracks appear in the laws of physics, there may be opportunities for new physics and technology.

John G. Cramer's 2016 nonfiction book (Amazon gives it 5 stars) describing his *transactional
interpretation of quantum mechanics*, ** The Quantum Handshake -
Entanglement, Nonlocality, and Transactions**, (Springer, January-2016) is
available online as a hardcover or eBook at: http://www.springer.com/gp/book/9783319246406
or https://www.amazon.com/dp/3319246402.

**SF Novels by John Cramer: **Printed editions of John's hard SF novels ** Twistor**
and

**Alternate View Columns Online:** Electronic reprints of 212 or more
"The Alternate View" columns by John G. Cramer published in ** Analog**
between 1984 and the present are currently available online at: http://www.npl.washington.edu/av
.

**References:**

*Dark
Matter Decay:*

"Dark
matter decaying after recombination: Lensing constraints with Planck data",
A. Chudaykin, D. Gorbunov, and I. Tkachev, *Physical Review D***94**,
0223528 (2016); preprint arXiv:1602.08121
[astro-ph.CO].

*Unimodular
Gravity: *

"Dark energy as the weight of violating energy conservation", Thibaut Josset, Alejandro Perez, and Daniel Sudarsky, preprint arXiv:1604.04183v3 [gr-qc].