COSMOLOGY: ON THE COSMOLOGICAL CONSTANT PROBLEM

ScienceWeek http://scienceweek.com
The following points are made by Thomas Banks (Physics Today 2004
March):

1) Since the mid-1980s, astronomers and astrophysicists have been
accumulating evidence that the expansion of the universe is
accelerating. The simplest way to incorporate that acceleration
into the description of cosmology, within the framework of
general relativity, is to add a cosmological constant (CC) term
to the Einstein equations. Before Edwin Hubble discovered the
expansion of the universe, Albert Einstein had originally
introduced such a term to obtain a static solution of his
cosmological equations. After the cosmic expansion was
discovered, Einstein considered his introduction of the CC to be
the greatest mistake of his career.

2) Many physicists were reluctant to consider the CC as an
explanation for astronomical data, because the value it would
need to have is ridiculously small compared to current
theoretical expectations -- some 10^(120) times too small.
Theorists interpreted that discrepancy as an indication that they
would one day find an elegant explanation for why the parameter
was exactly zero. Although some still cling to that hope, the
author concludes that observation has once again upset the
expectations of overconfident theorists.

3) The framework that gives rise to the enormous mismatch between
calculation and observation is called "effective quantum field
theory in background spacetime", or EFT for short. EFT always
involves a short distance cutoff scale below which the
approximations of EFT break down. The natural length scale
introduced by quantum gravity (QG) is the Planck length -- the
combination of Newton's gravitational constant, Planck's
constant, and the speed of light that has units of length. Naive
dimensional analysis and explicit calculations in EFT suggest
that the cosmological constant should be proportional to the
fourth power of the corresponding Planck energy of about 10^(28)
eV. That is 10^(120) times too big.

4) Any dynamical solution of the CC problem within EFT should
involve particles whose mass is on the order of the energy scale
of the CC, about 10^(-3) eV. There have been many published
attempts to resolve the problem by invoking such particles, but
all of them have failed. EFT does provide a loophole for
resolving the CC problem: Apart from calculable contributions,
there are contributions from energy scales higher than those
corresponding to the cutoff. In principle, those two types of
contributions can cancel, but from the EFT point of view, the
cancellation to 1 part in 10^(120) would be incredibly
fortuitous. The author believes that the resolution of the CC
problem does not involve some clever trick in EFT. Rather, QG
will force on theorists a fundamental revision of the rules of
the game. This belief is not yet the accepted dogma of the field.
There are as many ideas about how to solve the CC problem as
there are theorists who think about it.(1-5)

References (abridged):

1. G. 't Hooft, in Salamfestschrift: A Collection of Talks From
the Conference on Highlights of Particle and Condensed Matter
Physics, A. Ali, J. Ellis, S. Randjbar-Daemi eds., World
Scientific, River Edge, NJ (1994), available at
http://www.arXiv.org/abs/gr-qc/9310026; L. Susskind, J. Math.
Phys. 36, 6377 (1995)

2. J. H. Schwarz, in Quantum Aspects of Gauge Theories,
Supersymmetry, and Unification, A. Ceresole, C. Kounnas, D.
Loest, S. Theisen, eds., Springer-Verlag, New York (1999),
available at http://www.arXiv.org/abs/hep-th/9812037

3. T. Banks, in Strings, Branes, and Gravity: TASI 99, J. Harvey,
S. Kachru, E. Silverstein, eds., World Scientific, River Edge, NJ
(2001), available at http://www.arXiv.org/abs/hep-th/9911068; D.
Bigatti, L. Susskind, http://www.arXiv.org/abs/hep-th/9712072; O.
Aharony et al., Phys. Rep. 323, 183 (2000)

4. L. Susskind, in The Black Hole: 25 Years After, C. Teitelboim,
J. Zanelli, eds., World Scientific, River Edge, NJ, (1998),
available at http://www.arXiv.org/abs/hep-th/9309145; A. Sen,
Nucl. Phys. B 440, 421 (1995); A. Strominger, C. Vafa, Phys.
Lett. B 379, 99 (1996)

5. J. Bekenstein, Phys. Rev. D 7, 2333 (1973); 9, 3292 (1974); S.
Hawking Phys. Rev. D 13, 191 (1976)

Physics Today http://www.physicstoday.org

--------------------------------

COSMOLOGY: ON THE ANTHROPIC PRINCIPLE

The following points are made by Lawrence M. Krauss (Nature 2003
423:230):

1) The recognition, in the light of observational data, that
Einstein's infamous cosmological constant might not be zero has
changed almost everything about the way we think about the
Universe, from reconsidering its origin to re-evaluating its
ultimate future. But perhaps the most significant change in
cosmological thinking involves a new willingness to discuss what
used to be an idea that was not normally mentioned in polite
company: the "anthropic principle".

2) This idea suggests that the precise values of various
fundamental parameters describing our Universe might be
understood only as a consequence of the fact that we exist to
measure them. To paraphrase the cosmologist Andrei Linde, "If the
Universe were populated everywhere by intelligent fish, they
might wonder why it was full of water. Well, if it weren't, they
wouldn't be around to observe it!".

3) The reason that physicists have been so reluctant to consider
the anthropic principle seriously is that it goes against the
grain of current attitudes. Most physicists have hoped that an
ultimate physical explanation of reality would explain why the
Universe must look precisely the way it does, rather than why it
more often than not would not. Into the fray has entered James
Bjorken. In a paper (Phys. Rev. D 2003 67:043508) entitled
"Cosmology and the Standard Model", Bjorken proposes a new
"scaling" approach, based on well-established notions in particle
theory, for exploring how anthropically viable a small
cosmological constant might be.

4) The realization that an extremely small, but non-zero,
cosmological constant might exist has changed the interest of
physicists in anthropic explanations of nature precisely because
the value it seems to take is otherwise so inexplicable. In 1996,
physicist Steven Weinberg and his colleagues Hugo Martel and Paul
Shapiro argued that if the laws of physics allow different
universes to exist with a cosmological constant chosen from an
underlying probability distribution, then galaxies, stars and
presumably astronomers might not ultimately evolve unless the
cosmological constant were not much larger than the one we
apparently observe today.

Nature http://www.nature.com/nature

--------------------------------

Notes by ScienceWeek:

The "cosmological constant" is a mathematical term introduced by
Einstein into the equations of general relativity, the purpose to
obtain a solution of the equations corresponding to a "static
universe". The term describes a pressure (if positive) or a
tension (if negative) which can cause the Universe to expand or
contract even in the absence of any matter ("vacuum energy").
When the expansion of the Universe was discovered, Einstein
apparently began to regard the introduction of this term as a
mistake, and he described the cosmological constant as the
"greatest mistake of my life". But the term has reappeared as the
proposed source of apparent accelerated cosmic expansion.

--------------------------------

ON QUINTESSENCE AND THE EVOLUTION OF THE COSMOLOGICAL CONSTANT

The following points are made by P.J.E. Peebles (Nature 1999
398:25):

1) Contrary to expectations, the evidence is that the Universe is
expanding at approximately twice the velocity required to
overcome the gravitational pull of all the matter the Universe
contains. The implication of this is that in the past the greater
density of mass in the Universe gravitationally slowed the
expansion, while in the future the expansion rate will be close
to constant or perhaps increasing under the influence of a new
type of matter that some call "quintessence".

2) Quintessence began as Einstein's cosmological constant,
Lambda. It has negative gravitational mass: its gravity pushes
things apart.

3) Particle physicists later adopted Einstein's Lambda as a good
model for the gravitational effect of the active vacuum of
quantum physics, although the idea is at odds with the small
value of Lambda indicated by cosmology.

4) Theoretical cosmologists have noted that as the Universe
expands and cools, Lambda tends to decrease. As the Universe
cools, symmetries among forces are broken, particles acquire
masses, and these processes tend to release an analogue of latent
heat. The vacuum energy density accordingly decreases, and with
it the value of Lambda. Perhaps an enormous Lambda drove an early
rapid expansion that smoothed the primeval chaos to make the near
uniform Universe we see today, with a decrease in Lambda over
time to its current value. This is the cosmological inflation
concept.

5) The author suggests that the recent great advances in
detectors, telescopes, and observatories on the ground and in
space have given us a rough picture of what happened as our
Universe evolved from a dense, hot, and perhaps quite simple
early state to its present complexity. Observations in progress
are filling in the details, and that in turn is driving intense
debate on how the behavior of our Universe can be understood
within fundamental physics.

Nature http://www.nature.com/nature

--------------------------------

Notes by ScienceWeek:

Active vacuum of quantum physics: This refers to the idea that
the vacuum state in quantum mechanics has a zero-point energy
(minimum energy) which gives rise to vacuum fluctuations, so the
vacuum state does not mean a state of nothing, but is instead an
active state.

If a theory or process does not change when certain operations
are performed on it, the theory or process is said to possess a
symmetry with respect to those operations. For example, a circle
remains unchanged under rotation or reflection, and a circle
therefore has rotational and reflection symmetry. The term
"symmetry breaking" refers to the deviation from exact symmetry
exhibited by many physical systems, and in general, symmetry
breaking encompasses both "explicit" symmetry breaking and
"spontaneous" symmetry breaking. Explicit symmetry breaking is a
phenomenon in which a system is not quite, but almost, the same
for two configurations related by exact symmetry. Spontaneous
symmetry breaking refers to a situation in which the solution of
a set of physical equations fails to exhibit a symmetry possessed
by the equations themselves.

In general, the term "latent heat" refers to the quantity of heat
absorbed or released when a substance changes its physical phase
(e.g., solid to liquid) at constant temperature.

The inflationary model, first proposed by Alan Guth in 1980,
proposes that quantum fluctuations in the time period 10^(-35) to
10^(-32) seconds after time zero were quickly amplified into
large density variations during the "inflationary" 10^(50)
expansion of the Universe in that time frame.

ScienceWeek http://scienceweek.com

--
Best,
Frederick Martin McNeill
Poway, California, United States of America
mmcneill@fuzzysys.com
http://www.fuzzysys.com
http://members.cox.net/fmmcneill/
*************************
Phrase of the week :
We have entered the cell, the mansion of our birth,
and have started the inventory of our acquired wealth.
-- Albert Claude (1899-1983)
:-))))Snort!)
*************************

COSMOLOGY: ON THE COSMOLOGICAL CONSTANT PROBLEM

ScienceWeek http://scienceweek.com
The following points are made by Thomas Banks (Physics Today 2004
March):

1) Since the mid-1980s, astronomers and astrophysicists have been
accumulating evidence that the expansion of the universe is
accelerating. The simplest way to incorporate that acceleration
into the description of cosmology, within the framework of
general relativity, is to add a cosmological constant (CC) term
to the Einstein equations. Before Edwin Hubble discovered the
expansion of the universe, Albert Einstein had originally
introduced such a term to obtain a static solution of his
cosmological equations. After the cosmic expansion was
discovered, Einstein considered his introduction of the CC to be
the greatest mistake of his career.

2) Many physicists were reluctant to consider the CC as an
explanation for astronomical data, because the value it would
need to have is ridiculously small compared to current
theoretical expectations -- some 10^(120) times too small.
Theorists interpreted that discrepancy as an indication that they
would one day find an elegant explanation for why the parameter
was exactly zero. Although some still cling to that hope, the
author concludes that observation has once again upset the
expectations of overconfident theorists.

3) The framework that gives rise to the enormous mismatch between
calculation and observation is called "effective quantum field
theory in background spacetime", or EFT for short. EFT always
involves a short distance cutoff scale below which the
approximations of EFT break down. The natural length scale
introduced by quantum gravity (QG) is the Planck length -- the
combination of Newton's gravitational constant, Planck's
constant, and the speed of light that has units of length. Naive

dimensional analysis and explicit calculations in EFT suggest
that the cosmological constant should be proportional to the
fourth power of the corresponding Planck energy of about 10^(28)
eV. That is 10^(120) times too big.

4) Any dynamical solution of the CC problem within EFT should
involve particles whose mass is on the order of the energy scale
of the CC, about 10^(-3) eV. There have been many published
attempts to resolve the problem by invoking such particles, but
all of them have failed. EFT does provide a loophole for
resolving the CC problem: Apart from calculable contributions,
there are contributions from energy scales higher than those
corresponding to the cutoff. In principle, those two types of
contributions can cancel, but from the EFT point of view, the
cancellation to 1 part in 10^(120) would be incredibly
fortuitous. The author believes that the resolution of the CC
problem does not involve some clever trick in EFT. Rather, QG
will force on theorists a fundamental revision of the rules of
the game. This belief is not yet the accepted dogma of the field.
There are as many ideas about how to solve the CC problem as
there are theorists who think about it.(1-5)

References (abridged):

1. G. 't Hooft, in Salamfestschrift: A Collection of Talks From
the Conference on Highlights of Particle and Condensed Matter
Physics, A. Ali, J. Ellis, S. Randjbar-Daemi eds., World
Scientific, River Edge, NJ (1994), available at
http://www.arXiv.org/abs/gr-qc/9310026; L. Susskind, J. Math.
Phys. 36, 6377 (1995)

2. J. H. Schwarz, in Quantum Aspects of Gauge Theories,
Supersymmetry, and Unification, A. Ceresole, C. Kounnas, D.
Loest, S. Theisen, eds., Springer-Verlag, New York (1999),
available at http://www.arXiv.org/abs/hep-th/9812037

3. T. Banks, in Strings, Branes, and Gravity: TASI 99, J. Harvey,
S. Kachru, E. Silverstein, eds., World Scientific, River Edge, NJ
(2001), available at http://www.arXiv.org/abs/hep-th/9911068; D.
Bigatti, L. Susskind, http://www.arXiv.org/abs/hep-th/9712072; O.
Aharony et al., Phys. Rep. 323, 183 (2000)

4. L. Susskind, in The Black Hole: 25 Years After, C. Teitelboim,
J. Zanelli, eds., World Scientific, River Edge, NJ, (1998),
available at http://www.arXiv.org/abs/hep-th/9309145; A. Sen,
Nucl. Phys. B 440, 421 (1995); A. Strominger, C. Vafa, Phys.
Lett. B 379, 99 (1996)

5. J. Bekenstein, Phys. Rev. D 7, 2333 (1973); 9, 3292 (1974); S.
Hawking Phys. Rev. D 13, 191 (1976)

Physics Today http://www.physicstoday.org

--------------------------------

COSMOLOGY: ON THE ANTHROPIC PRINCIPLE

The following points are made by Lawrence M. Krauss (Nature 2003
423:230):

1) The recognition, in the light of observational data, that
Einstein's infamous cosmological constant might not be zero has
changed almost everything about the way we think about the
Universe, from reconsidering its origin to re-evaluating its
ultimate future. But perhaps the most significant change in
cosmological thinking involves a new willingness to discuss what
used to be an idea that was not normally mentioned in polite
company: the "anthropic principle".

2) This idea suggests that the precise values of various
fundamental parameters describing our Universe might be
understood only as a consequence of the fact that we exist to
measure them. To paraphrase the cosmologist Andrei Linde, "If the
Universe were populated everywhere by intelligent fish, they
might wonder why it was full of water. Well, if it weren't, they
wouldn't be around to observe it!".

3) The reason that physicists have been so reluctant to consider
the anthropic principle seriously is that it goes against the
grain of current attitudes. Most physicists have hoped that an
ultimate physical explanation of reality would explain why the
Universe must look precisely the way it does, rather than why it
more often than not would not. Into the fray has entered James
Bjorken. In a paper (Phys. Rev. D 2003 67:043508) entitled
"Cosmology and the Standard Model", Bjorken proposes a new
"scaling" approach, based on well-established notions in particle
theory, for exploring how anthropically viable a small
cosmological constant might be.

4) The realization that an extremely small, but non-zero,
cosmological constant might exist has changed the interest of
physicists in anthropic explanations of nature precisely because
the value it seems to take is otherwise so inexplicable. In 1996,
physicist Steven Weinberg and his colleagues Hugo Martel and Paul
Shapiro argued that if the laws of physics allow different
universes to exist with a cosmological constant chosen from an
underlying probability distribution, then galaxies, stars and
presumably astronomers might not ultimately evolve unless the
cosmological constant were not much larger than the one we
apparently observe today.

Nature http://www.nature.com/nature

--------------------------------

Notes by ScienceWeek:

The "cosmological constant" is a mathematical term introduced by
Einstein into the equations of general relativity, the purpose to
obtain a solution of the equations corresponding to a "static
universe". The term describes a pressure (if positive) or a
tension (if negative) which can cause the Universe to expand or
contract even in the absence of any matter ("vacuum energy").
When the expansion of the Universe was discovered, Einstein
apparently began to regard the introduction of this term as a
mistake, and he described the cosmological constant as the
"greatest mistake of my life". But the term has reappeared as the
proposed source of apparent accelerated cosmic expansion.

--------------------------------

ON QUINTESSENCE AND THE EVOLUTION OF THE COSMOLOGICAL CONSTANT

The following points are made by P.J.E. Peebles (Nature 1999
398:25):

1) Contrary to expectations, the evidence is that the Universe is
expanding at approximately twice the velocity required to
overcome the gravitational pull of all the matter the Universe
contains. The implication of this is that in the past the greater
density of mass in the Universe gravitationally slowed the
expansion, while in the future the expansion rate will be close
to constant or perhaps increasing under the influence of a new
type of matter that some call "quintessence".

2) Quintessence began as Einstein's cosmological constant,
Lambda. It has negative gravitational mass: its gravity pushes
things apart.

3) Particle physicists later adopted Einstein's Lambda as a good
model for the gravitational effect of the active vacuum of
quantum physics, although the idea is at odds with the small
value of Lambda indicated by cosmology.

4) Theoretical cosmologists have noted that as the Universe
expands and cools, Lambda tends to decrease. As the Universe
cools, symmetries among forces are broken, particles acquire
masses, and these processes tend to release an analogue of latent
heat. The vacuum energy density accordingly decreases, and with
it the value of Lambda. Perhaps an enormous Lambda drove an early
rapid expansion that smoothed the primeval chaos to make the near
uniform Universe we see today, with a decrease in Lambda over
time to its current value. This is the cosmological inflation
concept.

5) The author suggests that the recent great advances in
detectors, telescopes, and observatories on the ground and in
space have given us a rough picture of what happened as our
Universe evolved from a dense, hot, and perhaps quite simple
early state to its present complexity. Observations in progress
are filling in the details, and that in turn is driving intense
debate on how the behavior of our Universe can be understood
within fundamental physics.

Nature http://www.nature.com/nature

--------------------------------

Notes by ScienceWeek:

Active vacuum of quantum physics: This refers to the idea that
the vacuum state in quantum mechanics has a zero-point energy
(minimum energy) which gives rise to vacuum fluctuations, so the
vacuum state does not mean a state of nothing, but is instead an
active state.

If a theory or process does not change when certain operations
are performed on it, the theory or process is said to possess a
symmetry with respect to those operations. For example, a circle
remains unchanged under rotation or reflection, and a circle
therefore has rotational and reflection symmetry. The term
"symmetry breaking" refers to the deviation from exact symmetry
exhibited by many physical systems, and in general, symmetry
breaking encompasses both "explicit" symmetry breaking and
"spontaneous" symmetry breaking. Explicit symmetry breaking is a
phenomenon in which a system is not quite, but almost, the same
for two configurations related by exact symmetry. Spontaneous
symmetry breaking refers to a situation in which the solution of
a set of physical equations fails to exhibit a symmetry possessed
by the equations themselves.

In general, the term "latent heat" refers to the quantity of heat
absorbed or released when a substance changes its physical phase
(e.g., solid to liquid) at constant temperature.

The inflationary model, first proposed by Alan Guth in 1980,
proposes that quantum fluctuations in the time period 10^(-35) to
10^(-32) seconds after time zero were quickly amplified into
large density variations during the "inflationary" 10^(50)
expansion of the Universe in that time frame.

ScienceWeek http://scienceweek.com

--
Best,
Frederick Martin McNeill
Poway, California, United States of America
mmcneill@fuzzysys.com
http://www.fuzzysys.com
http://members.cox.net/fmmcneill/
*************************
Phrase of the week :
We have entered the cell, the mansion of our birth,
and have started the inventory of our acquired wealth.
-- Albert Claude (1899-1983)
:-))))Snort!)
*************************