|Subject: The back-reaction
Date: Fri, 09 Aug 2002 19:30:49 +0300
From: Dimi Chakalov <email@example.com>
To: Robert Brandenberger <firstname.lastname@example.org>
CC: email@example.com, firstname.lastname@example.org,
email@example.com, firstname.lastname@example.org, email@example.com,
Dear Professor Brandenberger,
In your recent astro-ph/0208103 [Ref. 1], you mentioned your hypothesis that the back-reaction of cosmological fluctuations might lead to a dynamical relaxation of the cosmological constant [Ref. 2]. Please keep me in touch with your work on this issue.
I'm wondering why you didn't mention QSSC; see [Ref. 3] for a recent review. It seems to me that the challenges of vacuum energy are severe,
I'm trying to grasp the vacuum energy and the so-called curvature of spacetime along the lines suggested by C. Isham and J. Butterfield [Ref. 4]. I believe there is a fourth, completely unexplored, road to quantum gravity: "the power of the universe as a whole to organize itself" [Ref. 5]. Some details are available at
I suspect the problems with your back-reaction [Ref. 2] are relevant to the putative global mode of time pertaining to the universe 'as a whole' (please see the URLs above). Without it, you encounter the enormous, if not insurmountable, difficulties of uniquely defined energy density of the gravitational field at a given point,
and the "talk" between matter and geometry (J. Wheeler) sounds like a jabberwocky,
Am I wrong?
I will appreciate the opinion of your colleagues as well.
[Ref. 1] Robert H. Brandenberger. Principles,
Progress and Problems in Inflationary Cosmology. Mon, 5 Aug 2002 21:52:20
"As is illustrated in Fig. 2, at the time the microwave
radiation last scattered (which occurred when the temperature was about
a factor 10^3 of the present temperature), the maximal distance which light
could have communicated information starting at the Big Bang (the forward
light cone) is much smaller than the distance over which the microwave
photons are observed to have the same temperature (the past light cone).
This is the famous "horizon problem" of SBB cosmology. Within the context
of SBB cosmology it is also a mystery why the Universe today is observed
to be approximately spatially flat, since a spatially flat Universe is
an unstable fixed point of the FRW equations in an expanding phase. This
problem is called the "flatness problem". Finally, as illustrated in Fig.
3, within standard cosmology there is no causal mechanism which can explain
the nonrandom distribution of the seed inhomogeneities which develop into
the present-day large-scale structure. This constitutes the "formation
of structure problem".
"The inflationary Universe scenario  is based on the
simple hypothesis that there was a time interval in the early Universe
beginning at some time t_i and ending at a later time t_R (the "reheating
time") during which the scale factor is exponentially expanding.
"In extrapolating the evolution of cosmological perturbations
according to linear theory to these very early times, one is implicitly
making the assumption that the theory remains perturbative to arbitrarily
high energies, and that the classical theory of general relativity remains
the appropriate framework for describing space-time. Both of these assumptions
are clearly not justified.
"The Achilles heel of our current inflationary models
in without doubt the "cosmological constant problem". There is some as
of yet unknown mechanism which prevents the bare cosmological constant,
which in theories with quantum fields is predicted to be at least 62 orders
of magnitude larger than the observational limit (this number comes from
assuming the cancellation of vacuum energies on scales larger than the
supersymmetry breaking scale taken to be about 1TeV), from gravitating.
How do we know that this unknown mechanism does not also lead the transient
"cosmological constant" given by the potential energy of the scalar field
to be gravitationally inert, thus eliminating the basis of scalar field-driven
"In particular, it is possible that some of the problems are consequences of neglecting the intrinsically nonlinear structure of general relativity (see e.g.  for some speculations along these lines)."
( R.H. Brandenberger, Back reaction of cosmological
[Ref. 2] R.H. Brandenberger, Back Reaction
of Cosmological Perturbations. Invited lecture at COSMO-99 (ICTP, Trieste,
Sept. 27 - Oct. 2, 1999).
"It is well known that gravitational waves propagating
in some background space-time affect the dynamics of the background. This
back-reaction can be described in terms of an effective energy-momentum
tensor [x] . (...) In recent work [1; 2], we demonstrated that the back
reaction problem can be set up in a way which is gauge-invariant (under
linear coordinate transformations).
"Since the back-reaction of cosmological fluctuations
in an inflationary cosmology acts (see (14)) like a negative cosmological
constant, and since the magnitude of the back-reaction effect increases
in time, one may speculate (12) that back-reaction will lead to a dynamical
relaxation of the cosmological constant (see Tsamis & Woodard (4) for
similar considerations based on the back-reaction of long wavelength gravitational
waves). (...) Furthermore, we speculate that this dynamical relaxation
mechanism for [lambda] will be self-regulating.
"The most interesting result which emerges is that, in
an inflationary background, the effective energy-momentum tensor which
describes the back-reaction has the form of a negative cosmological constant.
The absolute value of the induced effective energy density grows in time
and, in a model with a long period of inflation, can become significant,
which leads to the speculation that the effect may lead to a dynamical
relaxation of the cosmological constant. However, the effective energy-momentum
tensor defined in this work describes the effect of fluctuations on the
homogeneous mode of the gravitational field. If the speculations in the
previous section are to hold up, the analysis must be extended to give
back-reaction effects on local quantities. Work on this issue is in progress."
[Ref. 3] J.V. Narlikar, R.G. Vishwakarma,
G. Burbidge. Interpretations of the Accelerating Universe. To appear in
the October 2002 issue of the "Publications of the Astronomical Society
of the Pacific".
"The usual tools of mathematical physics depend so strongly
on the real-number continuum, and its generalizations (from elementary
calculus 'upwards' to manifolds and beyond), that
it is probably even harder to guess what non-continuum structure is needed
by such radical approaches, than to guess what novel structures of dimension,
metric etc. are needed by the more conservative approaches that retain
manifolds. Indeed, there is a more general point: space
and time are such crucial categories for thinking about, and describing,
the empirical world, that it is bound to be ferociously difficult to understand
their emerging, or even some aspects of them emerging, from 'something
[Ref. 5] L. Smolin
(2001). Three Roads to Quantum Gravity. London: Weidenfeld & Nicolson,