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<DIV>Compilation of various pieces of original remarks and
answers<BR>==============================================</DIV>
<DIV> </DIV>
<DIV>REMARK:<BR>... the cosmological constant with its usual Planck scale value
is present in<BR>Eq. 11 of the manuscript. Then, in going on to Eq. 24, a
subtraction is<BR>introduced (the square root of the metric determinant is
replaced by the<BR>square root minus one). This constitutes the usual ad hoc
subtraction of the<BR>bare cosmological constant.<BR> <BR>ANSWER:<BR>... at
first sight, the subtraction could seem ad hoc, but it is not quite so.<BR>(i)
Standard argument: it follows from generally accepted rules of quantum <BR>field
theory, e.g. in the path-integral formalism it corresponds to a
<BR>normalization of measure;<BR>(ii) Our argument: the "one" (constant)
corresponds to a contribution <BR>without any external lines, i.e. it does not
influence external fields by <BR>construction, and therefore it should be
excluded.</DIV>
<DIV> </DIV>
<DIV>REMARK:<BR>Following Eq. 24, the expression is expanded about the present
time, and<BR>a residual is obtained which vanishes today but which has a
similar<BR>time-dependence as that of dark energy. Hence, a connection with dark
energy<BR>is postulated. However, the expansion about a fixed time does not make
sense.<BR>There is nothing special about the present time which allows a
subtraction to<BR>be linked with the present time.</DIV>
<DIV> </DIV>
<DIV>ANSWER:<BR>In principle, we could expand about any fixed time. It is
only a technical assumption.</DIV>
<DIV>But to obtain present experimental values (e.g. density) we should
use present</DIV>
<DIV>experimental data (e.g. the present Hubble constant).</DIV>
<DIV> </DIV>
<DIV>REMARK:<BR>The purpose of this paper is to derive the contribution to the
vacuum<BR>energy of the universe from the single loop of a free quantum matter
field, in<BR>order to achieve better understanding of the cosmological constant
problems.<BR>Needless to say that this calculation has been approached
previously in many<BR>different ways. Authors adopt a very simple approach and
postulate that<BR>the mentioned quantum loop should be cut-off at the Planck
scale. Then,<BR>using the Schwinger-DeWitt expansion and taking only the
massless scalar<BR>field case they notice that only the a0 coefficient gives
contribution to the<BR>proper cosmological constant. Furthermore, they notice
that making the<BR>expansion of the metric around the flat background, the first
order term<BR>can be eliminated by the coordinate transformation and therefore
end up<BR>with the second order term which is a product of the squares of the
Hubble<BR>parameter H and the cut-off parameter, that is the Planck mass. As a
result<BR>they arrive at the induced cosmological constant which has a ”correct”
order<BR>of magnitude.</DIV>
<DIV> </DIV>
<DIV>ANSWER:<BR>Ideologically, our work consists of two parts. The first part
presents the<BR>very idea, whereas the second part presents a realization of
that idea. We do<BR>not insist that the realization proposed is the best and
final one.<BR> <BR>REMARK:<BR>Despite the above scheme looks appealing, it
has obvious weak points.<BR>For instance, if authors incorporate the field with
the mass M, the next<BR>Schwinger-DeWitt term a_1 will produce contribution
which will be a product<BR>of the squares of the mass M and the Planck mass.
Indeed, even for<BR>neutrino this contribution will be 60 orders of magnitude
greater than the<BR>”correct” value. The origin of this occurences is that the
scheme suggested<BR>by the authors is not correct from the quantum field theory
viewpoint. In<BR>fact, after the effective action is calculated, one can not
perform<BR>the expansion around the flat background, because the cosmological
constant term<BR>should be covariant, exactly as other terms in the effective
action of gravity.<BR>The explanation of the coordinate dependence of the linear
in H term is<BR>that the effective action of gravity is covariant and therefore
can not include<BR>terms which are odd in metric derivatives. The discussion of
this point has<BR>been given recently in gr-qc/0801.0216, where one can also
find many other<BR>references on the subject.</DIV>
<DIV> </DIV>
<DIV>ANSWER:<BR>A massive field with the mass M poses a problem. We can propose
the<BR>following two independent solutions of that problem: a “theoretical” and
a<BR>“technical” one.<BR>The “theoretical” solution would assume, rather a
widely accepted idea, that<BR>the mass of a particle is not a fundamental entity
but rather a derived one.<BR>In principle, all masses in the standard model are
generated via the Higgs<BR>mechanism. According to this point of view we could
legitimately assume<BR>that all masses should be neglected at this stage.<BR>The
“technical” solution instead would order us to treat the M^2 part<BR>of the a_1
coefficient analogously to the a_0 coefficient. In fact,
functional<BR>dependence on metric field, and only metric dependence matters, in
the both<BR>terms is identical. The only difference resides in coefficients and
<BR>consists in different powers of M and s (UV cutoff), i.e. we have <BR>M^0
s^-2 and M^2 s^-1, respectively. Therefore, actually the contribution<BR>of M^2
part of a_1 would be even less than that of a_0.</DIV>
<DIV> </DIV>
<DIV>REMARK:<BR>... the cosmological constant problem is much deeper than the
conflict between<BR>the calculation based on the Planck cut-off and the
observable value.<BR>At the first place this problem involves the fine-tuning
between the induced<BR>and vacuum components of the cosmological constant, as it
is explained,<BR>e.g., in [2].</DIV>
<DIV> </DIV>
<DIV>ANSWER:<BR>Firstly, the huge value of the vacuum energy density is a very
annoying<BR>feature in itself, and, it seems, it is desirable to explain it
somehow,<BR>independently of the further issue of the cosmological
constant.<BR>Secondly, there is an old and a bit controversial idea of induced
gravity.<BR>Intriguingly, it appears that it also yields a correct order of
magnitude of the<BR>coefficient in front of the Hilbert–Einstein gravitational
action. But one of<BR>the arguments against that idea says that the huge value
of the cosmological<BR>constant invalidates the very idea, at least in its
Sakharov’s version (demand<BR>one-loop dominance in Visser’s classification
[7]), i.e. when there are only<BR>induced terms, without bare ones. Now, the
tamed cosmological term and<BR>the Hilbert–Einstein gravitational action with
the purely induced coefficient<BR>(only) of a correct order of magnitude, both
would fit the Sakharov’s version<BR>of induced gravity idea consistently.</DIV>
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