Hello everybody so I would like to say a
few words about colleague and friend
Pierre Binetruy who very sadly passed away exactly five months ago after a long
struggle against a severe disease and as
Stavros mentioned during the first
day Pierre was initially a member of this
organizing committee, so it seemed to us
natural to devote some time during
this conference to honor the memory of
Pierre. He was really a driving force in the
community of particle physics and
of cosmology. I would like to present
you some highlights, I mean his career is
extremely rich so I'm just going to
focus on a few points but I would like to
emphasize that his career in some sense
is very instructive because it somehow
reflects the evolution of the community
in particle physics and cosmology and in
some respect he was able to anticipate
the big shifts in the community in
the science. So Pierre started his
career as what I would call a pure
particle physicist; he got his
PhD in 1980, his supervisor was Mary Kay
Gayard and later on from the mid 80s he
started to get interested by
cosmological aspects. He was really
interested by the interface between
particle physics and cosmology, so
this was at the time when he got a
position in France, a permanent position
in France in
Annecy and later on he moved to Orsay as
a professor and much later he
came here as a professor in Paris Diderot. His interest
into cosmology developed and he still
evolved in the last part of his career
because he got more and more interested
by gravitational physics and he played a
crucial role in France in respect to
this new field of physics somehow.  So let
me start with particle physics. 
He worked on many topics but I would
say that most of his research was
focused on supersymmetric
theories and he was interested by all
aspects of supersymmetric theories.
He was interested by the
phenomenology and the link with
experiments, so he was following
carefully the evolution of the
experiments, he was also interested by
really more fundamental aspects of
supersymmetry, he worked a
lot on supersymmetry breaking for
example the question of mass hierarchy
question of anomalous ones.
He was interested in how
superstring theory would appear in
terms of supersymmetric series at low energies and  you can see
as an example of rather fundamental work,
this was a physics reports given, written,
with Girardi and Grimm where he was describing a kind of geometric formulation of super
gravity coupling so it's a kind of very
formal work on super gravity
and finally he was also interested, as I
said, as I mentioned before, he was
interested in the interface between
particle physics and cosmology and he
worked more and more on this aspect. So
his triple interest can be
reflected in the title of his textbook which he published a few years ago
which is a extremely good text books if
you don't know about it and in the title
you see supersymmetry theory experiment
and cosmology so it's a good summary of
his triple interest into all
these aspects of
supersymmetric theories. So let's move
now to cosmology since I'm in front of
an audience of cosmologists and I'm a
cosmologists myself so I will spend more
time to try to give you a few ideas
about his works in this field. He
started to be interested by cosmology at
least in terms of publication in
the mid 80s and he wrote with Mary
Kay Gayard one of the first paper,
maybe the first I don't know, which was
interested in the construction of
inflationary model in the context of
superstring theory and this was one of
the first paper where they encountered
all the difficulties, you are aware
of them, to construct a good model of
inflation in the context of
superstring theory. Another important
work was his work on quintessence for
example so much later after the
discovery by the supernova of the
accelerated expansion of the universe
and at that time people were
working on quintessence models and the
idea was to play with potential values
potential of these quintessence models
and one form of potentials
which is an inverted power low potential
was suggested some time before by
Ratra-Peebles and Pierre tried to
construct supersymmetric models which
could give this kind of potential
with an inverted power. This
is a kind of very useful type of model
to have what are called tracking
quintessence models so this was in the
context of supersymmetric models.
Another work which had a very strong
impact on the community was his work on
what is called now D-term inflation, I think
it was called like this in the title of
the paper so this is a work with the Gia Dvali and the idea was to
consider inflationary models in the
context of super gravity models so if
you are in super gravity you can
build a model by introducing some
Kähler potential here some super
potential and from these two ingredients
you can construct a Lagrangian for the
scalar fields so you get the kinetic
terms for the scalar fields and
you have a potential and in general this
potential is what is called an F
potential so because this combination
here is an F term and this is a
potential which is derived which depends
as you can see from the Kähler potential
and from the super potential in the
derivatives. If you take the limit
where M Planck goes to infinity you
recover what what is called the global
supersymmetry limit where this potential
reduces to this very simple form and if
you try to play with this type of model
with the F term potential you are faced
with the following problem which is
called the ETA problem so I am not sure
you can see it clearly but ETA is
essentially one of the slow-roll parameters
which depends on the second derivative
of the potential so it's a dimensionless
parameter and if you want to have a good
model of inflation this small parameter
this parameter has to be small like the
first slow-roll parameter. The problem is
when you try to build a model of
inflation and if you take into account
the super gravity corrections you see
that the super gravity potential has
this exponential K over M Planck square
which appear here so when you try to
take into account this correction
from this exponential term you can
expand it and you get this extra term
here which gives in some sense an extra
contribution to the mass of the scalar
field. Here for simplicity I have
many scalar fields but I have reduced
to only one scalar field which is inflaton scalar field and I'm using the
canonically normalized form of it and
then what appears is that you get
a contribution to the mass of the scalar
field which is of the order of V over M
Planck square so this is written here in
so in the red sorry you then you don't
see very well but this contribution is
of the order of the Hubble parameter so
in some sense when you write when
you consider the effective mass of
the scalar field you get something which
is of the order of the Hubble parameter
and obviously you cannot satisfy the
condition that ETA is much smaller than
one. The idea of Pierre and with Gia
was to consider what is called the
Fayet-Iliopoulos  term, if you have a U(1) symmetry. So it means now you
have an extra term in the potential
which is called the D-term, hence the
name of D-term inflation and so
let's illustrate with a very
simple example which is given in
their paper so let's consider a
three scalar fields so the first scalar
field is not charged under U(1)
and the two other have a charge plus one
and minus one and under this U(1)
symmetry and this is the super potential
which is associated. Then you can compute
the F term potential which is of this
form and now there is this extra
potential which is the D-term potential 
which include this parameter Xi
which is the Fayet-Ilopoulos parameter
and now if you look at the minimum of
this potential, if you consider
that Phi 0 is fixed so Phi 0 is fixed
and you look for the minimum of this
potential you find that if Phi 0 is
bigger than a critical value then the
minimum corresponds to Phi plus and Phi minus are
our 0 and you get this value for the minimum of the potential. So here
Phi 0 is going to play the role of the
inflaton and you see that you have
found a kind of flat direction for this
Phi 0. So of course if you include the
1-loop corrections this flat direction
you get some effective potential
for Phi 0 so you get a potential for the inflaton, where you can have
slow-roll inflation and now you can check that the slow-roll conditions are not
spoiled anymore by the exponential term
which come from the the F term potential
because in this setup the F term
potential vanishes so it's a way to go
around this ETA problem just by using
another part of the potential
as the dominant part during inflation.
So there are some further refinement on
this issue in a more recent paper by Pierre and G. Dvali, Renata Kallosh and
Van Proeyen. So let me move
now to another topic where Pierre's work
had a very strong impact
and I was privileged to be associated to
this work with Pierre and this is
a work in branes cosmology. So this is in
the context of branes worlds and so the
basic idea of branes worlds,  there are
two ingredients two major ingredients
for branes worlds
the first one is you have extra
dimensions so it means you have a higher
dimensional space-time which is called
the bulk sorry for the colors but this
is the bulk here and inside this higher dimensional space-time you assume
that there is an object which is
called a brane so it's a lower
dimensional space-time and the
key assumption is that matter is
confined in this brane. So you see that
this is in contrast with Kaluza klein
theories, Kaluza-Klein theories you
have extra dimension but matter can live
everywhere in the bulk so in the brane
world matter is really confined in
a subspace. So brane worlds have been
extremely, have been an extremely active
topic because there are many motivations
to study branes worlds so there are
strings motivations because you find
branes called D-branes in the context of
of string theory, there is a model of
this type which is called the Horava
Witten theory where you have one extra
dimension, of course you have  the
link with AdS/CFT correspondence if
the bulk is AdS is something which was
discussed earlier during the conference;
in particle physics it can be a kind of
solution or another approach to the
hierarchy problem so widely electro weak
scale is much lower than the Planck
scale and in gravity can provide a new
type of compactification. So let me
go to the work we did and so
I met, I think I met Pierre for the first time
in 98,  it was in a kind of very small
conference in an isolated village in
South of France and he gave a very
interesting talk on Java written models
and at the end of the talk he said
in the future it would be interesting to study the cosmology in
such kind of setup and so I went  to
see him just after the talk and we
started to discuss and we started a kind
of long-term collaboration on this
problem and Cedric Deffayet, who was Pierre's PhD student at that time, joined
us for this work. So here is the
idea to study a brane which is inside
a five dimensional bulk space-time so
because we are studying the cosmology we
are assuming the usual symmetries of
isotropy and homogeneity in the three
ordinary dimensions so it means that 
the five dimensional metric with the
symmetries of this form where Y is the
extra dimension, so then now you can
solve, you can try to solve the five
dimensional Einstein equations. So where
you have the Einstein tensor and on the
right you have the energy momentum
tensor and now the energy momentum
tensor is mainly due to the presence of
the brane because all the matter is
concentrated on the brane which means
that this energy momentum tensor is a distribution; so here you have
a delta function so if the brane is
located at Y equals 0 you have a delta
function just just at the level,
at the location of the brane and inside
the brane because we are studying
cosmology we have the energy density and
the pressure which are just time
dependent functions and you can solve
the Einstein equations by using the
junction conditions, junction conditions
tell you how the jump of the
extension curvature tensor is related to
the matter content in the brane.
So at the end of some calculation, I
don't give you the details, you arrive to
a kind of Friedman equation but which is
very unusual it's a modified Friedmann
equation where on the right hand side
instead of having something which is
linear in the energy density you have
something which goes like the
square of the energy density in the
brane.  So it means that it leads to a
completely different evolution
cosmological evolution for example
between nucleosynthesis and today and
this is incompatible with all what we
know about cosmology. So the results the
main result of this paper was somehow negative because we concluded
that this kind of brane world was
incompatible with observations but so
this work appeared in May, and just a
few weeks afterwards there was a paper
which appeared which is a very famous
paper due to Randall and Sundrum so in
this paper they don't consider at all
cosmology so the promise is fully static
but the setup is very similar to our setup
because they look at a five dimensional
bulk, the main difference and the crucial
difference is that they assume that this
bulk is anti-de Sitter which means that
there is a cosmological constant which is
negative and then they assume that there
is some matter, some concentration of
matter in the brane which they called a
brane tension and there is a tuning
between the brane tension and this
cosmological constant negative
cosmological constant. And the main result of their work is to show that in this kind
of setup you recover standard gravity on
scales which are bigger than the length
scale associated with this negative
cosmological constant. But now you see
that it was very simple and natural
to extend our results just to use our
equation like this, so this one, to take
into account the fact that there was now
a cosmological constant in the
bulk, so it appears here, there is just
you just have to add something and now
if you assume that the brane content is
made of two components one component is the tension of the brane the same
tension as in Randall-Sundrum and in
addition to this tension you have this
cosmological the usual cosmological
energy density you see that you can just
expand this quadratic term, there will be a sigma b
square which is going to concern the
cosmological constant because of this
and then you have a linear term which
gives you back which is of the usual
form so here you recover the standard
Freidman equation and you have correction
which become important on in the very
early universe. So this was in some sense
one of the pioneering works in
the field of brane cosmology. So later
in, so of course I'm skipping many many
works by Pierre, I just want to stress a
few of them especially the ones I know
the best it's always easier but so
in the last part of his scientific career Pierre got more and
more interested in gravitational physics
and somehow he anticipated that
gravitational physics was going to open
up a completely new window for physics
what we see today explicitly and so he studied various aspects of , first he
decided to be involved in the LISA
collaboration and he pushed very
strongly so that friends would join this
LISA program and in particular APC,
his laboratory, so he also considered various aspect of
gravitational waves,
so some of his works were mentioned
yesterday by Chiara, for example
he studied the production of
gravitational waves from cosmic strings.
He also wrote a review with Chiara and
two other people about the cosmological
backgrounds of gravitational waves
and what LISA could tell us about,
about them. He also worked on primordial gravitational waves
from inflation in a kind of new
framework and he was also part of the
LisaPathfinder collaboration so his
name appears in the paper which was
mentioned twice yesterday about this
this fascinating results by
LisaPathfinder which did much much better than expected. So this is about
the scientific career of Pierre but Pierre
was not only a very bright physicist, he
was also a teacher, a remarkable teacher
and the kind of very inspiring teacher
which is able to, who is able to transmit
his passion to students so as he was a
professor in Orsay, he was a professor in
in Paris Diderot here and so he had
hundreds of students over the years but
very recently he decided somehow to have
a larger audience because he
wanted to share his passion not only
with university students but with
everybody and so he decided to invest
his time and energy to a MOOC on
gravitation, so an online course on
gravitation, for, aimed at the general
public. So they were two courses.
There was a French version and an
English version so the title is almost
the same except the English version there is an addition on
gravitational waves, so you see that it's
evolving in the title and I so I'm not
sure about the figure but I think at
least 90,000 people registered to this
MOOC so, this had a very big impact and for him
it was a kind of revolution that the
revolution to transmit knowledge not
only to a few privileged people in
university but everywhere in the world.
So teaching gravitation to a very
large public was also the reason for
this book a popular book on
gravitational waves which he published a
few years ago and there is an English
version which is going to appear soon.
Finally it was not only a physicist and
a teacher but he was also in some sense
an organizer. He played a crucial role
in trying to organize, trying to
give some structure in the French
research, even beyond the French research.
So I think it's a rare example of a
theorist who is ready to spend time
and energy to develop structures which
are going to help for science. And in
some sense it was a very crucial and
precious interface between the
administration with their own priorities and
the science, the scientists with the
scientific priorities. So one very
well-known example of Pierre activities
was the founding of working group which
was called GDR SUSY supersymmetry
to put together all the French physicist
working on supersymmetry, theorists
experimentalists, and to discuss together and to try to have new ideas.
I was never a part of this
GDR but I was told that it was
extremely fruitful and Pierre was
able to even to convince people to try
new directions, you know, he was able to
motivate people into trying new
things. So Pierre played also a
crucial role in the foundation of a new
lab which is across the road which is
APC and he was the director of APC for
eight years until twenty
thirteen.He also founded with George
Smooth who is here the PCCP Paris Center
for cosmological physics and with
Marie Verleure
who is also here as the main administrator
of this Center so of course I'm
not going to give you a list of all the
committee's he was a member of because it could take a few pages but I would like to
emphasize that he was really an expert
on all the intricacies of the French
system and just to illustrate this as a
kind of amusing note this is a slide
which I recovered, a slide that Pierre
prepared I think five years ago just to
try to explain to the lab the structure
of the landscape in the Paris era of all
the physics in the Paris era with the
universities the labs and the various
connection so I am not going to try to
explain to you this diagram but
Pierre was really an expert on this he
was able to draw it on a blackboard
in a few seconds and he was quite
impressive. And lately he really pushed
a lot to invest energy to invest funding
into gravitational
research so he was convinced from the early days of APC
the APC laboratory that gravitational
physics was going to become a central
topic and he wanted to involve France in
the special program on gravitational
waves because no lab at all
was involved in the space program
on gravitational waves so APC,
so he pushed APC to be involved in LISA
and LisaPathfinder and he was President
of the LISA France consortium, that unified
the nine laboratories and very recently
and this was approved one year ago and
it's starting to be moving, he was responsible for the foundation of a
new working group this time devoted to
gravitational waves. So as you can see
from these few examples and I just chose
a few examples, like somebody else could
have chosen completely different examples, you can see that Pierre managed to lead
several, in some sense, several successful
careers in parallel and of course
unfortunately for us, he crossed the horizon five months ago much too early and this
is a great loss for his friends for his
colleagues and the scientific community
so I was slightly comforting idea, if
you, because he died very young if you
count in terms of proper years, but if, we
like physicists to define some kind of
effective parameter, so if you define the
 effective number of careers that
Pierre had, you see that it's
significantly more than one and you can
multiply by the number of years and so
he lived many many years in this respect.
okay but and moreover I'm sure that
several elements of his legacy are going
to survive in the future and be able
to make a big impact
thank you very much
