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New Physics at the quantum origin of
cosmic structure
Daniel Sudarsky
ICN- UNAM , Mexico
Work in collaboration with:
A. Perez (Marseille) y H.Sahlmann ( Penn State-Utrecht)
gr-qc/0508100, C QG 23, 2317 (2006).
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The last decade is considered as a big success,
for inflationary cosmology.
•
The Universe seems to be spatially flat (i.e. to have a total
density equal, or close, to the critical density)
• Theoretical predictions of the spectrum of primordial in homogeneities resulting from quantum fluctuations of the
inflaton.
• Observational data (COBE, Maxima, Boomerang, WMAP) in
agreement with such predictions. AMAZING!
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However
• There is something very odd in our understanding of the problem:
The Universe ``starts” as a homogeneous and isotropic space-time
(H&I), and there is a scalar field (the inflaton) which is in a vacuum
state, which is of course also H&I. How is it that we end up with a
situation that is not H & I, given that the dynamics preserves these
symmetries?
• Is this just the usual problem of measurement in Quantum
Mechanics? Not exactly! It is a critical version : The Schroedinger
Cat, but we are the Cat!
• Most people in the Field: “There is no problem”, but you will
receive different answers, which indicates some discomfort with
the view of the others. (Hartle : Need to extend QM for Cosmology)
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Let us consider the simple case of a harmonic oscillator in its
ground state.

• There are fluctuations of X with size , but this only means that if we
did measure X in an ensemble of identical systems, the resulting values
would have a statistical spread  .
• What can we say about one system in particular?
• What if we do not measure anything?, or if we chose to measure E?
• Can we interpret  as an indication that X somehow ``jumps” in such
interval? Jumps that occur in time?
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• Note that the most likely value of X is 0 and not  !
Decoherence
A B C …..
D E F …..
G H I …..
……………
A 0 0 ….
0 E 0…..
0 0 I ….
………
0 0 0…
0 E 0…
0 0 0…
……….
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Does focusing on quantum
correlations deal with the issue?
• Consider an EPR experiment with 1/2 spin
particles:
• Let N1.S1 & N2.S2 be two the observables. If
the initial state has J=0, the correlation in these
observables is Cos  = N1. N2, but the state
remains invariant under rotations, until a
measurement!
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You might feel uneasy to accept:
• Q.M. does not describe Our Universe, as it was never H&I (the
ensemble was) ( Only the superposition of many U is represented by
the H& I Quantum state) ( This is not normal QM!).
• Our Universe is Still H&I.
• Use of our limitations to make measurements to identify “irrelevant
DOF”,
Decoherence functional, that helps explain the lack of
H&I that makes us possible.
• That once we have a diagonal Density Matrix, we still must break the
H&I by selecting a specific element in the diagonal.
• Knowing that it does not matter when the Universe stopped being
H&I , but not being able to even address the issues ( when , why, due
to what..?).
• I’ll try to convince you that this is not ``JUST PHILOSOPHY”, and
that the early Universe offers the `Lab” where some of the issues
can be ( at least in principle) studied.
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Desiderata: A scheme that
• Permits the assignment to a Quantum state to the
system at ``every time”.
• Views QM as a theory about the description of the
system, and not just of our knowledge about it.
• Allows consideration of issues such as “When did
the H&I at such and such scale originate?”
• Take the view that the marriage of GR and QM
might involve changes in both! ( Penrose).
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The standard scheme augmented with the ``self induced
collapse” hypothesis.
• Collapse: Is the only known mechanism, capable of taking a symmetric
state into an asymmetric state while the dynamics preserves the symmetry.
The NEW PHYSICS lies in the fact that in this case we can not rely on an
external agent to induce the collapse.
• SEMICLASSICAL GRAVITY (corrected) ( Note that Gravity is treated
very differently than the matter) & coupled to the inflaton according to:
– Quantum State subject to :
• Motivation: “The QG DOF are not excited”, except at the jumps.
• Q reflects the jumps in the geometry that must accompany the collapse in
the state. It is assumed to vanish before and after the collapse.
• Goal: To extract characteristics of the NEW PHYSICS from the
observations.
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Pre and Post Collapse Cosmology
• Metric
• Scalar Field :
• Quantize
• Einstein’s Eqs.:
Introduce
&
and
where
and
which is 0 for ``slow roll”.
• Semi-classical version:
• The Fourier Decomposition :
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The state before & after the Collapse
Before the Collapse Y=0:
Assume that at time h the mode k collapses according to (Scheme 1) :
Where the x’s are random ( around 0 and with spread 1).
(Scheme 2: as above but with <y> =0
)
Then, after the collapse
we have:
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•
Study of the Observational
quantities
Metric perturbation :”the Newtonian potential ”(observed in
)
– Einstein’s Semi-Class Eqs.
– U(k) late time physics , F(k) depends on details of the post collapse state .
– The Quantity of interest is
• Is then the result of ``a random walk”.
• Its ``most likely” magnitude:
• In the continuum it becomes :
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The Structure of C(k)
• C(k) contains information about the collapse (through F)
– In scheme 1 we find :
– With
•
and
In general, we will have :
• Agreement with observations requires, =0 ó h(k)k
independent of k, (or very small corrections).
• If C(k) = 1 and U(k) is independent of k we find:
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• U(k) Contains information about late time processes (``reheating”, acoustic oscillations , etc). We take it here as
constant.
• The result is independent of RD iff C(k) is independent of
k , and = 0 (“slow roll”).
• This occurs if the time of collapse goes like 1/k.
• In order to obtain the exact standard result, it would require
a time of collapse such that C=1.
• In this way we find
• Where the “slow roll” parameter
– Could eliminate the need of ``fine tuning” (in Scheme of collapse
#2: <> =0 ):
– As the quantity : ( a˙/a ) <> / ˙ +
(Mukhanov) is constant in the regime of interest.
Y
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Points to Note
• The prediction refers only to the most likely value, but as
in any random walk we expect fluctuations. These can be
studied in
for different values of m. ( Cosmic
Variance). A fresh look at this might reveal information
about N: the number of steeps in the random walk: that is
the number of independent k’s in the sums.
• This scheme deals with various aspects :
– Clarifies ( at least to us) the use of statistics for one single Universe
( for each
).
– The transition is from one quantum state to another ( not to a
classical one or to an ensemble of states).
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– The collapse is self induced. This represents NEW PHYSICS possibly related with
Penrose’s ideas about Q.G.
– Observables selecting basis:
– The collapse occurs at
and /or
=c/k preferably late .
( I&R).
• OPEN ISSUES
– What triggers the collapse? .
– What is the physics that selects this basis?
– Are there other observable consequences of this new scheme?
• A Penrose Inspired Model : Collapse occurs when the energy of
gravitational interaction among alternatives reaches M PLANCK.
– Then
–
=c/k con c =
IT WORKS
( c is very small) !!
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Conclusions
• Something (related to QM) is missing in our
understanding of the origin of cosmic structure.
• Something like a self induced collapse is required to
take us from a H&I state to another one lacking such
symmetry.
• The present analysis seems offer a path to alleviate the
need of fine tuning .
• In our scheme there would not be Tensor Modes (GW)
contributions to the CMB anisotropies ( except
secondary ones)! The Ideas are testable.
• NEW PHYSICS might be there, just waiting to be
explored
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Why we feel we need something
more?
• We want to go from a symmetric (H&I) to an
asymmetric Universe.
• If we want to understand how did, the conditions
that allow our own existence, come about.
• Available approaches found in the Literature do
not seem to offer a fully satisfactory answer. (In
particular there is no room to address issues like
when and why did the universe trasit from H&I
state to one that is not).
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Is this the standard interpretational problem of measurement in
quantum mechanics?
We know QM offers sometimes multiple and incompatible interpretations
( the time of collapse in an EPR experiment). But it always offers at least
one self-consistent account which assigns the physical system a state at all
times.
• In our case there are many questions unanswered :
–
–
–
–
–
–
When does the measurement occur ?
Which is the measured observable ?
Which physical system causes the measurement?
What is its relation with our observations?
If there is no measurement how are H&I broken?
Each Fourier mode of the quantum field is essentially an harmonic oscillator
initially in its ground state. The fluctuation spectrum P(k) is related to this. How
is it, that our predictions for a single experiment ( one for each k), based on
expectation values work so well? Should we not expect fluctuations.?
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Other Problems of the existing
proposals
• Decoherence:
– The density matrix is diagonal in a single base. On the other hand the
density matrix remains H & I, and only when we do interpret it as
representing an ensemble, and NOT our Universe, that its elements
might lack that symmetry .
• Decoherence without Decoherence (*):
– That a given mode becomes small does not mean that it must be ignored (
its conjugate momentum would be big).
– A situation where the uncertainties are larger than the minimal ones
required by Q.M. can not be automatically considered as classical.
•
Multiples Universes Perspective:
– Ours was never H&I . The wave function in Q.M.. represents only
ensembles ?. What selects the base in which its elements are
described?.Each one of its elements is described classically or Quantum
Mechanically?
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There have been many proposals to address these issues; in
particular, the transition from a quantum to a classical regime
(Which should be accompanied by the breakdown of H&I!)
• Proposals :
•
– Decoherence
– Decoherence without
decoherence
– Stochastic Gravity
– Alternative to Inflation
•
Common Characteristic :
– Identification of expectation
values of quantum
uncertainties, with statistical
properties of an ensemble, an
element of which would be
OUR UNIVERSE. ¿How is it
described?
Other open issues:
– Is there a measurement? What causes it?
– What selects the observables involved?
When does it happen?
– How do we justify the use of statistics
when we have a single system?
– Why do we trust <0|(x)  (0)|0 >, but
not <0| | ( x )|0> ?
– Did or did not OUR UNIVERSE start in
|0> ?
– If not, how do we make predictions?
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