P. Antilogus- Measurement of the cosmological constant

8/3/2019 P. Antilogus- Measurement of the cosmological constant

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Measurement of the cosmological constantP. Antilogus a

aIPN Lyon , France

The type Ia Supernovae (SN Ia) provided the first direct indication of a non zero cosmological constant ().After an introduction of the scientific context, the status of the cosmological constant measurement will bereviewed. The usage of SN Ia to probe the vacuum energy and more generally to study the dark energy seems quitepromising. In a close future SN Ia should provide precise and well controlled measurements. The program nearbySuperNova Factory (SNFactory), centered on detailed studies of400 nearby SN Ia, and the proposal SuperNovaAccelerating Probe satellite (SNAP), which should be a break through in the study of the acceleration of theUniverse expension, will be introduced.

1. Introduction

The concept behind the expression cosmolog-ical constant changed quite a lot since its in-troduction in general relativity. Today, followingthe point of view of S.Weinberg, the low value ofthe cosmological constant appears as the bone inour throat not only for cosmology but also forelementary particle theory. The reason for suchpoint of view will be briefly explained in the firstpart of this note.

The type Ia supernovae (SN Ia) will be the coreof the second part of this document. SN Ia ap-pear today as the most promising probe to studythe cosmological constant/acceleration of the uni-verse expansion. Ground based measurements af-ter their first success can pretend to reach a pre-cision of 10% on the measurement of . To in-vestigate further the enigma of its value, not onlywork on the statistic will be needed but specificwork on the systematic will be required. Twoprojects introduced here, the nearby SNFactoryprogram and the SNAP project, will in a closefuture pursue these objectives. Before the end of

the decade, space observation using the SNAPsatellite, let us expect a break through in theunderstanding of the dark energy, energy at thesource of the observed acceleration of the universeexpansion.

2. From the cosmological constant to the

dark energy

In the original version of the general relativ-ity, published by A.Einstein in 1915, the universehappened to be dynamic : at large scale the speedof the objects are not small compared to the speedof light. At first A.Einstein did not accept theidea of a non static universe. He proposed in 1917to weaken one of the original requirement of itstheory which was to find back, in a weak field, the

Newton gravitational law. Having this constrainsatisfied only at small scale ( at the scale of thesolar system ), he was able to introduce the cos-mological constant : the matter density, whichpush toward a gravitational collapse, can be bal-anced by an uniform density /4G, allowing,if has the right value, the universe to be static.

DeSitter in the following years proposed astatic cosmological model with no matter at all.This was somehow unexpected from the point ofview of Einstein which was considering that themass distribution of the universe was setting theinertial frame.

The work of V.Slipher between 1910-24 endedup to the conclusion that spiral nebula (= todaygalaxies) can have a strong reddening z = /,up to 6% in his work, indicating than astronom-ical objects are not static. E.Hubble between1920-30 with the Palomar telescope discoveredgalaxies and the universe expansion, v = H0r :


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the universe is not static.Quite before this final prove, in 1923, Einstein

in a letter to Weyl withdrew the cosmologicalconstant : If there is no quasi-static world, goodbye cosmological constant . And in the 50s atthe end of his life Einstein said: the cosmologicalconstant is the biggest blunder of my life.

So exit the cosmological constant? From apure general relativity argument may be. Butin the 60s with the development of the quantumfield theory a new concept appeared to play amajor role in physics : the vacuum energy.

This new energy density, as all sources of en-ergy density, should be taken into account in gen-eral relativity. For the vacuum the energy densitytensor has the following form :

< T >= < V > g

which gives a term with the same propriety thanthe original Einstein cosmological constant term:

< V >= =

8G

If this new cosmological constant seems im-possible to avoid, the difference between its ex-pected and observed value is today one of the

major problem of the fundamental physics [1].The present cosmological observations imply

|| 1029 g/cm3

103eV

4 1047GeV4

In quantum field theory the fundamentalmode/vacuum of any field ( the zero pointof an harmonic oscillator ) diverges. Consider-ing that the physics is understood up to a givencut-off/scale kmax 1 , we get for the sum of all thenormal modes of a field : || k4max/16

2.Takingkmax at the Planck scale, gives

|| 1092 g/cm3

1019GeV4

1074GeV4

120 orders of magnitude bigger than what is ob-served. Taking the electroweak scale instead still

gives a discrepancy of 55 orders of magnitude.Everything looks like if the cut-off which shouldbe considered is only of the order of 0.001 eV.Something has to be completely wrong in the

1An optimistic choice for this cut off is the Planck

scale 1019GeV. Nevertheless, the Electroweak scale

100GeV well understood today seems the lower value

than could be considered for this cut-off.

above discussion. Nevertheless the Casimir effect,which is sensitive to the energy difference between

two kinds of vacuum, shows the reality of thezero point energy.

Since the 70s and the success of the elec-troweak theory, the situation becomes even morestriking. On top of the harmonic oscillator con-tribution to the vacuum energy, any broken sym-metry, through the potential energy difference be-tween the broken-unbroken symmetry, will gen-erate a contribution to the vacuum energy. Forthe broken symmetry in the Standard Model, weexpect a contribution of the order : || 1027g/cm3 (200GeV)4 ending to an extra 56orders of magnitude of discrepancy with what isobserved.

Today the concept of Dark Energy has beenintroduced to generalize further the idea of cos-mological constant : it corresponds to any energydensity, , related to its associated pressure, p, byan equation of state p = w with 1 w < 1

3.

Such energy density, from the general relativitypoint of view, will contribute at some point toaccelerate the universe expansion. The cosmolog-ical constant ( or vacuum energy ) corresponds tothe simple case w =-1.

Recent theoretical developments consider a

possible variation/dynamic of the cosmologicalconstant/w, like in quintessence model where ascalar field goes slowly with time to its minimum.

3. The measurement of

3.1. Results overview

In the 90s big progresses have been made incosmological observations to measure the matterand the vacuum energy densities 2

DASI/BOOMERANG/MAXIMA...:3oK-Cosmic Microwave Background,tot = M + = 1.

+.06.05

Dark matter: galaxies cluster + other,M = 0.4 0.1

SCP (1998) : supernovae at high z, = 0 a 99 % cl.

2M and are respectively the matter and the vacuum

energy density divided by the critical density3H

2

0

8G


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No Big Bang

1 20 1 2 3

expands forever

-1

0

1

2

3

2

3

closed

recollapses eventually

Supernovae

CMB

Clusters

mass density

vacuu

me

nergydensity

(cos

mologicalconstant)

open

flat

Perlmutter, et al. (1999)Jaffe et al. (2000)Bahcall and Fan (1998)

Figure 1. Constrains in the M/ plane fromthe available observations. It can be noticed thanthe constrains from the CMB and the SN Ia arecomplementary as they gives orthogonal con-tour : the CMB is sensitive to M+ and theSN Ia, with the present observed range in z, toM-.

The universe is weighted with some good preci-sion. Today the cosmology enter in the field of themeasure (see figure 1). It will allow beyond theconcepts of Cosmological Constant, M and to study in detail the dark side of the universe: the Dark Matter and the Dark Energy.

3.2. The measure with SN Ia

The apparent/observed luminosity f of an as-trophysical object is related to its intrinsic lumi-nosity L by f = L/4d2L , where dL, the lumi-nosity distance, is a function of the cosmologi-

cal parameters H0, M, and the redshift z.Thus sources of known constant intrinsic lumi-

nosity, also called standard candle, can be usedto measure relative distances. If at the same timered shift measurements are performed M and can be accessed. Only for the extraction of H0 thevalue of the intrinsic luminosity itself is required.The SN Ia as explained in the next section aregood standard candle. Since the first results pre-sented in 1998-1999 (see figure 2), with the firstindication of > 0, they emerged as the mostpowerful tool to measure the acceleration of theuniverse expansion.

Figure 2. Magnitude ( log dL) versus redshiftfor 4 kinds of flat universe (tot= 1) compared tothe 42 high-z SN Ia of the SCP published sample[2]. The data are in favor of a positive value for: for a flat universe = 0 is excluded at 6 .

3.3. The SN Ia

There is two distinct processes at the origin ofsupernovae explosion :

the gravitational collapses of the core of ared giant ( SN II ) or of a super-giant starwithout hydrogen ( SN Ib , SN Ic ) into aneutron start.

the nuclear explosion of a white dwarf.


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The first case is the end of life expected for anystars of more than 8 M. SN II correspond to

the release of 2-3 1053 ergs , 99% of this energybeing taken away by the . The second case isat the origin of the SN Ia and will be describedfurther in this section.

The favored model for the SN Ia explosion,which provides the best agreement with the ob-servation, is the following :

The initial star is a white dwarf, composedof carbon and oxygen, orbiting in a binarysystem ( 50% of the stars )

This white dwarf goes through a long cooldown and increases its mass by accretion ofmatter from the companion star.

When the degenerate core (Fermi gas) reach 1.4 M , there is a collapse/explosion. Asthe mass of the core get close to the Chan-drasekhar limit of a gravitational collapse,the C and O at high density and temper-ature can undergo nuclear reactions. Thepressure in the degenerate core (due to elec-trons) is decoupled from the increasing tem-perature (due to the nuclear reactions) : nu-clear reactions can run away.

The nuclear reactions produce 0.6-0.7 Mof 56N i.

The energy released, higher than the whitedwarf binding energy, blows up the star :1051 ergs of kinetic energy are taken awayby the ashes (2/3 of the produced energy).

The source of the SN luminosity comes from thenuclear decay chain of the 56N i, the ash of theinitial nuclear reactions :56N i 56 Co , = 8.8 daysfollowed by56Co 56 F e , = 110 days

There is three phases in the SN Ia light curve.During the first 15 days the increase of the trans-parency end up to a fast increase of the lumi-nosity. Then as the amount 56N i fuel decreasesthe luminosity starts to reduce. 40 days afterthe maximum a slower luminosity decrease is ob-served corresponding to the long lifetime of the56Co.

2000 4000 6000 8000 100000

0.2

0.4

0.6

0.8

1

2000 4000 6000 8000 100000

0.2

0.4

0.6

0.8

1

2000 4000 6000 8000 100000

0.2

0.4

0.6

0.8

1

2000 4000 6000 8000 100000

0.2

0.4

0.6

0.8

1

-14 days

maximum

+10 days

+20 days

Figure 3. As the ashes of the SN Ia explo-sion expand with time, the light collected is sen-

sitive to the composition (spectral features) andthe speed (width of the spectral features) of deeperand deeper layers of the SN Ia. By observingsuch time series the SNFactory project will im-prove our understanding of the SN Ia explosion.

The interest of the SN Ia for the observationalcosmology is then clear :

As they are events with close initial condi-tion, all have almost the same intrinsic lu-

minosity : they are good standard candle. At its maximum the SN Ia luminosity is of

the same order than a full galaxy ( 109),they can be observed at high z ( up to z 1.2 from the ground ) .

Due to their specific origin compared to theother kind of supernovae, the SN Ia explo-


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sion can be easily identified by their spectralfeatures.

Even more important for the usage of thisprobe, many observables associated to the SN Iaexplosion like light curve shape or spectral fea-tures (see figure 3) are related to the energy re-leased. They allow to identify small differencesin the intrinsic luminosity of different SN Ia andfurther improve their status of standard candle.

No Big Bang

1 20 1 2 3

expands forever

Flat

= 0

Universe-1

0

1

2

3

2

3

closedopen

90%

68%

99%

95%

recollapses eventually

flat

Supernova Cosmology ProjectPerlmutter et al. (1998)

42 Supernovae

Mass Density

VacuumE

nergyDensity

(CosmologicalConstant)

It is possible that will find

aresult

that disproves the flat universe

predictionof "Inflation"

SNAP

Figure 4. The expected errors on M and with

1 year of SNAP data compared to the present re-sults. It should be noticed than SNAP is designedto study the dark energy and will be able to testmany theoretical propositions as subjected on thisplot.

Dust

Empty

Evolving SNe

Accelerating ()

Open (no )

Flat (no )0.0 0.5 1.0 1.5 2.0

-1.0

-0.5

0.0

0.5

1.0

redshift

mag

fainte

r

SN 1997ff

SN 1998eq

SN 1997ap

Figure 5. The SN Ia at the highest z observed to-

day are compatible with an accelerating () uni-verse. In such model, as shown on this plot, abovez 1 when the mass density was dominating theuniverse evolution, the universe undergo a cleardeceleration, before the today observed accelera-tion. Effects like evolving SN Ia ( SN Ia ina young universe may have a different chemicalcomposition / energy release than in an old uni-verse ) or grey dust (extra-galactic dust whichcould dim the light over the full spectra for objects

far away) mimic an accelerating universe at allz.

4. The SNFactory and SNAP projects

To study the dark energy with SN Ia, differentprojects are going on or are planned. They willimprove the statistical precision of the results andwill provide a control of the systematics at theneeded level.

The main improvements on the statistics willcome from :

The ground based measurements at z < 11.2, which are in progress today (SCP [4],High-Z Team [5], Megacam/SNLS [6])

Space measurements at high z (0.1 < z 0,measures at the 10% scale of and M arein progress today. The % level physics will bereached this decade (planned CMB satellites tar-get, SNAP proposal).

More than the measurement of the cosmolog-ical constant itself, the goal of the observationalcosmology with SN Ia is the study of the Dark En-ergy, energy at the source of the acceleration ofthe Universe expansion. With the expected pre-cise SN Ia cosmological measurements, a breakthrough in this objective is just around the cor-ner.

REFERENCES

1. S. Weinberg, Rev. Mod. Phys. 61 (1989) 1.2. S. Perlmutter et al. , Astrophys. J. 517 (1999)

565.3. A.Riess et al. , Astrophys. J. in press ( astro-

ph/0104455 )4. Supernova Cosmology Project, S. Perlmutter

et al. , cf http://panisse.lbl.gov:80/public/5. High-Z Supernovae Team, B. Schmidt

et al. , cf http://cfa-www.harvard.edu/cfa/oir/Research/supernova/HighZ.html

6. SuperNova Legacy Survey,cf http://snls.in2p3.fr/

7. nearby SuperNova Factory,cf http://snfactory.in2p3.fr/

8. SuperNova Accelerating Probe satellite,

cf http://snap.lbl.gov/

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P. Antilogus- Measurement of the cosmological constant