Chaire Galaxies et Cosmologie

Acceleration of expansion and Dark Energy

Françoise Combes

The outlinesThe outlines• The content of the Universe and likely evolutionThe content of the Universe and likely evolution• History of the cosmological constant: assumed equal to zero

during 80yrsg y

• How the fundamental physics of the infinitely small controlHow the fundamental physics of the infinitely small control the fate of the Universe at large scale

• Discovery in 1998 of the acceleration of expansion, the mystery deepens! Analogy with inflation?

• Tracks for solutions…

Composition of the Universe

• Ordinary matter 5%• Ordinary matter 5%

• Exotic dark matter 25%

• Dark energy 70%

??crit ??crit = 10-29g/cm3

or cosmological constant

Evolution of the contentD k d i t i l tl ( 5 G 0 5)• Dark energy dominates since only recently ( <5 Gyr, z=0.5)

• It will dominate in the future

Zero curvature for the Universe• The observation of the cosmic micro-wave

background CMB (COBE, WMAP, Planck)• size of the sound horizon seen under an

angle of ~1°

curvature = m+ -1

tot=1

Why a cosmologicalconstant?constant?

• This constant is introduced in 1917 byEinstein, who wanted to represent a static Universewith = /8G• R-1/2gR -g = - 8GT

• His model of universe was a sphere of finite massp

Soon after, the expansion of the Universe was discovered by therecession of galaxies (Slipher 1924) Hubble law V=Hdrecession of galaxies (Slipher, 1924) Hubble law V HdBut also: de Sitter showed that it could exist an inertial framein a matter-free universe =0, R(t) =R0 exp(Ht), with ( ) 0 p( )

R(t) is the characteristic scale of the universe, with the metric

Prof. Dr. W de Sitter

What inflates the balloon? What is the physical process at the origin of expansion or collapse of the Universe? It is !No other explanation

How to obtain a static universeCurvature of the Universe

• Friedmann equationsCurvature of the Universe

Hubble cste

Pressure

The constant is homogeneous to c2/a2 and for Einstein a2 wasgthe characteristic size of his spherical universe

The estimation of the universe age, typically the inverse of Hubbleconstant, has varied much with time, Ho=500km/s/Mpc at the start,today 70 km/s/Mpc For Einstein t = infinite !today 70 km/s/Mpc. For Einstein t0 =- infinite !

Different models for the universeLi + 1

de Sitter UniverseR( ) Ht

Line m+ = 1

R(t) ~eHt

EdS R(t) ~t2/3EdS R(t) ~t

Standard CDM

The static modelf i iof Einstein was

highly unstable

Big Crunch Lemaître (1933): equivalent to a fluidqof pressure P=-c2

Energy of the vacuumgy• The first to suppose that it could exist a vacuum energy in

i h i l hi h ld hquantum mecanichs, equivalent to which could have a gravitationnal action is Wolfgang Pauli en 1920

• His computations showed that the radius of Einstein’s Universe• His computations showed that the radius of Einstein’s Universedid not include the Moon!

• Indeed when trying to have the order of magnitude• Indeed, when trying to have the order of magnitude

• fundamental state• fundamental state• V h d

max

• Summation gives a finite value when integrated until a• Summation gives a finite value, when integrated until a maximum frequency max maxcorresponding to the electron’s radius. Then the energy density is so large that the e ec o s ad us. e e e e gy de s y s so a ge a eradius of Einstein’s Universe is of 31km! = c2/a2

The quantum vacuum3 colors for quarks

• Around the years 1960-70, a more fundamentalapproach of the problem: the field theory,Quantum chromodynamique (QCD), descriningthe nuclear interactions: weak and strong

+ 3 anti-colors

• the density of universe (=1) ~ 10-29 g/cm3

• or in energy 10-47 GeV4 ( )

• the computation of the vacuum energy is to sum all degrees of freedom of all possible quantum fields

According to the cut-off scale, one finds• 2 109 GeV4 if the cut-off scale is the electroweak interaction• 1072 GeV4, if the cut-off is the Planck scale• Other possibility QCD=10-6 GeV4 still 41 orders of magnitude!

Coincidence problem?• This value of quantum vacuum energy must appear as an energy

term in Einstein’s equation q= 8G qq q q

• For representing the reality, there should be measured= E+q

A quasi-null value. There must be an extremely fine tuning betweenq y gthese two quantities at 60 or 120 orders of magnitude!

How to cancel this constant? The fermions contribute a positive energyand bosons a negative energy, but they are in minority!

This leads to the supersymmetry hypothesis, with exchange of fermions bosons. But a perfect symmetry should hold, whichoccurs only at the very beginning of the Universe. Today the

t i b k (Z i 1975)symmetry is broken (Zumino 1975)

Reality of this vacuum energy?y gy

• Casimir effect (1948) between two uncharged platesg p• The vacuum energy is everywhere, but quantizedVirtual photons: electromagnetic fieldp g

Between the plates, the wavelength mustp , gbe a sub-multiple of the thicknessk = L . The number of photons is limitedk L . The number of photons is limitedIf L is small less energy

Attractive force between the plates, measured in severalexperiments, since ~30 yrsp , y

Orders of magnitude• F(Casimir) ~A /L4

• Pressure = F/A = 10-3 Pa for L=1 mPressure F/A 10 Pa for L 1 m• Perfect conditions (reflexion,

temperature= 0, parallel plates..)p , p p ) Better geometry plane/sphere

ton)

ano-

New

tFo

rce

(na

Separation L (nano-m)

F

Mohideen 2005

Casimir Force• The research continues to test the gravity force at small scale• The Newton law is verified down to =10m

Search under the form of anadditionnal Yukawa potentialadditionnal Yukawa potential

V= Gmm’/r (1+e-r/)

Adelberger et al 2003, Lambrecht & Reynaud 2012

Astonishing discovery in 1998Astonishing discovery in 1998

• Riess et al (1998) 10 supernovae Ia 0.16 < z < 0.62+ 16 at high z, 34 local onesg ,• Distance- luminosity computed from the relation between

luminosity and shape of light curve• Obtention of H0, m,: SN Ia are 10-15% more remote

than expected if =0• Age of Universe 14.2 + 1.7 Gyr

confirmed by a second teamMore statistics 7 sigma

The SNIa are more remote than expected from their z!

Estimations of distances

Positive Flat Negativecurvature universe curvaturecurvature universe curvature

Cygnus A

Distance-luminosity DL, such thatLapparent= Lintrinsic/4DL2

yg

Angular distance DA, such that t= Dimi t i i /DAapparent Dimintrinsic/DA

The distances • Notion of distance difficult in an expanding universe

• Measured with expanded rulers?

Angular distanceCorr. From expansion To present time

Light travel timeFrom this objectFrom this object

Relative distancesMpc ~3 million al DL= Distance-luminosity

Lookback timeComoving distance

0 01 0 1 1 10 100

DA= angular distance

0.01 0.1 z =1 10 100

DL= Distance-luminosityDL = (1+z)2 DA DL= Distance-luminosityDL = (1+z)2 DA, Objects less luminousAlmost cst sizes

DA= angular distance

Almost cst sizes

Gravitationnal lens effectDA= angular distance

2 objects at rest: comoving distance=cste

Standardisablecandels

Magrelativecandels

• SN Ia are explosions, f hi h h li h l h hfor which the light curve, althoughnon standard is « standardisable »

h h lf id h d d• The half-power width dependson intrinsic luminosity Jours après le picAlso a color correction

White dwarf

Supernovae Ia explosions

• A binary star, with a white dwarf• A SN Ia can radiate during a few days as much as its own host

galaxy• Always the same light curve shapedue to the radio-activityof nickel

SN1995ar days

Nobel prize in 2011 for 3 teamsNobel prize in 2011 for 3 teams• Saul Perlmutter, The Supernova Cosmology Project, Berkeley• Adam Riess (Baltimore) and Brian Schmidt (Australia)The High-z Supernova Search Team

In total about 50 SN Ia with a light curve well calibrated, have allowed to demontrate the acceleration of the Universe

HubbleDiagramme

Distance vs zThe blue curveThe blue curve

m=0.3, = 0.7i l l f d b th d tis clearly favored by the data

relative to the other curve = 0 = 0

The supernovae appear weaker in an accelerated universe

If h i l i h ld h b i l• If the universe accelerates, it should have been in slower expansion in the past

• In an universe in acceleration there is more time between aIn an universe in acceleration, there is more time between a given redshift z and today

• The light takes more time to reach usg• The distance-luminosity is larger• The SN, of redshift z, appear then weaker

R(t) characteristic size = R0 / (1+z)As well as photon wavelength repos (1+z)

The various possible modelsA given size, R(t), corresponds to a given redshift z

The various possibilities

Recent advancesC fi ti d tibilit• Confirmation, and compatibility of term constant

Suzuki et al (2011)Suzuki et al (2011)

With the other constraintsEquation of state EOS P = - w w=-1 expected for a constant

Quintessence: dynamicalw> -1 in general

E tExcept energy« phantom »w < -1w 1

wq= q

Acceleration (3P+)

• Suzuki et al (2011)

Acceleration ~ -(3P+) w < -1/3

Problem of fine tuningProblem of fine tuning

The ratio between baryonicThe ratio between baryonicmatter and exotic darkmatter remains constant= 5

But the term of dark energywhich was negligible, becomesdominant at our epoch

Although this model runs top, it does not look natural..

Carroll 2001

Inhomogeneous universe?• A possibility was soon proposed: =0 globally in the universe but

we are living in a large void, or underdense bubbleg g ,• As overdense regions collapse and decouple from expansion, voids

are in accelerated expansion

• The universe expansion is treated with the approximation of p pphomogeneity: could inhomogeneities produce an effect called« back-reaction »?

• Qualitatively, the effect at z=0 goesIn the right sense, quantitativelyThis remains to be proven(Bose& Majumdar2012: deceleration)(Ad k l 2015 li ibl )(Adamek et al 2015: negligible)

Buchert 2014

Acceleration of expansion: inflation• An other period of the Universe in strong acceleration• The inflation is supposed to occur just before the Big-BangThe inflation is supposed to occur just before the Big Bang

• Supposedly due to a scalar field (like dark energy?)Supposedly due to a scalar field (like dark energy?)

• Why an inflationnary epoch is needed at the beginning of the• Why an inflationnary epoch is needed at the beginning of the Universe?

• Invented by Alan Guth (1981) to solve• the horizon problem the horizon problem• the universe flatness problem• to provide a source of primordial fluctuations at the origin of• to provide a source of primordial fluctuations, at the origin of

galaxies and structures

Primordial inflation at t < 10-32sPrimordial inflation at t < 10 s

The scalar field driving inflation is called inflatonThe scalar field driving inflation is called inflaton

The universe is void at the start (just quantum fluctuations)Corresponds to the de Sitter solution

Aft th di ti d i t d th th tt d i t dAfter the radiation-dominated era, then the matter-dominated era,the Universe becomes void again (70%?) with another inflation phase

Horizon problemp

• The horizon at the CMB epoch was smallerpthan 2 degrees

• How can the CMB temperature be the same within 10-5 everywhere?

(regions non causally related)

Flatness problemFlatness problem• If tot is different from 1 within epsilon, it will depart from 1

i ll H d 1 i hi 0 5%exponentially. However today tot=1 within 0.5%

tottot

Time (seconds)

Inflation solves the horizon problemLimit of observable Universe today

Horizon of universetoday

INFLATION

TimeHorizon et the epoch of CMB

Time

Guth (1997)Inflation dilutes also magnetic monopoles

Inflation solves the flatness problem

• For a Universe with a rapid inflation period– After expansion, the Universe becomes locally flat– By analogy, locally we do not perceive the Earth

curvature – Solves the fine tuning problem, since inflation has a

dilution effect, whatever the initial conditions, it will i 1give =1

What is the nature of this dark energy?

• Equation of state P = w Positive density, homogeneous in all q y, gthe universe

• Contributes to space curvature, and therfore to expansion

• Acceleration ~ -(3P+)w < -1/3

• But in the 2nd equation, it is clear that the equivalent pressure is of opposite sign to that of a normal fluid. Instead of a deceleration, ther e is an acceleration

This could be a scalar field

• As for inflatonTh l fi ld h i l I ld l hThe scalar field has no particle, nor mass. It could also have a tensor,

of energy-impulsion T

In e er point of space one can define (x t) as an electromagneticIn every point of space one can define = (x,t), as an electromagnetic field, but the latter is vectorial

• The Einstein equation is G = 8T• The Einstein equation is G = 8T

Space curvature= Matter density• T has the same form for matter and scalar fields• T has the same form for matter and scalar fields• Scalar fields have the same effect than matter as far as gravity is involvedas far as gravity is involved

Inflation scalar field

Normal gas: T = (+p)uu + pg

Scalar field : T = - [ /2 + V()] g

Energy Pressure

• The important part is V(), the scalar potential.

• It has the same role as pressure p for gasesIt has the same role as pressure p for gases

• For a gas p must be positive, but: V() can have any valuevalue

• It is therefore possible to have a negative pressure ith V()with V()

The physics of inflationThe physics of inflation

In the case of primordial inflation, the field V()must be enormous

What is its origin?V() extreme

• Spontaneous symmetry breaking (in the early universe)

for =0 (unstable)

• The scalar fields (dilatons) predicted by the string theory can produce such potentialstheory can produce such potentials

V() extremefor =0 (stable)

Spontaneous symmetry breaking• The laws of physics are supposed to be much more symmetric

at very high energies (in the primordial universe)at very high energies (in the primordial universe)

• These symmetries are broken at low energy. The preferred state f th t i l t iof the system is less symmetric

• Scalar fields which were before at the minimum of their potential V() are then no longer at minimum

• The scalar field has therefore a vacuum energy, V() > 0

• then runs towards the new minimum and the symmetry is broken

• It is a phase transition

• Primordial inflation

Spontaneous symmetry breaking

• V() has a minimum at = 0 before transition

• V() has a minimum at > 0 after the symmetry breaking() y y g

• runs through quantum tunnelling from 0 towards the new minimumminimum

Original nflation Slow-roll inflationg

Link with a cosmological constantg• One of the initial explanations for inflation was also a

cosmological constant

• A constant is equivalent to a scalar field = which q keeps the same value in all point of space and time

• Gives a pressure p = - Gives a pressure p

Could there be a link between the two constants, a common origin?common origin?

• The initial value would then be greatly reduced by the different processes of phase transitions which will allowdifferent processes of phase transitions, which will allow matter to dominate, then would win again

Ratra-Peebles 1988

Models of quintessenceModels which try to link the two cosmological constants are calledquintessence they are models with a dynamical scalar fieldquintessence, they are models with a dynamical scalar field

Differences in duration10-32 s versus Gyrs

Energy scales1015 Gev 1 milli-eV10 Gev 1 milli eV

Expansion rates1050 x

Relative evolution of perturbationsRelative evolution of perturbations• The largest perturbation observable has the scale of the Hubble

radius todayradius today

Lesgourgues 2006

Possible sources for the dark energyPossible sources for the dark energy

• Spontaneous symmetry breaking and phase transition p y y g p(as for primordial inflation)?

• String theories: many predict the existence of a scalar g y pfield (the dilaton) in the limit of low energies, similar to an inflaton

• Branes: the string theory also suggests that our universe is a brane included in a higher dimension space, and in this frame a scalar field could drive inflation

Branes and inflation

• In the frame of some string theories,

the universe is in reality 4 space dimensions

• Our universe is a 3D brane moving in a larger• Our universe is a 3D brane moving in a larger ensemble at 4D, called “bulk”

• The gravity propagates in the bulk (4D) the other forces• The gravity propagates in the bulk (4D), the other forces only in the brane (3D)

Th l fi d “i fl ” ld f h i• The scalar fied “inflaton” would come from the gravity part which propagates in the bulk

I th d l h i i

A cyclic modelIn the model where our universe is a3D brane in a larger ensemble or 4D “bulk”:or 4D bulk :

Imagin a 3D braneat each end

• One of the brane would be the real universe, the other one the ‘mirror’ universemirror universe

• The two branes can go towards one another, and even cross each gother, which gives rise to the cyclic model of Steinhardt & Turok

k ti i th Bi B d t th lli iekpyrotic scenario: the Big-Bang corresponds to the collisionOf two branes

Holographic principle and quantum gravity• The holographic theory introduced at microscopic scaleThe cosmological constant should tend towards zeroThe cosmological constant should tend towards zero

• In the usual frame the enormous value of vacuum energy comesIn the usual frame, the enormous value of vacuum energy comesfrom the huge number of degrees of freedom

• But in holographic theory, according to the principle ofBut in holographic theory, according to the principle of Bekenstein-Hawking, the number of degrers of freedom is reduced

• Horava (1999) proposed a theory, with the action S( ) p p y,

• M= infrared scale, inverse of the system sizeN d f f d R2 d ti t f Ri t• N degrees of freedom, R2 quadratic terms of Riemann tensor

Degrees of freedom at the surfaceg

• G constant of gravity (Newton)• N is the surface surrounding the system in units of PlanckN is the surface surrounding the system in units of Planck• Action Einstein-Hilbert

• ~M2, or r2 ~1 r is the size of the holographic screen• The entropy S is limited S < r2 M 2 S < M 2• The entropy S is limited S < r2 Mp

2 S < Mp2

• The expected cosmological constant tends to zero (Horava & Minic 2000)Minic 2000)

• The challenge is to find a holographic theory which works atThe challenge is to find a holographic theory which works atmicroscopic level

Holographic principleg p p p

• The quantity of informations contained in a given volume q y gcannot exceed that stored in the surface of this volume. Theyare stored as 4 bits of information in each Planck region. C j f G T’H f (1993)Conjecture of G. T’Hooft (1993)

• Limit of Bekenstein-Hawking based on the entropy S of black holes S < Area/4holes S < Area/4

• Quantification at Planck scale?• Quantification at Planck scale?• Space is no longer continuous• Limits the number of degrees of• Limits the number of degrees offreedomP bl f L t i iProblem of Lorentz invariance Solved for black holes?

Fundamental physics and astrophysics• The problem of links the quantum microscopic physics to

large scale astrophysics, i.e. Cosmos scalesg p y ,• The vacuum energy, summing the zero-point energies of all

micro oscillators, is predicted to be 120 orders of magnitude larger than what is observed

• In 19e century, physicists invented the ether,filling the vacuum, allowing propagation of electro-magnetic waves• But Lorentz invariance, and relativity swept all that• Today as a referentiel frame for the universe: the CMB 3KAt large scale. Theories of Einstein ether, with a vector field(preferred referential frame), covariant

SummaryHistory of the cosmological constantSince Einstein in 1915, to its discovery in 1998, confirmation of the Universe constants CMB lenses etcthe Universe constants, CMB, lenses, etc..

Astrophysical problems op ys c p ob eBetter probes, supernovae IaInflation: inflaton field again?

Fundamental physics problemVacuum energy and Casimir effectVacuum energy and Casimir effectQuantum Physics

Numerous tentatives: unimodular gravitySupersymetry (SUSY), String theories, Quantum gravityHolography, Loop quantum gravity