Can you detect dark energy in the

laboratory?

Clare Burrage

University of Nottingham

2 (Planck 2013 Results. XVI. Cosmological Parameters)

The Universe today

3 Credit: ESA/Planck

The cosmological constant problem

The Einstein equations:

The energy density of the vacuum looks like a cosmological

constant

Observed value: Expected value:

4

Possible Solutions

Can a dynamical mechanism explain the smallness of the

cosmological constant?

If Λ = 0 is the acceleration caused by a new kind of matter?

Does gravity work differently on the largest scales?

5

Possible Solutions

Can a dynamical mechanism explain the smallness of the

cosmological constant?

New fields

If Λ = 0 is the acceleration caused by a new kind of matter?

New fields

Does gravity work differently on the largest scales?

Can indirectly introduce extra degrees of freedom

6

Modified gravity

A massive graviton has more degrees of freedom than a

massless one

– At low energies one of these behaves like an additional

scalar mode

f(R) theories contain an extra scalar degree of freedom

because of the presence of higher derivatives

Many brane world models have an extra scalar mode

corresponding to the position of the brane in the extra

dimension

7

New fields are light

The cause of the acceleration of the expansion of the

universe today is (approximately) coherent across the

observable universe

– This corresponds to very light masses

8

DARK ENERGY INTERACTIONS

9

What’s the problem with scalar fields?

Expect a new scalar field to couple to matter fields with at

least gravitational strength (Planck suppressed

couplings)

Bosons that couple to matter mediate forces

In the non-relativistic limit:

10

Results of the Eöt-Wash experiment at the University of Washington 11

Dark energy interactions

Can we forbid interactions that give rise to fifth forces?

Yes, quintessential axion / pseudo-Goldstone boson

models

Can we dynamically suppress the fifth forces?

Yes, chameleon-like models

Are there other observational signatures we could look

for?

12

PSEUDO-GOLDSTONE

BOSONS AS DARK ENERGY

13

Pseudo-Goldstone bosons

If the field is a pseudo-Goldstone boson then it posses an

approximate global symmetry

Forbids couplings to the Standard Model Lagrangian of the

form

These are the couplings that give fifth forces

Shift symmetry also keeps scalar potential flat

14

A brief history of axionic quintessence

Carroll, 1998. A pseudo-Goldstone boson dark energy would

forbid fifth forces.

Kim, Nilles, 2002. Quintessence could be the model

independent axion of string theory.

Arvanitaki, Dimopoulos, Dubovsky, Kaloper, March-Russell,

2009. String Axiverse – simultaneous presence of many light

axions.

Panda, Sumitomo, Trivedi, 2010. Axion monodromy applied to

quintessence.

(McAllister, et al. 2008. Wrapped branes in string compactifications

implies closed string axions with approximate shift symmetries.)

Kim, Nilles, 2013. Pseudo-Goldstone boson from discrete

symmetries in the UV

15

Allowed couplings

The scalar field can couple to a total derivative

This makes it an axion-like particle

Many laboratory and astrophysics based searches, based

on oscillations between scalar and photon in a magnetic

field

16

17 (Baker et al. 2013)

Dark Energy modifies electromagnetism

The Earth’s gravitational field

will source a profile for the scalar field

Maxwell’s equations become

18 Romalis, Caldwell. 2013

Dark Energy modifies electromagnetism

A magnetic field can give rise to an anomalous electric field

Voltage measured

19 Romalis, Caldwell. 2013

Disformal couplings

We can also have couplings to the Standard Model of the

form

Higher order operator so might expect effects to be

negligible

Counter example: Massive gravity where disformal coupling

strength

Axion-like coupling strength

20

Disformal couplings

Fifth forces return through loop corrections

Giving a force law

Fifth force experiments (over ~1 mm) constrain

21 Kaloper. 2003

Disformal couplings

Disformal couplings produce distinctive signatures in

laboratory searches for axions

• Changes the probability of a photon converting into dark

energy in the presence of a magnetic field

(CB, Brax, Davis, 2012)

Changes the propagation of light through the Universe, and

induces

• CMB spectral distortions

• Modifications to distance duality relations

(CB, Brax, David, Gubitosi, 2013)

22

CHAMELEONIC DARK

ENERGY

23

24 Common chameleon. Photo credit: Nanosanchez

A scalar field theory

• With self interactions

• Which couples to matter

Evading fifth force constraints requires . .

The chameleon mechanism is relevant if .

f(R) modifications of gravity correspond to

The chameleon

Khoury, Weltman. 2004

The effective potential

High density, no pressure Low density, no pressure

The mass of the chameleon changes depending

on its environment

‘Small’ Objects

• The object only causes a small perturbation of the scalar

field

• Find a gravity like form for the scalar potential

• The force is the gradient of the potential

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‘Large’ Objects

• Inside Outside

28

Suppressing the fifth force

The increased mass makes it hard for the chameleon field

to adjust its value

The chameleon potential well around massive objects is

shallower than for standard light scalar fields

Chameleon

Newtonian

potential

Chameleon fluctuations

• The chameleon Lagrangian is non-linear

• This makes the mass of chameleon fluctuations depend

on the background configuration

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Screening mechanisms

Start with a non-linear scalar field theory

• Solve the equations of motion for the background

The Lagrangian for fluctuations (to second order):

31

Large Z makes it

hard for the scalar

to propagate

- Galileons

- Massive gravity

- Vainshtein

mechanism

Large m means the

scalar only

propagates over

shorter distances

- Chameleon

Small β makes the

interaction with

matter fields

weaker

- Symmetron

TESTING DARK ENERGY WITH

SCREENING MECHANISMS

32

Searches for dark energy interactions

Interactions with dark energy strongest in diffuse

environments

Constraints from high precision experiments performed in

near vacuum

Can exploit:

• Particle physics experiments

• High precision photon measurements

• Atomic structure measurements

• (Astrophysical observations)

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Scalar Bremsstrahlung

Contribution to the width of Z decay

Decay rate:

• Prediction from the Standard Model:

• Measurement at LEP:

Dark Energy correction negligible if

Brax, CB, Davis, Seery, Weltman. 2009 34

In an atom a scalar field profile is

sourced by the:

• Nuclear electric field

• Density of the atomic nucleus

Leads to a perturbed Schrodinger equation

Atomic precision measurements

Brax, CB. 2010 35

Schwob et al. 1999

Atomic precision measurements

Perturbed atomic energy levels:

1 sigma uncertainty on the 1s - 2s transition in hydrogen is

10-9 eV.

Requires:

Constrains:

36

Chameleon ‘After-glow’

Chameleons in a vacuum chamber are light, to pass

through the walls they would need to become heavier.

If the chameleons are not energetic enough this is

forbidden and they remain trapped in the vacuum chamber

37

Gies, Mota, Shaw. 2008. Ahlers, Lindner, Ringwald, Schrempp, Weniger. 2008.

Diagram from Upadhye, Steffen, Chou. 2012.

GammeV-CHASE

Results from the Gammev Chameleon Afterglow Search at

Fermilab

38 Steffen et al. 2010

Local EP violation

In the Lagrangian the chameleon couples to all particle species in the same way

At the macroscopic level the chameleon force behaves differently for screened (large) and unscreened (small)

objects

Looks like a violation of the equivalence principle

The parameter which controls the suppression of the dark energy force

The chameleon ‘charge’ of an object

39

Hui, Nicolis, Stubbs. 2009

Proposed EP Violation Tests

The gas in dwarf galaxies may be unscreened but the stars

are screened

• They will fall differently towards local over densities

Can use diffuse clouds of cold atoms to measure gravity in

the laboratory

• Atoms are unscreened over a much larger region of

parameter space than macroscopic objects

40

CB, Copeland, Hinds. (to appear)

Jain, VanderPlas. 2011

Dark energy and BECs

Coherent waves in Bose-Einstein condensates can be

used for interferometry

Credit: Centre for Cold Matter, Imperial 41

Dark energy and BECs

Interference of waves in condensates at different heights

has already detected gravitational effects

A measurement of G or g would be sensitive to the

equivalence principle violating effects of dark energy

Can also look for chameleon effects directly by putting the

condensate in different environments

42

Dimopoulos, Geraci. 2003. Baumgärtner et al. 2010

Conclusions

Attempts to explain the current acceleration of the

expansion of the Universe commonly introduce new fields

These new fields should couple to the Standard Model and

therefore we expect fifth forces

Understanding why we haven’t seen these forces leads to

two types of dark energy theory

• Pseudo-Goldstone boson

• Chameleonic

Possible to search for both kinds of field in the laboratory

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PROBLEMS WITH SCREENING

MECHANISMS

44

Strong coupling – A simple example

• Perturb around a background

• The Lagrangian is

• Where

45 Luty, Porrati, Rattazzi 2003

Strong coupling – A simple example

• Self interactions of the canonically normalised scalar

are suppressed by

• Around a static, spherically symmetric source of mass M

When the graviton mass is ~ H0, the rescaled strong

coupling scale (at the surface of the Earth)

corresponds to distances ~ 1 cm

46

Strong coupling in massive gravity

• There are additional higher order terms and interactions

with the metric

• Perturb around the scalar and metric field configuration

due to the Earth

• Then canonically normalise the scalar

• The interactions for fluctuations in the Lagrangian

become

Strong coupling problems for massive gravity

• The theory becomes non-perturbative at the lowest

energy scale controlling these interactions

• The lowest scale at the surface of the Earth is

• For gravity to be valid on the distance scales probed by

laboratory experiments requires

Chameleon cosmology

During radiation domination the field is initially frozen due

to Hubble friction

Decoupling of Standard Model particles ‘kicks’ the

chameleon towards smaller values

Brax, van de Bruck, Davis, Khoury, Weltman. 2004

Chameleon cosmology

The kicks drive the chameleon towards the steep part of

the potential with high velocity

Classically the field rapidly climbs up the potential and falls

back down

A chameleon catastrophe

Rapid (non-adiabatic) changes in the mass of the field

excite quantum fluctuations

– Very high energy fluctuations are excited

– With small occupation numbers

The death of the chameleon?

Production of high energy particles leads to a break down of calculability

This can only be evaded for weak couplings and very fine tuned initial conditions

This fine tuning requires knowledge of the full particle content of the Universe

Picture credit: Karen Watson