Massive neutrinos and their impact on cosmology

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Massive neutrinos and their impact on cosmology Paolo Serra in collaboration with R. Bean, Dept. of Astronomy, Ithaca, NY 14853 A. De La Macorra, Istituto de Fisica, UNAM, Mexico G. L. Fogli, E. Lisi, A. Marrone, Dipartimento di Fisica e Sezione INFN, Bari A. Melchiorri, Dipartimento di Fisica Universita’ “La Sapienza” e Sezione INFN, Rome A.Palazzo, J. Silk, R. Trotta, Astrophysics, Denis Wilkinson Building, Oxford A. Slosar Faculty of Mathematics and Physics, University of Ljubljana, Slovenia Paolo Serra Physics Department University of Rome “La Sapienza”

description

Massive neutrinos and their impact on cosmology. Paolo Serra in collaboration with R. Bean, Dept. of Astronomy, Ithaca, NY 14853 A. De La Macorra, Istituto de Fisica, UNAM, Mexico G. L. Fogli, E. Lisi, A. Marrone, Dipartimento di Fisica e Sezione INFN, Bari - PowerPoint PPT Presentation

Transcript of Massive neutrinos and their impact on cosmology

Page 1: Massive neutrinos and their impact on cosmology

Massive neutrinos and their impact on cosmology

Paolo Serra

in collaboration with

R. Bean, Dept. of Astronomy, Ithaca, NY 14853

A. De La Macorra, Istituto de Fisica, UNAM, Mexico

G. L. Fogli, E. Lisi, A. Marrone, Dipartimento di Fisica e Sezione INFN, Bari

A. Melchiorri, Dipartimento di Fisica Universita’ “La Sapienza” e Sezione INFN, Rome

A.Palazzo, J. Silk, R. Trotta, Astrophysics, Denis Wilkinson Building, Oxford

A. Slosar Faculty of Mathematics and Physics, University of Ljubljana, Slovenia

Paolo Serra

Physics Department

University of Rome “La Sapienza”

Page 2: Massive neutrinos and their impact on cosmology

Neutrinos in cosmology

• Neutrinos are the most abundant particles in the Universe after photons

• This means that they play a role in many different epochs and aspects of cosmology, for example:

– Leptogenesis

– Big bang nucleosynthesis

– Structure formation

Page 3: Massive neutrinos and their impact on cosmology

Neutrinos in cosmology Neutrinos have a great impact on the two most

important observables in cosmology:

CMB (Cosmic Microwave Background radiation)

LSS (Large Scale Structures)

For these arguments see talk by S. Pastor

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So cosmology can help particle physics to constrain neutrino masses

Page 5: Massive neutrinos and their impact on cosmology

Neutrino mass from Cosmology (reprinted from Fogli, Lisi, Marrone, Melchiorri, Palazzo, Serra, Silk, Slosar ,

hep-ph/0608060)see talk by A. Palazzo

Data mi

1. WMAP < 2.3 eV

2. WMAP+SDSS < 1.2 eV

3. WMAP+SDSS+SNRiess+HST+BBN

< 0.78 eV

4. CMB+LSS+SNAstier < 0.75 eV

5. CMB+LSS+SNAstier+BAO < 0.58 eV

6. CMB+LSS+SNAstier+Ly-(P. Mc Donald et. al, see talk by M. Viel)

< 0.21 eV

7. CMB+LSS+SNAstier+BAO+Ly- < 0.17 eV

onsperturbatiry inflationa invariant scale and adiabatic with

model CDM usual theof framework In the

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Constraints placed by different cosmological data-set on in terms of standard deviations from the best fit in each case

Reprinted from Fogli et al. hep-ph/0608060

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Some considerations• WMAP data alone, in the cosmological framework considered, are able to constrain m<2 eV at 95%. This limit, as already

stated, is the most conservative

• The constraints on mtend to scale linearly adding several different data-set

• Including SDSS Lyman-data dramatically improves the constraints on mup to m<0.17 eV (case 7 considered);

this limit generates a tension with bounds on mobtained by the Heidelberg-Moscow experiment (Klapdor claim). In fact:

eVmeVmeV 2.1)2(81.043.0

Page 8: Massive neutrinos and their impact on cosmology

Reprinted from Fogli et al. hep-ph/0608060

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Solving the tension• The laboratory bounds on mcould be due to new physics

beyond the light Mayorana neutrinos or systematic in the mass matrix (see talk by Vogl this morning)

• Bounds derived from astrophysics (and physics) are always affected by many systematic uncertanties which could be not well estimated

• We don’t know the fundamental nature of the two most important ingredient of the standard cosmological model, say dark matter and dark energy: their possible unknown parameters and behaviours could solve these problems

This means that we can always consider more complicated cosmological models to obtain consistency with laboratory data.

In this case, an analysis based on Bayesian evidence could be very useful to assess the need for new parameters

Page 10: Massive neutrinos and their impact on cosmology

Now particle physics can help cosmology to establish the best model

Page 11: Massive neutrinos and their impact on cosmology

More complicated models

We must remember that cosmological bounds are always model dependent !

Relaxing some hypothesis we can obtain different constraints on cosmological parameters (mostly looking

for parameter degeneracies)

We consider just two possibilities:

1. Relaxing the assumption w=-1 (P=-

2. Adding an extra background of relativistic particles

Page 12: Massive neutrinos and their impact on cosmology

Our Analysis

2at eV )6.08.1( m

eV 2.93

32

mh

De La Macorra, Melchiorri, Serra, De La Macorra, Melchiorri, Serra, BeanBean

astroph/0astroph/0608351We analyzed the latest CMB, Galaxy Clusters, SNI-IA data with a dark energy parametrized with an equation of state:

We restricted the analysis to three-flavour neutrino mixing withdegenerate masses so that:

We assume a cosmological model with primordial adiabatic and scalar invariant inflationary perturbations and with a prior on the sum of neutrino masses given by the Heidelberg-Moscow experiment, say:

wP

Page 13: Massive neutrinos and their impact on cosmology

• Figura con la degenerazione ....

10fit best in the

difference aimply masses, neutrino of sum on theprior Moscow-Heidelberg theAdding

BEST2

prior M-H with BEST22

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Possible physical origin for w<-1 ?

Phantom fields (Caldwell, astro-ph/9908168) • They have w<-1 but suffer of several theoretical

problems: Big Rip, instability of Perturbations...

Interacting dark energy• Dark energy can interact with other particles, for

example neutrinos.

• The main motivation for these possibility is that the dark energy scale is , comparable to the neutrino masses

eV 10 -3

Page 15: Massive neutrinos and their impact on cosmology

Possibilities for an interacting dark energy

Coupled neutrino-dark energy models predict an apparent equation of state wap less than -1, even if the real equation of state is larger than -1

In general we can include an interaction between dark matter (or neutrinos) and via the function f(which gives an interacting dark matter energy density

1 whave toallows which w wand 0 xhave wefffor

)1)(

(- x where1

w with 1)(

apap0

03

IM0ap3

00

f

f

ax

w

af

fIMIM

Page 16: Massive neutrinos and their impact on cosmology

Relaxing the assumption N=3

• Models with massive neutrinos suppress power on small scales, the suppression beeing proportional to P/P≈-8/m

• Adding relativistic particles further suppress power on scales smaller than the horizon at matter-radiation equality

• This means that, if the matter density is increased, there is parameter degeneracy between the number of relativistic species Nand the sum mof neutrino masses

Page 17: Massive neutrinos and their impact on cosmology

Likelihood contours for the case of N neutrinos with equal masses, calculated from WMAP 2006+LSS, Melchiorri-Serra-Trotta,

in preparation)

H-M

Page 18: Massive neutrinos and their impact on cosmology

Results • A cosmological scenario based on a cosmological constant is unable to provide a

good fit to current data when a massive neutrino component as large as suggested in the Heidelberg-Moscow experiment is included in the analysis

• A better fit to the data is obtained with a dark energy described with an equation of state

• At present, the Heidelberg-Moscow experiment is the only one able to esclude a cosmological constant at such high significance

• However, recent combined analysis with Lyman-alpha forest data seem to be in discord with the Heidelberg-Moscow result and, partially, also with the CMB. Future data will allow to solve these tension

• Cosmological results are always model dependent. Changing the number of relativistic particles is one possibility, but we can also think

obout other ways.

2at -1 w with 3.1 w

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Page 20: Massive neutrinos and their impact on cosmology

Laboratory bounds on neutrino mass

2/1

22

i

iei mUm

Experiments sensitive to absolute neutrino mass scale :

Tritium beta decay:

eVm

eVm

1.2

2.2

(Mainz)

(Troitsk)

)2(8.1 eVm

Best fit gives a negative mass !!!

Page 21: Massive neutrinos and their impact on cosmology

CMB Anisotropies (Spergel et al. 2006)

Cosmological perturbations:The Observables

lC ),( spectrumpower

T

TWMAP

Page 22: Massive neutrinos and their impact on cosmology

The lenght scale below whichNeutrino clustering is suppressedis called the neutrino free-streamingscale and roughly corresponds to thedistance neutrinos have time to travelwhile the universe expands by a factorof two. Neutrinos will clearly not cluster in an overdense clump so small that its escape velocity is much smaller than typical neutrino velocity. On scales much larger than the free streaming scale, on the other hand,Neutrinos cluster just as cold dark matter.This explains the effects on the power spectrum. The relative lowering of the matter power spectrum is given by: mP

P

8

But remember that, the most spectacular result in cosmology is:LOWERING OF THE MATTER POWER SPECTRUM

Page 23: Massive neutrinos and their impact on cosmology

/(x) power spectrum P(k)

Percival et al. 02

Galaxy Surveys

redshift surveys (2dF,SDSS)

linear non-linear/<1 />1

60 Mpc

bias uncertainty …

Cosmological perturbations:The Observables

Page 24: Massive neutrinos and their impact on cosmology

Neutrinos and the CMB

• The CMB is affected mostly by the number of neutrinos Ntrough the Integrated Sachs-Wolfe effect)

• However, there are also (small) effects due to the mass of neutrinos

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Effects of neutrinos on CMB and LSS (from Tegmark)

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m eV m eV

m eV m eVMa ’96

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Parameter dependance of the luminosity distance

0for sin sinn and 0for sinh sin

density

)1()1()1(sin

kk

K

2))1(3(3

0

2

1

2

11

0

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curvature

energydark

zwzdzncHD

W

Kw

Wm

z

KKL

Page 28: Massive neutrinos and their impact on cosmology

A brief explanationA classic result of the perturbation theory is that if all the matter contributing to the Cosmic density is able to cluster, the fluctuations grow as the Cosmic scale factor:

aIf only a fraction can cluster the equation is generalized to

ap

In the radiation dominated era p=0 and so we don’t have clustering. In the recent -dominated epoch again, p=0. Fluctuations grow only in the matter dominated epoch.

4

1241 * p

Page 29: Massive neutrinos and their impact on cosmology

In matter dominated era

If all the matter contributing to the energy density can cluster we have:

But if a fraction of matter is in form of massive neutrinos

the situation is different.

They contribute to the total energy density with a fraction f but they cluster only on scales bigger than the free-straming scale; for smaller scales they can’t do it, so we have:

ap

and 14

1241 so 1 *

*

1p and1 * f

Page 30: Massive neutrinos and their impact on cosmology

From the entropy conservation we obtain that:

The neutrino density today will be:

That, for a massive neutrino, translates in an energy content given by:

eVkTKTT 43/1

1068.1945.111

4

33,

32

1121827.0)3(

4

3 cmTnTgnkkfff

eV

mh

eV

m

h

mnk

kk

c

k

kkk

2.932.93

1 22

,

Page 31: Massive neutrinos and their impact on cosmology

And the perturbation grows less than the scale factor

The result is a lowering of the matter power spectrum on scales smaller than the free streaming scales. This lowering can be expressed by the formula ( and m are degenerate!):

P/P≈-8/m

Page 32: Massive neutrinos and their impact on cosmology

Cosmological Neutrinos

Unfortunately, despite their high density, we can’t detect cosmological neutrinos directly (see Hagmann astro-ph/9905258 for a discussion about future impossibilities).

However, neutrinos have great impact on the two most important observables in cosmology:

CMB (Cosmic Microwave Background radiation)

LSS (Large Scale Structures)

Page 33: Massive neutrinos and their impact on cosmology

Neutrino energy content in the universe

In the early hot universe neutrinos are kept in equilibrium with the cosmic plasma through weak interaction reactions

They decouple from the plasma when:

At temperature the reaction

increases the photon temperature respect to the

neutrino temperature

MeVTdec 1

MeVT 5.0 ee T

T

Page 34: Massive neutrinos and their impact on cosmology

From the entropy conservation we obtain that:

The neutrino density today will be:

That, for a massive neutrino, translates in an energy content given by:

eVkTKTT 43/1

1068.1945.111

4

33,

32

1121827.0)3(

4

3 cmTnTgnkkfff

eV

mh

eV

m

h

mnk

kk

c

k

kkk

2.932.93

1 22

,

Page 35: Massive neutrinos and their impact on cosmology

The effects on CMB concern:

• Change of the position of the first peak with increasing neutrino masses

• Enhancement of the heights of the second and third acoustic peaks

We don’t discuss here the physical origin of these effects, for a reference see, Ichikawa, Fukugita, Kawasaki, astro-ph/0409768 Hu, Fukugita, Zaldarriaga, Tegmark Astrophys. J. 549, 669,

2001

In principle we can measure neutrino masses with CMB alone and this is very important: in fact, with respect to the large scale clustering data, we don’t have problems with possible unkown biasing and not well-controlled nonlinear effects

Page 36: Massive neutrinos and their impact on cosmology

Neutrinos and Large Scale Structures

• Neutrinos affect the growth of cosmic clustering, so they can leave key imprints on the large scale structures we can see today

• In particular, massive neutrinos suppress the matter fluctuations on scales smaller than the their free-streaming scale when they becomes non-relativisitic.

• The result is a lowering of the matter power spectrum on scales smaller than the free streaming scales. This lowering can be expressed by the formula ( and m are degenerate!):

P/P≈-8/m

Page 37: Massive neutrinos and their impact on cosmology

...but we have degeneracies...

• Lowering the matter density suppresses the power spectrum

• This is virtually degenerate with non-zero neutrino mass

Page 38: Massive neutrinos and their impact on cosmology

CMB anisotropies

CMB Anisotropies are weakly affected by massiveneutrinos. However they constrain very well thematter density and other parameters and, whencombined with LSS data can break several degeneracies.

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Phenomenological reason for this anticorrelation

• When is increased m must increase correspondingly in order to produce the same power spectrum (remember the degeneration betwenn and m)

• However, we have the well known (m,w) degeneracy coming from supernovae data (see the formula for the luminosity distance DL)

• The combined effect is the anticorrelation in the plane mw

0for sin sinn and 0for sinh sin

density

)1()1()1(sin

kk

K

2))1(3(3

0

2

1

2

11

0

n

curvature

energydark

zwzdzncHD

W

Kw

Wm

z

KKL

Page 40: Massive neutrinos and their impact on cosmology

Overview

• Weighing neutrinos with cosmology and comparison with some laboratory data

• Impact of massive neutrinos on dark energy properties

• Conclusions and perspectives

Page 41: Massive neutrinos and their impact on cosmology

The lenght scale below whichNeutrino clustering is suppressedis called the neutrino free-streamingscale and roughly corresponds to thedistance neutrinos have time to travelwhile the universe expands by a factorof two. Neutrinos will clearly not cluster in an overdense clump so small that its escape velocity is much smaller than typical neutrino velocity. On scales much larger than the free streaming scale, on the other hand,Neutrinos cluster just as cold dark matter.This explains the effects on the power spectrum. The relative lowering of the matter power spectrum is given by:

mP

P

8

Page 42: Massive neutrinos and their impact on cosmology

i

ieimUm 2

Laboratory bounds on neutrino mass (for these arguments, see

the talk by A. Palazzo)Experiments sensitive to absolute neutrino mass scale :

Neutrinoless double beta decay (only if neutrino are Majorana particles!):

Neutrinoless doule beta decay processes have been searched in many experiments with different isotopes, yielding negative results.Recently, members of the Heidelberg-Moscow experiment have claimed the detection of a signal from the 76Ge isotope.If the claimed signal is entirely due to a light Majorana neutrinomasses then we have the constraint:

eVmeVmeV 2.1)2(81.043.0

Page 43: Massive neutrinos and their impact on cosmology

Overview

• Weighing neutrinos with cosmology and comparison with laboratory data

• Laboratory data constraints on massive

neutrinos and their impact on cosmology and in particular on dark energy properties

• Conclusions and perspectives

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Results (II)

• Several theoretical models have been recently proposed that can reproduce W<-1, as coupled neutrino-dark energy models. Moreover, the energy scale of dark energy is of the same order of the neutrino masses, so a possibly link between neutrinos and dark energy must certainly be further investigated

• Cosmological results are always model dependent. Changing the number of relativistic particles is one

possibility, but we can also think obout other ways. What happen, for example, relaxing the flatness condition?

Page 45: Massive neutrinos and their impact on cosmology

Constraints on a non-flat universe using CMB+SDSS+2dFGRS+supernovae data sets. Reprinted

from Spergel et al. astro-ph/0603449