physics of atomic nuclei volume 71 issue 4 2008 [doi 10.1134%2fs1063778808040066] a. d. dolgov --...

8/22/2019 Physics of Atomic Nuclei Volume 71 Issue 4 2008 [Doi 10.1134%2Fs1063778808040066] a. D. Dolgov -- Cosmolog

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ISSN 1063-7788, Physics of Atomic Nuclei, 2008, Vol. 71, No. 4, pp. 651670. c Pleiades Publishing, Ltd., 2008.

ELEMENTARY PARTICLES AND FIELDSTheory

Cosmology and New Physics*

A. D. Dolgov**

Institute for Theoretical and Experimental Physics, Moscow, RussiaINFN, Ferrara, Italy

Received August 13, 2007

AbstractA comparison of the standard models in particle physics and in cosmology demonstrates thatthey are not compatible, though both are well established. The basics of modern cosmology are brieflyreviewed. It is argued that the measurements of the main cosmological parameters are achieved throughmany independent physical phenomena and this minimizes possible interpretation errors. It is shown thatastronomy demands new physics beyond the frameworks of the (minimal) standard model in particlephysics. More revolutionary modifications of the basic principles of the theory are also discussed.

PACS numbers: 04.90.+eDOI: 10.1134/S1063778808040066

1. INTRODUCTION

Particle physics celebrates an excellent agree-ment of the minimal standard model (MSM) withexperiment, except probably for neutrino oscillations.On the other hand, cosmology also demonstrates agood agreement of astronomical observations withthe standard cosmological model (SCM). So far sogood, but it seems that MSM and SCM are not com-patible and an explanation of the observed featuresof the Universe is impossible without new physicalphenomena. Astronomical observations have already

led and will certainly lead in the near future to aston-ishing discoveries which may shatter cornerstones ofcontemporary physics and modify our understandingof basic principles.

The notion of new physics includes quite differentlevels of novelty:

(1) New objects and/or interactions.(2) Breaking of established rules or conservation

laws.(3) New principles.

This list can possibly be extended.(I) Some new physics is quite natural to expect.

For example, almost inevitable are the following:

(1) New fields or/and particles: stable or quasi-stable, heavy or light.

(2) Breaking of charges/quantum numbers:(a) electric (impossible? or at least nontrivial with

higher dimensions);

The text was submitted by the authors in English.**E-mail [email protected]

(b) baryonic (practically certain, cosmologicallydiscovered);

(c) total leptonic (expected);(d) leptonic family (discovered in neutrino oscilla-

tions!).Less probable:(3) Topological or nontopological solitons.(4) New types of interactions, especially new long-

range forces, and, in particular, modified gravity atlarge distances.

(5) Higher dimensions. It is unclear if astronomyis more sensitive to them or high-energy physics. Ifthey are small, of microscopic size, then chances tofeel them are better in high-energy collisions. Inthe case of large higher dimensions, astronomy maysuccessfully compete with high-energy physics.

(II) Unnatural new physics includes(1) Breaking of Lorentz invariance.(2) Violation ofCPT.(3) Breaking of the spinstatistics relation.(4) Breaking of unitarity and quantum coherence.(5) Violation of energy conservation.

(6) Violation of causality and possible existence oftime machine.(7) Breaking of the least action principle and of

Hamilton and Lagrange dynamics.(III) Unexpected new physicsanything which

is not in the list above and a priori will never be there.The content of the paper is the following. In Sec-

tion 2, the SCM is described. In Section 3, astronom-ical data characterizing the present-day Universe arepresented. In Section 4, the necessity of inflation is

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652 DOLGOV

advocated and basis features of inflationary cosmol-ogy are described. Section 5 is devoted to cosmo-logical baryogenesis, and in related Section 6, cos-mological mechanisms ofCPviolation are discussed.In Section 7, the problems of vacuum and dark en-ergies are considered. Basic features of primordialnucleosynthesis are briefly presented in Section 8.Formation of astronomical large-scale structures isdiscussed in Section 9. In Section 10, cosmologicalmanifestations of the violation of the spinstatisticstheorem for neutrinos are considered. In Section 12,we conclude.

2. STANDARD COSMOLOGICAL MODEL

As we have already mentioned in the Introduc-tion, the strongest demand for new physics comesfrom cosmology. In this connection, natural questionsarise: How reliable is the SCM? How much we cantrust it? The answers to both questions are positive.In the following short few-page review, we will advo-cate this statement. More detailed recent reviews onthe basics of modern cosmology can be found in [1].

The SCM is very simple and quite robust. Thetheoretical setting is the following:

(1) General relativity describing gravitational in-teractions. It is very difficult (if at all possible) tomodify this theory at large distances without breakingsome well-established fundamental physical princi-ples.

(2) Assumption (or one can say, observationalfact) of homogeneous and isotropic distribution ofmatter in the early Universe in a zeroth approxima-

tion. This is supported by the smoothness of the cos-mic microwave background radiation with accuracybetter than 104. Perturbations are treated in thefirst order analytically or numerically stimulated whenperturbations rise up to unity.

(3) Knowledge of cosmic particle content and formof their interaction. Sometimes an equation of state issufficient:

pj = fj(j) (1)

with pj and j being pressure and energy densitiesof matter. In fact, there are different forms of matterwith different equations of state, which is indicated by

index j here.The metric describing an isotropic and homoge-neous space has the form

ds2 = dt2 a2(t)f(r)dr2.It is a solution of the Einstein equations with f(r) =(1 + kr2/4) and k = 0, 1. Theory and observationsagree that k 0 with good precision. It means thatthe spatial geometry of our Universe is the Euclideanone.

The rate of the cosmological expansion is char-acterized by function a(t) or more precisely by itslogarithmic derivative called the Hubble parameter:

H = a/a. (2)

The Hubble parameter is time dependent, H 1/t,where t is the age of the Universe. Thefamous Hubble

law is already here:V = Hl, (3)

where V is the velocity of a distant object (which isnot gravitationally bound with our Galaxy or localgalactic cluster) and l is the distance to it.

The equations which govern the expansion of theUniverse, i.e., time dependence of the cosmologicalscale factora(t), are the following:

a

a= 4

3m2Pl( + 3p), (4)

where mPl = 1.2

1019 GeV is the Planck mass. TheNewton gravitational coupling constant is expressedthrough it as GN m2Pl .

Equation (4) looks likes Newtons second law de-scribing the acceleration of a test body induced bymatter inside radius a. An important fact is that notonly mass (energy) creates gravitational force but alsopressure. It allows for accelerated expansion, if ( +3p) < 0. As is usual in general relativity, for distancesl larger than the inverse Hubble parameter, i.e., forl >1/H, the expansion becomes superluminal. Thesetwo effects are necessary for making the Universesuitable for our life.

Equation (2) looks like the conservation of energyof a test body:

H2

a

a

2=

8

3m2Pl k

a2. (5)

If multiplied by a2/2, the left-hand side is the kineticenergy, while the first term on the right-hand side isnegative potential energy, and the second term is justa constant.

The critical (or closure) energy density is definedas

c =3H2m2

Pl8 . (6)

It is equal to the real total energy density for a spatiallyflat Universe, that is, fork = 0.

The measure of energy density of different speciesj of any gravitating matter is expressed through thedimensionless parameter

j = j/c. (7)

Evidently, ifk = 0, then tot

j j = 1.

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COSMOLOGY AND NEW PHYSICS 653

A more adequate variable which is often used in-stead of time is the redshift, z:

z + 1 = a(t0)/a(t), (8)

where a(t0) is the value of the scale factor at thepresent time, so the value of the redshift today is z =0. For adiabatic expansion, z is equal to the ratio of the

cosmic microwave background radiation (CMBR)temperature at some earlier time with respect to itspresent-day value (see below).

There is one more very important equation, thoughnot an independent one, namely, the covariant energymomentum conservation,

DT T; = 0. (9)

In our special homogeneous and isotropic case, itlooks like

+ 3H( +p) = 0 (10)

and follows from Eqs. (4) and (5).

General relativity implies automatic conservationofT (9), due to the Einstein equations:

G R 12

gR =8

m2PlT. (11)

Indeed, the covariant divergence of the left-hand sideidentically vanishes and so must T;. This is a resultof general covariance, i.e., invariance of physics withrespect to an arbitrary choice of the coordinate frame.

In the recent (and not so recent) literature, thereare some papers, where the assumption of time-dependent constants is considered, in particu-

lar, time-dependent gravitational coupling constantGN = GN(t) and cosmological constant (t) (aboutthe latter, see below Section 7). The authors ofthese works use there the same standard Einsteinequations (11) with nonconstant mPl. Enforcing thecondition of conservation of the Einstein tensor, G,and the energymomentum tensor of matter, T,the authors derive some relations between GN(t) and(t). However, this procedure is at least questionable.If the Einstein equations are derived as usual by func-tional differentiation of the total action with respect tometric, A/g = 0, then the equation must containadditional terms proportional to (second) derivatives

of GN over coordinates. If the least-action principleis rejected, then there is no known way to deducean expression for the energymomentum tensor ofmatter.

The equations of state are usually parametrized as

p = w. (12)

In many practically interesting cases, parameter w isconstant, but it is not necessarily true and it may be afunction of time. In this case, to determine w(t), one

has to solve dynamical equation(s) of motion for thecorrespondingfield(s).

Simple physical systems with w = 1, 2/3,1/3, 0, 1/3, 1 are known. They are, respectively,vacuum state (vacuum energy), collection of nonin-teracting plane domain walls, straight cosmic strings,nonrelativistic matter (withp

), relativistic matter

(with p = /3), and the so-called maximum rigidequation of state (p = ). In the last case, the speedof sound is equal to the speed of light (that is why itis the most rigid). It can be realized by a scalarfield inthe course of cosmological contraction. It is strangethat matter with w = 2/3 is absent in this sequence.

One can see from Eq. (4) that, if w < 1/3, thecosmological matter antigravitates despite positiveenergy density. Correspondingly, the Universe ex-pands with acceleration. It is worth noting, however,that, if > 0, any matter in a finite region of space hasnormal attractive gravity. Only infinitely large piecesof matter may antigravitate.

Fornormal matter, > 0 and || > |p|, and thus < 0, so energy density drops down in the course ofexpansion, as is naturally expected. However, for thevacuum case, the energy dominance condition, |p| 6 the subdominant baryonsbecome dominant. Thus, inflation could last at most6 Hubble times which is by far too short.

Thus, initial conditions with an excess of particlesover antiparticles are not compatible with inflationand dynamical generation of excess of B over B isnecessary. The mechanism for that was suggestedby Sakharov [16]. To this end, the three followingconditions should be fulfilled:

(1) Nonconservation of baryons, theoretically nat-

ural; proved to be true in MSM and in GUT. Cosmol-ogyisan experimental proof: We exist, ergo baryonsare not conserved.

(2) Breaking ofC and CP, experimentally estab-lished in particle physics.

(3) Deviation from thermal equilibrium. It is al-ways true in an expanding Universe for massive par-ticles or/and in the case of first-order p.t. in theprimeval plasma.

There are plenty of models of baryogenesis in theliterature; for reviews, see [14, 17]. There is only onenumber to explain, the ratio of baryonic charge den-sity to the number density of CMBR photons:

=nB nB

n=

nBn

today

6 1010. (29)

A plethora of scenarios can do that, but all requirenew physics. In principle, baryogenesis is possible inthe MSM of particle physics because it contains allthe necessary ingredients [18]:

(1) C and CP are known from experiment to bebroken.

(2) Baryons are not conserved because of chiralanomaly (in non-Abelian theory). The charge non-conservation is achieved by some classical configura-

tion of the Higgs and gauge boson fields, sphalerons(see, however, criticism in [19]).

(3) Thermal equilibrium would be strongly brokenif the EW p.t. were first-order phase transition.

So far so good. However:(1) Heavy Higgs makes a first-order p.t. improba-

ble. Another possible source for deviation from equi-librium due to nonzero masses of W and Z is tooweak:

f

feq H

mW

mPl 1015. (30)

(2) CPviolation at high T, T TEW 100 GeV,is tiny: the amplitude of CP breaking in MSM isproportional to the product of the mixing angles andto the mass differences of all down and all up quarks:

A J(m2t m2u)(m2t m2c)(m2c m2u) (31) (m2b m2s)(m2b m2d)(m2s m2d)/T12,

where

J = sin 12 sin 23 sin 31 sin (32)



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660 DOLGOV

is the Jarlskog determinant. At T 100 GeV, whensphalerons were in action, A 1019, which is toosmall.

It is interesting that it is necessary to have threequark families to create CP violation in MSM athrough a CP-odd phase in the CKM matrix. Thus,if baryogenesis is efficient in MSM, there is an ex-

planation

why we need three families. Unfortunately,this is not the case, and eitherCPbreaking is differentin particle physics and cosmology and we do not needthree families, or some modification of MSM wouldallow us to create observable baryon asymmetry withthree (and only three) families.

For example, one may avoid these problems andcreate baryon asymmetry in EW theory with threefamilies if one assumes time variation of fundamentalconstants [20] such that

mPl mEW, mqj mEW, mqj mqj . (33)But this is very new physics. May baryogenesis be

an indication of time-varying constants, TeV gravity,and large higher dimensions?!The next currently very popular scenario of cre-

ation of a charge asymmetric Universe is {baryo-through-lepto-genesis}. According to it, the cosmo-logical lepton asymmetry, L, could be produced bydecays of heavy, m 1010 GeV, Majorana fermions.Subsequently, L transformed into B by EW(sphaleron) processes [21] (for recent reviews,see [22]). All three of Sakharovs conditions aresatisfied:

(1) L is naturally nonconserved.(2) Heavy particles to break thermal equilibrium

are present.(3) Three CP-odd phases of order unity could be

there.The model might successfully explain the origin

of the baryon asymmetry but again demands newphysics: new heavy particles and new sources ofCPviolation are necessary.

6. CP VIOLATION IN COSMOLOGY

There are three possible ways for breaking CPsymmetry:

(1) Standard, explicit by complex constants in theLagrangian.(2) Spontaneous [23]. This can be realized if there

exists a complex scalar field with two (or several)degenerate vacuum states. The Universe as a wholeshould be charge symmetric but locally could beasymmetric. Unfortunately, domain walls betweenvacua with different CP-odd phases should naturallyhave a huge energy and thus they are cosmologicallydangerous [24]. A natural way to avoid this problem is

to make our domain much larger than the present-dayhorizon. However, this makes the model observation-ally indistinguishable from the standard one.

(3) Dynamical or stochastic [14, 25, 26]. Thismechanism is similar to the spontaneous one butwithout domain walls. It can also be realized by acomplex scalarfield displaced from the minimum of

its potential (e.g., by quantum fluctuations during in-flation) and not yet relaxed to the origin during baryo-genesis. However, the field would certainly vanish bythe present time and, if so, CPviolation in cosmologywould have nothing in common with the observed CPviolation in particle physics.

An attractive feature of this mechanism is that arich Universe structure with isocurvature perturba-tions and even antimatter domains may be created.Probably, it is the only chance to obtain observationalinformation about the mechanism of baryogenesis,because not only one number(29) is explained but awhole function (t,x) with interesting observational

features is predicted. For detailed discussions, seelectures [27].

7. PROBLEM OF VACUUM AND/OR DARKENERGY

7.1. Definition and History

As is well known, the Einstein equations allow anadditional term proportional to the metric tensor:

R 12

gR g = 8GNT. (34)

This addition was suggested by Einstein himself [28]in 1918 in an (unsuccessful) attempt to obtain sta-tionary solutions of Eq. (34) in a cosmological situ-ation. The idea was that the gravitational repulsioninduced by could counterbalance gravitational at-traction of the ordinary matter. The fine tuning looksunnatural and, what is more, the equilibrium is evi-dently unstable.

This was the beginning of a long and still lastingstory of the term. Its biographical sketch looks asfollows:

(1) Date of birth: 1918.

(2) Names: cosmological constant, term, vac-uum energy, or, maybe, dark energy.(3) Father: A. Einstein, who later, after Hubbles

discovery of the cosmological expansion, consideredhis baby as the biggest blunder of my life. Somemore quotations worth adding here. Lemaitre: great-est discovery, deserving to make Einsteins name fa-mous. Gamow: raises its nasty head again (afterindications in the 1960s that quasars are accumulatednearz = 2).



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(4) Several times and for a long time, the termwas assumed dead, probably erroneously. It is aliveand well today, but still not safemany want to killit.

This new term is called the cosmological constant,because the coefficient must be a constant indepen-dent of spacetime coordinates. Indeed, the Einstein

tensor is known to be covariantly conserved:D

R

1

2gR

0. (35)

This property is automatic in metric theories. There isa simple analogy with electrodynamics. The Maxwellequations have the form

F = 4J. (36)

Owing to antisymmetry ofF,

F 0, (37)

and the current must be conserved,

J

= 0. (38)On the other hand, the current is conserved becauseofU(1) invariance (gauge invariance) and the theoryis self-consistent.

In the case of general relativity, the situation isvery similar. Automatic conservation of the Einsteintensor (35) leads to conservation of the sum:

D

T(m) /(8m2Pl) + g

= 0. (39)

The energymomentum tensor is defined as a func-tional derivative of the matter Lagrangian and mustbe conserved owing to invariance of the theory with

respect to an arbitrary change of coordinates. Thus,DT

(m) = 0. (40)

Taking into account that, in metric theory, the metrictensor is covariantly constant

Dg 0, (41)

we come to an important conclusion that the cosmo-logical constant must be constant:

= const. (42)

There are plenty of models in the literature with atime-dependent cosmological constant, = (t). It

is evident from the discussion above that such modelsare not innocent. One needs to introduce additionalfields to satisfy the energy-conservation condition orto make more serious modifications of the theory,e.g., to consider nonmetric theories. The first attemptto make a time-dependent was done in 1933 byBronshtein [29]. It was strongly criticized by Landauowing to the reasons presented above.

A new understanding of the nature of the cos-mological constant came from quantum field theory.

In its language, is equivalent to vacuum energydensity:

T(vac) = vacg, = 8vac/m2Pl. (43)

Quantum field theory immediately led to very seriousproblems. Theoretically, the vacuum energy shouldbe huge, . The mismatch between theory andupper bounds from cosmology was at the level of10050 orders of magnitude, depending on the typeof contribution to vacuum energy. As a result, the sci-entific establishment took the eclectic point of view:

= 0. (44)This point of view is shared by many people even now.As Feynman said many years ago about radiative cor-rections in quantum electrodynamics: Correctionsare infinite but small. However, in contrast to elec-trodynamics, there are well-defined contributions tovacuum energy which are known to be 50 or moreorders of magnitude above its observed value (see

below).From the 1960s to the end of the millennium, thevacuum energy was assumed to be identically zero.Only a few physicists treated the problem as an im-portant one, starting from Zeldovich [30]. A nonnegli-gible number of scientists took a more serious attitudeto only recently at the end of the 20th centurywhen several independent pieces of data were accu-mulated which strongly indicated that empty spaceis not empty and it antigravitates, inducing acceler-ated expansion. It is still unknown what induces thisacceleration: vacuum with positive energy density orsome other form of energy with negative pressure,p m. For the measuredpresent-days values, vac 2.3m, the equilibrationbetween gravitational attraction and repulsion tookplace at z 0.7 in accordance with observations.

(4) LSS and CMBR fit theory well if v 0.7.The theory of LSS formation is not free from as-sumptions, but they are quite natural and testable.The basic inputs are gravitational instability basedon general relativity; assumption offlat spectrum ofa primordial fluctuations (verified by observation oflow multipoles of the angular spectrum of CMBR);assumption on the type of dark mattercold dark

matter (noninteractive?); and numerical simulationswhen perturbations become large.To conclude, it is established by different inde-

pendent astronomical observations that vacuum orvacuum-like energy is nonvanishing. Its relative con-tribution to the total cosmological energy density islarge on the cosmological scale,

v = 0.7 or vac 1047 GeV4, (45)and negligible on the particle physics scale. All differ-ent data are consistent with

m = 0.3 and tot = 1. (46)

7.3. Evolution of Vacuum(-like) Energyduring Cosmic History

It may be instructive to consider the role of vac-uum energy during the lifetime of the Universe. Atinflation, vac 10100nowv and was dominant. But itwas not really strictly constant vacuum energy butvacuum-likeenergy of an almost constant scalarfield,inflaton. After inflaton decay to elementary particles,the Universe was dominated by normal, presumablyrelativistic matter. If the reheating temperature washigher than the GUT scale, a p.t. from an unbroken to

broken GUT state should have taken place. At sucha p.t., the change in vacuum energy was huge:

vac 1060 GeV4. (47)Whethervac dominated or not depended on the orderof the p.t. For the second-order, vac might be alwayssubdominant, while for the first-order p.t., it coulddominate.

A similar picture took place at the EW p.t. with

vac 108 GeV4 (48)

and at the QCD p.t. with

vac 102 GeV4. (49)There is one important point related to the QCDp.t.: the magnitudes of vacuum energies of gluon andchiral condensates which have been formed at this p.t.are known from experiment!

After inflation until almost the present epoch, vacwas always subdominant, with the possible exceptionof short periods before completion of the p.t. It startedto dominate the energy density only recently at z 0.3.

7.4. Contributions to Vacuum Energy

According to quantum field theory, all fields arerepresented as an infinite collection of quantum os-cillators, each having energy /2 (as in the usualquantum mechanics). The contributions to vac frombosonic and fermionic fields have different signs be-

cause the bosonic field operators commute, whilefermionic ones anticommute. The energy density of abosonic vacuum fluctuation is

Hbvac =

d3k

(2)3k2akak + bkbkvac

=

d3k

(2)3k = 4,

while that of a fermionic one is

Hfvac =

d3k

(2)3k2akak bkbkvac

=

d3

k(2)3

k = 4,

where =

k2 + m2 and m is the mass of the corre-spondingfield.

One immediately sees that, if there is an equalnumber of bosonic and fermionic fields in nature andtheir masses are equal (at least pairwise), then theenergy of vacuum fluctuations vanishes. This wasnoticed by Zeldovich [30] three years before super-symmetry was discovered [32].

Indeed, if nature is supersymmetric, the numberof bosonic degrees of freedom is equal to the number

of fermionic ones, Nb = Nf, and, if supersymmetry isunbroken, the masses must be equal as well, mb =mf. In this case, indeed, vac = 0. In the real world,however, supersymmetry is broken and soft super-symmetry breaking, required by renormalizability ofthe theory, necessarily leads to

vac 108 GeV4 = 0. (50)This could be bad news for supersymmetry, but thelocal realization of the latter, which includes gravity,



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SUGRA [33], allows for vanishing vacuum energyeven in the broken phase but at the expense of fan-tastic fine tuning at the level of about 10120, becausethe natural value of the vacuum energy in brokenSUGRA is at the Planck scale:

vac m4Pl 1076 GeV4. (51)

As we have discussed in the previous subsection,in the course of cosmological expansion, the cosmicplasma underwent several p.t. at which the vacuumenergy changed by an amount much larger than theobserved value today

vac 1047 GeV4.Especially striking are QCD condensates which areknown to be nonvanishing in the todays vacuumstate. QCD is well established and experimentallyverified science. It leads to the conclusion that vac-uum is not empty but filled with quark and gluoncondensates,

qq = 0, GG = 0, (52)both having nonzero (negative and huge on the cos-mological scale) vacuum energy:

QCDvac 1045c. (53)The fact that this condensate must exist can be

seen from the estimate of the proton mass. A proton(or neutron) consisting of three light quarks, eachhaving mass of a few MeV, should have mass about1015 MeV, instead of 940 MeV. This discrepancyis solved by existence of the gluon condensate withnegative energy. Inside the proton, the vacuum gluoncondensate is destroyed by quarks and the protonmass is

mp = 2mu + md vacl3p, (54)where lp 1/m is the proton size and m is the pionmass.

However, outside the proton, the gluon conden-sate is nonvanishing and its energy density is abouta factor of1045 larger than the cosmological energydensity. The big question is who adds the necessarydonation to make the observed vac > 0 and whatkind of matter is it?

7.5. Intermediate Summary

We can summarize the state of the art as follows:(1) Huge contributions to vac are known, but the

mechanism of their compensation down to (almost)zero observed value is a mystery.

(2) Todays observed vac and m differ only by afactor of 2, despite very different evolution with time,vac = const and m 1/t2. Why?

(3) What is the nature of the antigravitating mat-ter? Is it just vacuum energy or something different?

Mostly, only problems 2 and 3 are addressed inthe literature either by modification of gravity at largescales or by an introduction of a new (scalar) field(quintessence) leading to accelerated expansion.

However, most probably, all three problems are

strongly coupled and can be solved only together afteran adjustment ofvac down to c is understood.

7.6. Possible Solutions

The list of suggestions which may in principlelead to a solution of all three problems summarizedin the previous subsection is the following (possiblyincomplete):

(1) Subtraction constant. If dark energy is simplyvacuum energy, then only one number has to be ex-plained and theoretically it may have any value. This

uncertainty reflects the unknown level of zero energyor in other words an arbitrary value of a subtractionconstant. There is of course an enormous fine tuningto fix this value just at c, but formally one cannotexclude this ugly solution. In the case where darkenergy is not vacuum energy and changes with time,the subtraction constant idea is aesthetically evenless appealing but still is not excluded.

(2) Anthropic principle [34]. This principle ex-cludes very large values of vacuum energy becauselife would not be possible in such Universes. It gives a

justification of a good choice of the subtraction con-stant. The fine tuning in this case drops down from

100 orders to 23 orders of magnitude. Lacking anybetter suggestion, this might be a feasible solutionbut still not especially attractive. This reminds oneof unsatisfactory solutions of the problems of the oldFriedman cosmology before the inflationary idea wasproposed [8].

(3) Infrared instability of massless fields (gravi-tons) in de Sitter spacetime [35]. Massless parti-cles are quite efficiently produced by the gravitationalfield in an exponentially expanding background. Theirenergy density may compensate the original vacuumenergy and slow down the expansion. The mechanism

looks natural and quite promising, but unfortunatelyit seems to be inefficient.(4) Dynamical adjustment, analogous to axion so-

lution of the problem of strongCPviolation in QCD.It looks most attractive to me and because of that it isdiscussed below in a separate subsection.

(5) Drastic modification of existing theory: higherdimensions, breaking general covariance and Lorentzinvariance, a rejection of the Lagrange/Hamiltonianprinciple, . . .. Maybe a solution is indeed somewhere



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664 DOLGOV

down this road, but it is difficult to say today, where itis exactly.

There are dozens of reviews on the vacuum-energyproblem now. An incomplete list of recent ones iscollected in [36].

7.7. Dynamical Adjustment

The basic idea of dynamical adjustment is ex-tremely simple: it is assumed that there exists a newfield (scalar or higher spin) coupled to gravity insuch a way that, in de Sitter spacetime, a vacuumcondensate of is formed which compensates theoriginal vac. This would be a manifestation of thegeneral Le Ch atelier principle on the cosmologicalscale: the system always reacts in such a way as todiminish an external impact.

The dynamical adjustment was historically thefirst [37] proposal to compensate vacuum energydown to a cosmologically acceptable level. Though nosatisfactory realization of the idea has been found upto now, it has very attractive properties. First, vacuumenergy is never compensated down to zero but onlyto some remainder which is generally of the order ofc. In this sense, the dynamical adjustment idea pre-dicted (and not postdicted) existence of dark energywith the density close to c and thus solved the aforementioned problems of compensation of the hugevacuum energy and of existence of a noncompensatedremnant with the proper magnitude. Byproducts ofdynamical adjustment have many features of lessambitious models of modified gravity, e.g., an explicitbreaking of Lorentz invariance, and a time-dependentunstable background with stable fluctuations over it.

The first attempt to realize the dynamical adjust-ment idea was based on a nonminimally coupledscalarfield [37]:

+ 3H + U(, R) = 0

with, e.g., U = R2/2. This equation has unstable,rising with time, solutions ifR < 0. Asymptotically, rises as t and the de Sitter exponential expan-sion turns into a Friedman power-law one, but thisis not due to compensation ofvac by because theenergymomentum of the latter is not proportional to

the vacuum one:T() = F g; (55)

and the change of the regime is achieved owing toweakening of the gravitational coupling:

GN 1/t2. (56)This is surely excluded. The models with vector [38]or tensor [2] fields were only slightly better but stilldid not lead to realistic cosmologies.

More recently, a scalar with crazy coupling togravity was considered [39, 40]:

A =

d4x

g

1

2(R + 2) (57)

+ F1(R) +DD

2R2 U(, R)

.

The equation of motion for has the form

D

D

1

R

2+ U() = 0. (58)

The second necessary equation is the trace of theEinstein equations. In the particular case with F1 =C1R

2, it reads

R + 3

1

R

2(D)

2 4 [U() + vac] (59)

6D2

2C1R1

R2 (D)2

R

= T

.

One can check that the solution to this equationstends to

R vac + U() = 0. (60)It has some nice features (almost realistic), e.g.,H = 1/2t, but is unstable and easily runs away fromanything resembling realistic cosmology.

A desperate attempt [40] to improve the model byintroduction of a nonanalytic kinetic term

(D)2

R2 (D)2

R|R| (61)was unsuccessful too.

More general action with a scalarfield [40]

A =

d4x

g[m2Pl(R + 2)/(16) (62)+ F1(R) + F2(, R)DD

+ F3(, R)DDR U(, R)]

was not yet explored. Moreover, R and R canalso be included.

To summarize general features of the adjustmentmechanism:

(1) Some compensating agent must exist!

(2) It is quite natural to expect that vac is notcompletely compensated and c.

(3) A realistic model is needed; it can indicate whatthe value of w is: is it (1), i.e., are the noncom-pensated remnants of vacuum energy is also vacuumenergy, or is w = 1 and does a new strange form ofenergy live in the Universe?



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8. BIG BANG NUCLEOSYNTHESIS

BBN or creation of light elements took place in therelatively late Universe, when it was from 1 to 200 sold and temperatures were between MeV and 6070 keV. The physics is well known at these energies.First, it is the usual low-energy weak interactionleading to neutronproton transformations:

n + e+ p + e, n + e p + e. (63)The rate of these reactions became slow with respectto the cosmological expansion rate at T 0.7 MeV.After that, the neutron-to-proton ratio remained con-stant (up to the slow neutron decay) and this de-termined the starting value of the n/p ratio withwhich nucleons arrived to form light nuclei. The latterstarted and proceeded very quickly almost instantly,at TBBN = 6070 keV. The exact value of TBBN de-pends upon the baryon-to-photon ratio, (29). Thisrelation allows one to determine from BBN, espe-cially from deuterium abundance. Though the deu-

terium measurements are quite dispersed, the resultis in reasonable agreement with determined byCMBR. At T = TBBN, all neutrons quickly formed4He (about 25% by mass) and a little 2H (3 105 bynumber), 3He (similar to 2H), and 7Li (1091010).The results span nine orders of magnitude and arewell confirmed by the data.

It is interesting that a relatively small variationof the Fermi coupling constant would dramaticallychange the chemical content of the Universe. A slightincrease in GF would lead to a later freezing of(np)transformation and a smaller number of neutrons.

In this case, the primordial Universe until formationof the first stars would be purely hydrogenic. In theopposite case of smallerGF, the Universe would behelium dominated. In both of these extremes, theproperties of the first stars and their evolution wouldbe completely different from those in our Universe.

As is summarized in review [6], there is very goodagreement between theory and data on light ele-ment abundances with determined form CMBR(see Fig. 3 taken from [6]). However, this picture maybe too optimistic because there is some conflict be-tween 4He and 2H. The former corresponds to lower. According to [41], Y = 0.238 0.002, while in [42]Y = 0.2421 0.0021 (1, only statistical error bars).These results are shown in Fig. 4 as the diagonallyhatched regions, where the upper one is the resultsof [42] and the lower one is the results of [41]. Inaddition, different individual measurements of pri-mordial deuterium demonstrate large dispersion andindicate both larger and smaller . Moreover, thetrend for smaller demonstrates 7Li. For a differentpoint of view from [6], see another review [43]. InFig. 5 [43], the baryon-to-photon ratio 10 = 1010is

10

0

10

1

Baryon-to-photon ratio

10

10

10

10

9

7

Li/H

10

5

10

4

10

3

3

He/H

2

H/H

0.23

0.25

0.27

Y

10

2

Baryon density

b

h

2

Fig. 3. [6] 4He, D, 2He, and 7Li (curves from top tobottom) predicted by the standard BBN. Boxes indicatethe observedlight element abundances (smaller boxes: 2statistical errors; larger boxes: 2 statistical and sys-tematic errors). The vertical band is the CMBR measureof the cosmic baryon density.

presented as determined from different light elementabundances and is compared with that found fromCMBR. There are noticeable deviations.

Most probably, the discrepancy will disappear withfuture more accurate measurements, but if it is con-firmed, a strong indication of new physics will bediscovered.

The data on 4He and 2H abundances permit one toobtain an upper limit on the number of effective neu-trino species, N, participating in BBN, because Naffects the cooling rate of the Universe and changesthe neutronproton freezing temperature. A fair esti-mate is N

= 3

1.

9. FORMATION OF LARGE-SCALESTRUCTURE

Formation of galaxies and their clusters is a veryessential part of modern cosmology. On one hand,it clearly demonstrates the necessity of new physicsand, on the other hand, comparison of theory with ob-servations shows good agreement of basic principleswith the data. For a review, see, e.g., [44].



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666 DOLGOV

4

10

10

8

10

10

0.23

0.24

0.25

4

He

0.95

1.00

1.05

X

b

/

X

f

2

H

4

He

7

Li

WMAP

Fermi

Bose

Boltzmann

4

He obs.

Fig. 4. Upper panel: the ratios of abundances of different

elements in the cases of purely bosonic neutrinos withrespect to the standard fermionic case as functions of thebaryon-number density, . The vertically hatched regionshows the WMAP 2 determination of. Lower panel:the absolute abundance of4He as a function of for thepurely bosonic, Boltzmann, and fermionic neutrino dis-tributions, corresponding to = 1, 0, +1, respectively.The two diagonallyhatched regions show the observationof primordial helium from [41] (lower) and [42] (upper),which marginally overlap at 1.

The theoretical input is very simple: rise of theinitial small density perturbations because of gravita-tional instability. To proceed with calculations of thestructure formation, one needs to know the spectrumof primordial fluctuations. Usually, power law (21) isassumed. As we have already mentioned, n = 1, ai.e., flat, HarrisonZeldovich, spectrum as predictedby inflation and confirmed by CMBR at large scalesl 10 Mpc.

The next important step is an assumption of theproperties of dark matter and dark energy. The formeris normally assumed to be noninteracting cold darkmatter, while dark energy is taken as the vacuumone. The corresponding cosmology is called -CDM.Interesting possibilities of self-interacting dark mat-

ter, e.g., mirror (for a recent review containing animpressive list of references, see [45]), or warm darkmatter, remain viable as well.

With these assumptions, one can make analyticalcalculations in a linear regime when perturbations aresmall, / 1. To this end, the standard physics,general relativity, and hydrodynamics in a gravita-tional field are used. The results are applicable tovery large scales at which perturbations remain small.These scales are accessible to CMBR. The angular

2

7

Li

10

4 6 8

3

He

2

H

4

He

WMAP

Fig. 5. [43] The BBN values for the early Universe(20 min) baryon abundance parameter10 inferred from

the adopted primordial abundances of2

H,3

He,4

He, and7Li. Also shown is the WMAP-derived value (400kyr).

fluctuations of the latter are in agreement with the -CDM picture.

For smaller scales, l < 10 Mpc, and larger per-turbations, / 1, when the nonlinearity of equa-tions becomes significant, one needs to make nu-merical simulations. The latter are of course over-simplified: the mass of individual particles is takento be about 106 M, where M = 2 1033 g is thesolar mass, and only gravitational interactions aretaken into account. Still, the description happenedto be quite successful and is confirmed (but strictlyspeaking not proven) by the data. Large density per-turbations at smaller scales (e.g., isocurvature ones)are not excluded. Their presence can invalidate thecosmological upper bounds on neutrino mass recentlystrengthened in numerous works [46] (possibly, thelist is not complete).

At this stage, we can present one more argumentin favor of nonbaryonic dark matter. Since protons(and 4He ions) strongly interact with photons, thefluctuations of baryonic matter can rise only after re-

combination, i.e., in neutral matter. Otherwise, pho-tonic pressure prevents baryons and electrons fromgravitational clumping. Density fluctuations at theMD regime rise as the first power of the scale factor.Thus, the density contrast in a purely baryonic Uni-verse may rise at most by 103. In the case of adiabaticfluctuations (proven by CMBR),

T

T< 104, (64)



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and fluctuations could not reach unity by today incontrast to what we see. Fluctuations in nonbaryonicdark matter do not interact with light and thus do notsuffer from the pressure of CMBR. Hence, fluctua-tions can rise at the MD stage prior to recombinationstarting from redshift z 104. This allows structuresto be formed by the present day.

Together with the knowledge of DM = 0.22 andB = 0.044, we are forced to conclude that dark mat-ter indeed exists and it is not the usual baryonic one.Though most of the baryons in the Universe are invis-ible, their number is by far smaller than the amount ofcosmological dark matter.

As for the possible forms of dark (invisible) mat-ter, there are several (too many?) candidates. Amongthem are the following (but the list is far from beingcomplete):

(I) Cold dark matter (CDM): lightest supersym-metric particle, m = 0.11 TeV; axion, m = 105 eV;mirror particles; primordial black holes.

(II) Warm dark matter (WDM): sterile neutrinosm = 0.11 keV.

(III) Hot dark matter (HDM): usual neutrinos orlight sterile neutrinos; they must be subdominant.Otherwise, the LSS formation would be inhibited.

Thus, new particles which are absent in MSMmust exist. It is a striking example of how astronomypredicts an existence of new elementary particles.One can make cold dark matter without new stableparticles with primordial black holes with a well-spread mass spectrum, from a minor fraction of thesolar mass up to millions of solar masses [47], but

the mechanism of formation of such black holes alsodemands new physics.

10. UNNECESSARY NEW PHYSICS,OR NEUTRINO STATISTICS

AND COSMOLOGY

This is a long-standing question if statistical prop-erties of bosons and fermions may be (slightly) differ-ent from the usual BoseEinstein and FermiDiracones. In fact, Pauli and Fermi repeatedly asked thequestion whether the spinstatistics relation could benot exact and electrons were not identical but a little

bit different.Possible violation of the exclusion principle for

the usual matter, i.e., for electrons and nucleons,was discussed in a number of papers at the end ofthe 1980s [48]. Efforts to find something more gen-eral than pure FermiDirac or BoseEinstein statis-tics [49] were taken, but no satisfactory theoreticalframeworks were found. Experimental searches forviolation of the Pauli principle for electrons [50] andnucleons [51] have also given negative results.

However, there is still a lot of experimental freedomto break Fermi statistics for neutrinos. In the casewhere the spinstatistics relation is broken, whileotherwise remaining in the frameworks of the tradi-tional quantum field theory, then immediately severaldeep theoretical problems would emerge:

(i) nonlocality;

(ii) faster-than-light signals;(iii) nonpositive energy density and possibly un-

stable vacuum;(iv) maybe breaking of unitarity;(v) broken CPTand Lorentz invariance.To summarize, there is no known self-consistent

formulation of a theory with a broken spinstatisticstheorem. So let us postpone discussion of (nonex-isting) theory and consider cosmological effects ofneutrinos obeying Bose or mixed statistics [52].

If neutrinos were Bose particles, they could form acosmological Bose condensate,

fb =1

exp[(E )/T 1] + C(k), (65)

and make both cold and hot dark matter. So instead ofnew particles obeying old physics, dark matter couldbe created from the old known particles but with verynew physics. More details can be found in [52].

A deviation from Fermi statistics would be observ-able in BBN [53, 54]. There are two effects resultingin a change of primordial abundances:

(i) The energy density of bosonic neutrinos wouldbe 8/7 of normal fermionic , resulting in a rise of

effective neutrino species by N = 3/7.(ii) A larger density of e would lead to smaller

temperature ofn/p freezing, which is equivalent to adecrease in N.

The net result is that the effective number of neu-trinos at BBN would be smaller than three: N(eff) =2.43.

We assume following [54] that the equilibrium dis-tribution for mixed statistics has the form

f(eq) = [exp(E/T) + ]1 , (66)

where interpolates between the usual Fermi statis-

tics, = 1, to pure Bose statistics = 1. Seem-ingly, as one can see from Fig. 4, the data are notice-ably better described by bosonic neutrinos. However,observational uncertainties are too large to make adefinite conclusion.

If, together with the spinstatistics theorem, CPTand/or unitarity is/are also broken, the usual equi-librium distributions would be distorted too and theeffects could be accumulated with time and becomelarge.



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668 DOLGOV

11. SOME MORE UNNECESSARY PHYSICS

Unfortunately, constraints of time and space donot allow for any detailed discussion of other unnec-essary new physics as, e.g., breaking of Lorenz invari-ance, violation of the CPT theorem, and possibility of(large) higher dimensions. The situation with all thatis unclear and it could be that the related phenomena

are not realized. Though the probability of existenceis low, the stakes are high and new physics withoutany restrictions, except for experimental ones, couldbe very interesting. Probably, the cosmos will be thebest place to look for these completely news effects.

A possibility of astronomical manifestations ofhigher dimensions, D > 4, looks exciting. It openspractically unrestricted room for theoretical imag-ination. However, it may be difficult to prove theirexistence. We live in 4D world and most probably willnot be able to penetrate other dimensions. It may bea nontrivial task to distinguish between phenomenawhich came to us from higher dimension or have a

simpler (or even more complicated) explanation inD = 4.

A very interesting effect which may arise fromhigher dimensions is electric-charge nonconserva-tion [55]. However, electric-charge might be visiblynonconserved if photons are a little massive, and inthis case black holes could capture charged particleswithout electric hairs left outside [56]. Maybe theevil axis could be explained by an electric-chargeasymmetry of the Universe.

Probably, in a 4D world, any energy nonconserva-tion is absolutely forbidden, and if it were observed,

this would be an unambiguous indication that we areconnected to D > 4 space.

12. CONCLUSIONS

Cosmology unambiguously proves that there isnew physics (far) beyond the minimal, and not onlyminimal, standard model of elementary particle world.As we have seen, inflation, which is practically anexperimental fact, demands a new field orfield whichhad induced exponential expansion, creating a cor-rect Universe. These fields have to be very weaklycoupled to the ordinary fields/particles and are absent

in MSM.Baryogenesis is impossible in MSM as well. Ei-

ther heavier fields or time variation of fundamentalconstants is necessary. In particular, the amplitudeof CP violation might be much larger in the earlyUniverse than in particle interactions at the presenttime.

It is proven that the bulk of matter in the Universeis not the ordinary baryons. There are several goodcandidates for dark matter particles, but it is still

unknown which one is in reality. This is a primaryproblem for experiment and/or astronomical analysis.There is the possibility to make cosmological darkmatter out of light massive neutrinos but at the ex-pense of breaking the spinstatistics theorem. Theprice is very high, but the consequences would beexciting.

The 70% bulk of matter in the Universe, darkenergy, is even weirder than simple dark matter.In contrast to the ordinary matter, this dark energyinduces gravitational repulsion. There can be a simplephenomenological description of cosmological accel-eration by a tiny vacuum energy or by a very lightscalar field (do we need that field if vacuum energycan do the job?), but only if one forgets about theformidable problem of a huge discrepancy, by 10050 orders of magnitude, between the natural valueof vacuum energy and the astronomically measuredvalue. If one recalls that there are experimentallyknown huge contributions to vacuum energy from thequark and gluon condensates, the problem of vacuumenergy compensation becomes even more striking.

One should also remember the cosmic conspiracyof the same magnitude of different forms of matter:baryonic, nonbaryonic, and dark energy. Maybe a so-lution of this problem will indicate some new physicaleffects and help to solve the vacuum energy problem.

Speaking about more revolutionary ideas of break-ing unitarity, spinstatistics theorem, CPT, least ac-tion principle, etc., one should be aware of Pan-doras box of consequences if sacred principles aredestroyed. To this end, a quotation from The BrothersKaramazov by Dostoevsky, If God does not exist,anything is allowed, may be appropriate.

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