Table Of Content“Dark energy” in the Local Void
M. Villata
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Abstract Theunexpecteddiscoveryoftheaccelerated 1 Introduction
] cosmic expansion in 1998 has filled the Universe with
O
the embarrassing presence of an unidentified “dark en- Since the end of the last century, observations of high-
C
ergy”, or cosmological constant, devoid of any phys- redshift type Ia supernovae have unexpectedly shown
h. ical meaning. While this standard cosmology seems that the cosmic expansion is currently in an accel-
p to work well at the global level, improved knowledge eration phase (e.g. Riess et al. 1998; Perlmutter et al.
- of the kinematics and other properties of our extra- 1999),whosephysicalcauseisunknown. Formally,this
o
r galactic neighborhood indicates the need for a better acceleration is ascribed to an additional term having
st theory. We investigate whether the recently suggested a negative pressure in the expansion equations, which
a repulsive-gravity scenario can account for some of the representsabout75%ofthe totalenergydensity ofthe
[
features that are unexplained by the standard model. Universe, in the simplest case corresponding to a cos-
1 Throughsimple dynamicalconsiderations,wefindthat mological constant, perhaps associated to the energy
v the Local Void could host an amount of antimatter
of the quantum vacuum. Besides this standard cos-
10 (∼5×1015M⊙)roughlyequivalenttothemassofatyp- mology of the ΛCDM model, various alternatives have
ical supercluster, thus restoring the matter-antimatter
8 been proposed to explain the cosmic speed-up, invok-
3 symmetry. Theantigravityfieldproducedbythis“dark ing scalar fields or modifications of general relativity,
. repulsor” canexplain the anomalous motion of the Lo-
1 such as extensions to extra dimensions or higher-order
0 cal Sheet away from the Local Void, as well as several curvatureterms(e.g.Amendola2000;Dvali et al.2000;
2 otherpropertiesofnearbygalaxiesthatseemtorequire
Carrollet al. 2004; Capozziello et al. 2005). In a vari-
1 void evacuation and structure formation much faster
: antofthesealternativetheories,Villata(2011)proposes
v than expected from the standard model. At the global
to extend general relativity to antimatter, intended as
i cosmological level, gravitational repulsion from anti-
X CPT-transformed matter, whose immediate result is
matter hidden in voids can provide more than enough
r thepredictionofagravitationalrepulsionbetweenmat-
a potentialenergytodriveboththecosmicexpansionand
ter and antimatter, which, with antimatter hidden in
its acceleration,with no need for an initial “explosion”
cosmic voids, could explain the accelerated expansion.
anddarkenergy. Moreover,the discretedistribution of
Knowledge of peculiar motions and spatial distribu-
these dark repulsors, in contrast to the uniformly per-
tionofgalaxiesallowsus toexploregravitationalinter-
meating dark energy, can also explain dark flows and
actionswithin and amongclusters. This is particularly
other recently observed excessive inhomogeneities and
true for our extragalactic neighborhood, where dis-
anisotropies of the Universe.
tancescanbemeasuredwithhigherprecision. Through
Keywords Gravitation—Cosmology: theory—Dark astudyperformedonadatabaseofabout1800galaxies
energy — Large-scale structure of Universe within3000kms−1,Tully et al.(2008)findthatthepe-
culiarvelocityoftheLocalSheetdecomposesintothree
dominant,almostorthogonalcomponents. Oneofthem
M.Villata
(of 185kms−1) is ascribed to the gravitational pull of
INAF,OsservatorioAstronomicodiTorino,ViaOsservatorio20,
I-10025PinoTorinese(TO),Italy the VirgoClusterandits surroundings,while asecond,
e-mail: [email protected] largercomponent(of455kms−1)seemstobeduetoan
attractiononlargerscalesnearlyinthedirectionofthe
2
Centaurus Cluster. The third component (259kms−1) Ni 2004; Hajdukovic 2010, 2011c,b; see also Cabbolet
is not directed toward anything prominent, but points 2010), or that it is even self-repulsive (e.g. Noyes 2008;
away fromthe LocalVoid. Some evacuationofvoids is Benoit-L´evy & Chardin 2012).
expectedinstandardcosmology,duetothedensitycon- In a recent paper, Villata (2011) argued that there
trast that pushes matter outward, but the high speeds is no need to change the sign of the gravitationalmass
ofgalaxiesattheedgeoftheLocalVoidindicatethatit ofantimatter (which wouldrepresenta violationofthe
shouldbeverylargeandveryempty,morethanusually weak equivalence principle) to get repulsion between
expected. Consequently, alternative models have been matter and antimatter; but he showedthat antigravity
considered. For instance, Dutta & Maor (2007) argue appears as a prediction of general relativity, once it is
thatdarkenergywithavaryingequationofstatecould assumed that this theory is CPT invariant and that,
havehigherdensitywheremassdensityislower,sothat consequently,matter is transformedinto antimatter by
repulsion from voids would be stronger. thesethreejointoperations(chargeconjugation,parity,
Moreover, as discussed by Peebles & Nusser (2010), and time reversal).
many other properties of galaxies in our neighborhood Besides representingthe universalsymmetry of field
are not explained by the standard model. Besides the theories,theCPTtransformationisconsistentwiththe
observedextreme emptiness of the Local Void (∼10−5 Feynman-Stueckelberginterpretationofantiparticlesas
probability), the presence of large, luminous galaxies particles traveling backwards in time, since this view
in the adjacent low-density regions is in contrast with explains the need of applying T (and P) in addition
expectations (< 1% probability). These and other ob- to C to describe the behavior of antimatter. In other
served features seem to indicate the need for a better words, a physical system (or a component of a physi-
theory,entailing a mechanismby which matter is more cal system) traveling in the opposite time direction is
rapidlyrepelledbyvoidsandgatheredintogalaxiesand observedfromourtimedirectionthroughaCPTtrans-
structures. formation, and this would be the reason why physical
In this paper we want to investigate whether the re- laws are CPT symmetric, since they must describe the
pulsivegravityscenarioproposedbyVillata(2011)asa behavior of physical systems as observed from either
potential explanation for the cosmic accelerationcould time directions, i.e. when they appear to be composed
also help solve some of these problems. A brief intro- of either matter or antimatter, or both.
duction to antimatter gravity is given in Sect. 2, while In general relativity, the equation of motion for a
in Sect. 3 this view is applied to the dynamics of our mattertestparticleinamatter-generatedgravitational
extragalacticsurroundings. Discussionandconclusions field is
can be found in Sect. 4.
d2xλ dxµdxν
=−Γλ . (1)
dτ2 µν dτ dτ
2 Antimatter gravity If we CPT-transform all the four elements in Eq. (1),
we get an identical equation describing the motion of
Theexistenceofantigravity,i.e.gravitationalrepulsion an antimatter test particle in an antimatter-generated
between matter and antimatter, has been debated at gravityfield,sinceallthefourchangesofsigncancelone
length during the last several decades, without reach- another. Thus, this CPT symmetry ensures the same
ing any firm conclusion. After strong opposition dur- self-attractive gravitational behavior for both matter
ing the second half of last century, the idea of anti- and antimatter. But, if we transform only one of the
gravity has experienced a period of renewed interest two components, either the field Γλ or the particle
µν
because of the discovery of the accelerated expansion (represented by the remaining three elements), we get
of the Universe in 1998. In particular, against anti- achangeofsignthatconvertstheoriginalgravitational
gravity in the Fifties–Sixties were proposed some the- attractionintorepulsion,sothatmatterandantimatter
oretical arguments that seemed to rule out its exis- repel each other.
tence (Morrison 1958; Schiff 1958, 1959; Good 1961), The equation for a massless particle (e.g. a photon)
but which were later criticized and questioned (e.g. is formally equal to Eq. (1), except for the parameter
Nieto & Goldman1991;Chardin & Rax 1992;Chardin τ, which can no longer be taken as the proper time,
1993, 1997; Hajdukovic 2011a), and then lost much beingdτ =0,butitwillbe anotherparameterdescrib-
of their effectiveness. At the same time, several au- ing the world line. Therefore, a (retarded) photon will
thorshavepursuedtheideaofantigravity,eitherassum- be repelled by an antimatter gravity field, as well as
ing that antimatter has negative gravitational mass, a CPT-transformed photon, i.e. an advanced photon,
and thus is self-attractive (e.g. Noyes & Starson 1991;
3
will be repelled by matter1. This may provide a test which can be decomposed into three quasi-orthogonal
for the theory of antigravity: the presence of antimat- components (Tully et al. 2008). One of them is due
ter in cosmic voids suggested by Villata (2011, 2012) to the well-known attraction towards the Virgo Clus-
might be revealed by its gravitational effect on the ra- ter and its dense surroundings (e.g. Tonry & Davis
diation coming from background sources, in a sort of 1981; Aaronson et al. 1982; Hoffman & Salpeter 1982;
antigravitationallensing. Tully & Shaya 1984; Tonry et al. 2000). The sec-
In the Newtonian approximation, the law of gravity ond, largest component has a less clear origin: it is
extended to antimatter becomes F(r) = ∓GmM/r2, ascribed to gravitational pull on scales larger than
where the minus sign refers to the gravitational self- 3000kms−1 nearly in the direction of the Centau-
attraction of both matter and antimatter, while the rus Cluster, but the identification and relative impor-
plus sign indicates the gravitational repulsion between tance of the “great attractors” is still debated (e.g.
matter and antimatter. Shaya 1984; Lynden-Bell et al. 1988; Scaramella et al.
The change of sign in the CPT-transformed (i.e. 1989; Raychaudhury 1989; Kocevski & Ebeling 2006;
antimatter-generated) gravitational field comes from Erdo˘gdu et al. 2006).
the inversion of the derivatives of the metric tensor The last component corresponds to what is his-
in the expression of Γλ . Thus, while the metric ten- torically known as the “local velocity anomaly” (e.g.
µν
sor, i.e. the potential, does not change sign and re- Faber & Burstein 1988; Tully 1988; Tully et al. 1992).
mains the same for matter and antimatter, the sign Itis large,259kms−1, andis anomalousbecause is not
change appears only in the field. This means that in directed towards any important structure. It can not
the above generalized Newton law, the plus sign indi- beduetoasimplegravitationalpull,otherwisealsothe
cating repulsion does not formally come from an in- Leo Spur galaxies, which would be in between, should
verted potential, but from its inverted gradient. In- be affected by it, while they appear to be at rest with
deed, the potential φ is usually defined as −∇φ = g, respect to this motion. Thus, the cause of this compo-
so that, being the attractive field g(r) = −GM/r2, nent must be on the other side, where the Local Sheet
the potential is φ(r) = −GM/r, and, with the same borders the Local Void. Moreover, this velocity vec-
potential, the repulsive field comes from its inverted torpointsjustinthe oppositedirectionwithrespectto
gradient: g¯(r) = GM/r2. This formally correct view anapproximatecenterofthevoid,andisorthogonalto
is actually not intuitive, so that it is preferable to re- thedisk-likestructureoftheLocalSheet. Whateverthe
versethe potentialandto getthe fieldaccordingtothe causeoftheanomalousmotion,itmustaffecttheLocal
usual −∇φ definition. The repulsive potential is thus Sheet more than the rest of our neighborhood (which
φ¯(r)=GM/r, and the gravitationalpicture of the cos- is indeed more distant from the void), and also seems
mic alternance of matter and antimatter suggested in to have the property to squash the closest structures,
Villata (2011) can be represented as an alternation of besides giving them high velocities.
potential wells and hills. Of course, from the antimat- These and several other features (see Sects. 1 and
ter point of view this situation would be seen upside 4), such as the extreme emptiness of the Local Void,
down. do not find a satisfactory explanation within the stan-
dard model, and seem to require the intervention of a
repulsive force. In particular, the flattened shape of
3 Dynamics of the Local Sheet the LocalSheet looks just like the signatureof a repul-
sive gravitationalfield. Indeed, while the effect of tidal
Our peculiar motion with respect to the general ex- forces in an attractive gravity field is to stretch struc-
pansion of the Universe can be inferred by the ob- tures along the radial direction, since the side closer to
serveddipoleanisotropyinthecosmicmicrowaveback- the field source is more attracted than the side farther
ground (e.g. Fixsen et al. 1996). This motion has well- away, the tidal effect of a repulsive field is to squash
known local contributions, including the orbital veloc- them, the near side being more pushed than the far
ity of the Sun in our Galaxy and the attraction of one: dF/dr =−2GmM/r3.
the latter towards M31. Once these components are Under some simple assumptions in linear perturba-
taken into account, it is found that the Local Sheet tion theory, the peculiar velocity field V of an ideal
pec
has still a very large peculiar velocity of 631kms−1, pressurelessfluidis relatedtothe gravitationalacceler-
ationg andthe expansiontimetbythe simpleformula
(see e.g. Peebles 1993; Peebles et al. 2011) V = gt.
1As a consequence, the energy of a retarded-advanced photon pec
Wecancheckwhetherthisequationcanrepresentarea-
pairinagravitationalfieldwouldbeconserved,thusinvalidating
theMorrison(1958)argumentagainstantigravity. sonable approximation for the peculiar velocity of the
4
LocalSheetwithrespecttothegravitationalattraction the totalenergy per unit mass,givenby V2/2+GM/d
by the Virgo Cluster. Rewriting it as (where V = H d+V is the total velocity with re-
0 pec
spect to the void center) at the Local Sheet and Leo-
V M Mpc2 t
pec =4.4×10−12 , (2) Spur/Virgo distances. In the intermediate case seen
kms−1 M⊙ d2 Gyr above, with MLV = 6.6 × 1015M⊙, dLS = 25Mpc
with t = t0 = 13.75Gyr (Jarosik et al. 2011), d = and VpLeSc = 634kms−1 for the Local Sheet, dLeo =
17Mpc and Vpec = 185kms−1 (Tully et al. 2008), we 32.5Mpc and VpLeeco = 375kms−1 for Leo-Spur/Virgo2,
get for the mass of the Virgo Cluster and surroundings and adopting H0 = 74kms−1Mpc−1 from Tully et al.
MVir = 8.8×1014M⊙. This value is in good agree- (2008),weobtain4.2×106and4.7×106km2s−2 forthe
mentwithpreviousestimates(e.g.Tully & Shaya1984; respective total specific energies. We then find a small
Mohayaee & Tully 2005), so that we may be confident difference of about 10%, which could also be due to
in Eq. (2), at least at the scale of our supercluster. the various uncertainties affecting both measures and
Assuming thatEq.(2)holds alsofor repulsiveaccel- model assumptions, or could come from slightly differ-
eration,wecantryaroughestimateofthemassofanti- entinitialconditionsforthedifferentlylocatedsystems.
matter(seeSect.2),possiblylocatedaroundthecenter This approximate energy conservation at different dis-
of the Local Void, needed to push the Local Sheet at tances from the antigravity center confirms that the
the observed velocity of 259kms−1. The expected dis- dynamics in the radial direction is actually dominated
tanceoftheLocalSheetfromthecenterofthevoidmay bythisrepulsiveinteraction,andsupportsourscenario.
be assumed in the range 25±5Mpc (e.g. Tully et al. If we go back in time conserving mechanical energy,
2008), which gives MLV = 2.7+−11..20 × 1015M⊙. How- we find V =0 at d=6.7Mpc for the Local Sheet, and
ever,it wouldbe strangethatthis repulsiveinteraction at d=6.0Mpc for Leo Spur, whereas one could expect
affected only the Local Sheet, leaving the rest of our muchsmallerdistances,approachingasingularity. This
neighborhood unaffected and at rest with respect to might mean that our data are too imprecise to allow a
the LocalVoid. Indeed, whatis measuredas apeculiar similarextrapolationinthe past, or that our simplistic
velocity of 259kms−1 is actually the peculiar velocity dynamicalassumptionof a dominant, point-like-source
of the Local Sheet relatively to the rest of the Local field can no longer hold at these earlier stages and also
Supercluster, i.e. mainly to the Virgo Cluster, and in surroundingfieldsshouldbetakenintoaccount,orthat
particulartotheLeoSpurgalaxies,whicharebothfar- some of the energy has been somehow dissipated, or a
ther than the Local Sheet from the approximate cen- combination of all these things.
ter of the Local Void by about 7–8Mpc. Thus, for Inanycase,whatwearefindingthroughoutthissec-
a more significant estimate of the mass in the Local tion is that the repulsive gravity field can account not
Void, we take the difference ofEq.(2) betweenthe dis- only for peculiar (anomalous) velocities and accelera-
tanceoftheLocalSheet(againassumedas25±5Mpc) tion of the Hubble flow, but even for the Hubble flow
and the Leo-Spur/Virgo radial distance from the void itself. There seems to be more than enough energy for
center (correspondingly estimated as 32.5±4.5Mpc), drivingallthe Universeexpansion,storedinthepoten-
whichyieldsMLV =6.6+−43..61×1015M⊙,i.e.significantly tialenergy,when,goingbackintime, matter getcloser
larger than the former result, but of the same order of
andclosertothepeaksoftheantimatterpotentialhills.
magnitude. These estimates come from the simplistic
No need for initial (artificial) velocities provided by an
assumption that the various components are affected,
explosive “Big Bang”, whose energy would not have
intheradialdirectionfromthevoidcenter,onlybythe
any identified origin. No need for unknown dark en-
dominantrepulsiveinteractionwithanantimattermass
ergy to drive the cosmic acceleration,or dark energy is
concentratedcloseto theassumedvoidcenter,anddis-
nothing else than the potential energy of gravitational
regarding other possible contributions in the same di-
repulsion.
rection. Thus, we are not claiming that these values
must be considered as extremely realistic, and we can
not even choose between the two results, but we can
4 Discussion and conclusions
say that an antimatter mass of ∼ 5×1015M⊙, within
a factor of 2, can easily account for the local velocity
There remains the question of why antimatter in voids
anomaly. This value is comfortably comparable to the
should not be visible. It seems that something “dark”
mass of a medium-size supercluster, which means that
must necessarily exist: dark matter, dark energy, and
we would have found the location for antimatter in a
matter-antimatter symmetric Universe.
Another argumentin favor of the above picture and 2VLS andVLeoarecalculatedfromEq.(2),andhavethecorrect
pec pec
mass estimate is the following one. We can calculate differenceof259kms−1 betweenthem.
5
now “dark repulsors”. On the other hand, were it oth- of the expanding Universe4, but at the cost of intro-
erwise, we would have understood everything a long ducing ad hoc elements that do not have a physical
time ago. explanation,liketheinitial“explosion”causingthecos-
Like matter, antimatter is self-attractive, so we can mic expansion and the dark energy that should accel-
expect that it forms anti-galaxiesandanti-stars,which erate it. As we have seen, antigravitycan explain both
would emit electromagnetic radiation, we should can theexpansionandits acceleration,andthistheoryalso
detect. However, as pointed out by Villata (2012, has the virtue of solving the long-standing problem
see also Sect. 2), antimatter, if emitting, should emit of matter-antimatter asymmetry. It might seem that
advanced radiation, which can be undetectable for at one is replacing something invisible (dark energy)with
least two reasons. First, it could be intrinsically unde- something else equally invisible (dark repulsors). The
tectable,atleastwiththeusualdetectorsandobserving difference is that the presence of the latter is theoreti-
procedures3. Then,evenifitweresomehowdetectable, callyexpectedifnotrequired,whilstthepresenceofthe
we know from Sect. 2 that advanced photons are re- formerisnotrequested,unexpected,andembarrassing.
pelled by matter, so that the chance of detecting the Moreover,somerecentobservationalfindingsareun-
fewthatpossiblysucceededinreachingusontopofthe derminingthestandardmodel(e.g.Walker & Pen˜arrubia
potential hill of our Galaxy is further greatly reduced. 2011onunexpectedlyuniformdistributionofdarkmat-
The possibility remains that antimatter emits also re- ter in dwarf galaxies5). In particular, the existence
tardedradiation(aswellasmattermightemitadvanced of “dark flows”, i.e. large-scale, peculiar bulk motions
radiation). In this case we should see antimatter stars, of galaxy clusters (e.g. Kashlinsky et al. 2010 and ref-
galaxies and clusters filling the voids, but well sepa- erences therein), of excess clustering on large scales
ratedfrommatteronesbygravitationalrepulsion. Yet, (Thomas et al. 2011), of anisotropy in the expansion
as already said, antimatter would be matter traveling acceleration(e.g.Cai & Tuo2012)seemtoindicatethe
backwards in time, so that, taking this concept to the need for a distribution of acceleration sources less ho-
extreme, we would observe its cosmic evolution in re- mogeneousthantheuniformlypermeatingdarkenergy,
verse, and its current evolutionary stage could be very thus favoring the discrete distribution in cosmic voids.
different from ours. For example, if antimatter were Letus returntoourextragalacticneighborhoodand
“created”inadistantfuture,nowitmightbecollapsed itsanomaliespartlymentionedinthe Introductionand
intosupermassiveblackholes,orbeinsomeothernon- described in detail in Peebles & Nusser (2010). All
emitting form, before definitively collapsing, 14 billion those observed properties, such as the extreme empti-
years ago. Perhaps to be “reborn” as matter, and re- nessoftheLocalVoid,theunexpectedpresenceoflarge
trace in the opposite direction the time already passed galaxiesat its edge,the existence of pure disk galaxies,
through, but well separated from the “anti-itself” by and the insensitivity of galaxy properties to environ-
gravitational repulsion. A further step would lead us ments, indicate the existence of a mechanism that can
to suggest a Universe “recurring over time”, in a cos- produce a fast evacuation of voids and rapid assembly
mic loop, but such a speculative rumination is beyond of matter into structures, which the standard theory
the scope of this paper. based on attractive-only gravity can not provide. Re-
In any case, there seem to be more reasons for anti- pulsivegravitycanbe the causeoffastevacuationand,
matterinvisibilitythanforvisibility,sothatwearenot also through the squashing tidal effect, can help a lot
surprised not to see anything in cosmic voids. Another to rapidly gather matter into galaxies and structures,
pointisthedifferent,quasi-sphericalsymmetryofvoids especially at the borders of voids.
withrespecttothesquashed/filamentaryshapeofmat- In conclusion, repulsive gravity between matter and
terstructures. Thiswouldsupporttheviewofdifferent antimatter, which is a natural outcome of generalrela-
evolutionarystages,where antimatter black holes close tivity extended to CPT-transformed systems, is an ex-
to the void centers produce spherical fields, and the cellentcandidatetoexplainnotonlythe cosmicexpan-
more uniformly distributed matter can only adapt in sion and its acceleration, but also the anomalous kine-
thepotentialvalleysamongthequasi-circularpotential maticsandseveralotherpropertiesofourextragalactic
hills. surroundings, as well as other observed features of the
Passing several cosmological tests, the ΛCDM stan-
dard model seems to provide a fairly good description
4However,inarecentpaper,Benoit-L´evy&Chardin(2012)have
shown that most of these observational constraints can also be
3Actuallythereissomeconfusionaboutadvancedradiationinthe explained by their quite different cosmology, based on the as-
sumptionofamatter-antimatter symmetricUniverse.
literature;fordiscussionsaroundtheissueofadvancedradiation
ingeneral,seee.g.Davies(1975),Cramer(1980),andreferences 5SeeHajdukovic(2011c)foranalternativeinterpretationofdark
therein. matterbasedonantigravity.
6
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Perlmutter, S., Aldering, G., Goldhaber, G., et al. 1999,
Astrophys.J., 517, 565
Raychaudhury,S. 1989, Nature, 342, 251
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