EXPERIMENTAL AND OBSERVATIONAL TESTS OF ANTIGRAVITY G. CHARDIN Universit e Paris Cit e CNRS Astroparticule et Cosmologie F-75013 Paris France

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EXPERIMENTAL AND OBSERVATIONAL TESTS OF ANTIGRAVITY

G. CHARDIN

Universit´e Paris Cit´e, CNRS, Astroparticule et Cosmologie, F-75013 Paris, France

Whereas repulsive gravity was considered as a fringe concept until the mid-1990’s, the growing

experimental evidence since this epoch for repulsive gravity, in what is now called Dark Energy,

for lack of a better understanding of its nature, has led to a vast literature in order to attempt

to characterize this repulsive component, and notably its equation of state. In the following, I

will show that we can use cosmology to test the hypothesis that antimatter is at the origin of

repulsive gravity, may play the role of a Dark Energy component and, more surprisingly, may

mimic the presence of Dark Matter, and justify the MOND phenomenology. More directly,

three experiments, AEgIS, ALPHA-g and Gbar, are attempting to measure the action of

gravitation on cold atoms of antihydrogen at CERN in a near future. Finally, I note that

CP violation might be explained by antigravity and I brieﬂy recall the motivations for this

assertion.

1 Introduction

It is interesting to remember that discussing repulsive gravity before the early 1990’s was con-

sidered as fringe physics, not to mention antigravity for antimatter that violates blatantly the

usual expression of the Equivalence Principle. Pioneering work on the question of antigravity

for antimatter was the Richtmyer lecture by Morrison1where he considers the small violation

of energy conservation associated with antigravity, and the review by Nieto and Goldman2dis-

cussing in a critical way the impossibility arguments against antigravity. While there are a priori

several possible ways to deﬁne antigravity, a ﬁrst attempt is to try to express them in terms of

the combinations of the three Newtonian parameters: inertial mass, active gravitational mass

and passive gravitational mass. Studying these eight combinations in Manfredi et al. (2018)3(re-

duced to four if we impose that the inertial mass is positive), we discovered to our surprise that

the Dirac particle-hole system, that is implemented in nature in the electron-hole system of a

semi-conductor4, has no Newtonian expression, even when we use the three above mass parame-

ters. Retrospectively, Tsvi Piran had reached a similar conclusion in his seminal paper on voids

considered as negative mass objects5. His proposition followed initial work on simulations with

Dubinski6, where the repulsive behavior of voids was apparent. Another key remark, that we

will use in our deﬁnition of antigravity, was made by Price7as early as 1993, ﬁve years before

the SN1a observations8,9that led to the discovery of what is now called Dark Energy: bound

arXiv:2210.03445v1 [astro-ph.CO] 7 Oct 2022

systems of positive and negative (Bondi10) gravitational mass objects become polarized (and

even levitate in symmetric systems) when forces other than gravitation bind the system. This

polarization leads to the deﬁnition of antigravity that we will use in the following, which cor-

responds to the behavior, as mentioned previously, of the Dirac particle-hole system. Clearly,

other deﬁnitions of antigravity have been proposed. In particular, Villata11,12,13 has invoked

CPT symmetry to consider a cosmology where antimatter is repulsed by matter but will not

behave as negative mass in General Relativity, i.e. repulsing itself. In particular, Villata makes

the hypothesis that antimatter will form structures similar to those formed by matter, i.e. stars,

galaxies and clusters. On the other hand, Wald14 had noted as early as 1980 that CPT and

time-reversal symmetries are a priori not respected by quantum gravity. As we will show, the

Dirac particle-hole deﬁnition of antigravity allows to justify the MOND phenomenology and the

existence of ﬂat rotation curves, at the origin of the Dark Matter enigma, while this does not

seem possible with the other combinations of Newtonian parameters.

As a ﬁnal remark in this short introduction, it is rather well known that symmetric matter-

antimatter cosmologies are excluded by the limits on the gamma-ray background in the 100

MeV range15,16, but this no-go theorem does not apply if gravitation repulsion between matter

and antimatter is at play.

2 Cosmological tests

After two decades of extensive cosmological measurements, the expression “precision cosmology”

has been quite often employed to characterize the new era that cosmology is supposed to have

entered through a set of large scale experimental programs, such as SDSS17, DES18, Planck19

and other experiments. As we will see, while some experiments, and in particular the CMB

experiment Planck HFI19, has recorded data of impressive precision, this does not mean that

our understanding of the cosmological model, or the uncertainty on its parameters, has reached

a similar level of precision. In fact, as several observers have noticed, our universe is impressively

close to a coasting universe, i.e. neither decelerating or accelerating, and such universes have in

their early phases drastically diﬀerent histories compared to the standard cosmological model.

For a review of coasting models, the reader is referred to the review by Casado20 and references

therein. A prominent coasting model is the Rh=ct universe, developed by Melia21, who

has reviewed extensively the concordance properties of this model, behaving as a Milne model

but with critical density and zero spatial curvature, and a priori not involving negative mass

components or antimatter. In the following, I will brieﬂy review the concordance properties

of coasting universes, focusing the attention on the Dirac-Milne universe23, ﬁrst because of my

personal bias, and more importantly for its strong concordance properties.

2.1 Age of the universe

While it is tempting to attribute the discovery of Dark Energy and a cosmological constant

to the SN1a observations published starting from 19988,9, it is important to realize that the

hypothesis of a cosmological constant was already considered as almost compulsory from the

early 1990’s24,25, as it was becoming clear that the age of the then favored Einstein-de Sitter

universe was severely too short, with its ≈9 billion years, to allow the existence of the oldest

stars and globular clusters observed in our universe, with ages as high as ≈13 billion years.

Soon after the 1998 SN1a observations, it had been noted26 that the coasting universe, which

can be described by the Milne or empty universe22, was a simple approximation of the successive

phases of acceleration and deceleration of the rising ΛCDM model. In particular, the ΛCDM and

Milne universes have basically the same age, equal exactly to 1/H0for a Milne universe, where

H0is the Hubble constant at the present epoch. It can also be noted, a fact already noted by

Milne, that the horizon of the Milne universe is at inﬁnite distance, removing the need for an

initial phase of inﬂation.

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EXPERIMENTALANDOBSERVATIONALTESTSOFANTIGRAVITYG.CHARDINUniversiteParisCite,CNRS,AstroparticuleetCosmologie,F-75013Paris,FranceWhereasrepulsivegravitywasconsideredasafringeconceptuntilthemid-1990's,thegrowingexperimentalevidencesincethisepochforrepulsivegravity,inwhatisnowcalledDarkEnergy,forlackof...

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EXPERIMENTAL AND OBSERVATIONAL TESTS OF ANTIGRAVITY G. CHARDIN Universit e Paris Cit e CNRS Astroparticule et Cosmologie F-75013 Paris France

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